Lesson: 1 Understand Multiples of Unit Fractions<\/strong><\/p>\n Lesson: 2 Understand Multiples of Fractions<\/strong><\/p>\n Lesson: 3 Multiply Whole Numbers and Fractions<\/strong><\/p>\n Lesson: 4 Multiply Whole Numbers and Mixed Numbers<\/strong><\/p>\n Lesson: 5 Problem Solving: Fraction Operations<\/strong><\/p>\n Performance Task<\/strong><\/p>\n Explore and Grow<\/strong><\/p>\n Draw a model of any fraction using unit fractions. Then write an addition equation to represent your model. Think and Grow: Multiples of Unit Fractions<\/strong><\/p>\n Any fraction can be written as a multiple of a unit fraction with a like denominator. Show and Grow<\/strong><\/p>\n Write the fraction as a multiple of a unit fraction.<\/p>\n Question 1. Explanation: Question 2. Question 3. Explanation: Question 4. Explanation: Apply and Grow: Practice<\/strong><\/p>\n Write the fraction as a multiple of a unit fraction.<\/p>\n Question 5. Explanation: Question 6. Explanation: Question 7. Explanation: Question 8. Explanation : Question 9. Explanation : Question 10. Explanation: Question 11. Explanation : We know that the numerator of a unit fraction is always one. So When a fraction is DIG DEEPER!<\/strong> Question 12. Explanation: Question 13. Explanation: Question 13.<\/p>\n Think and Grow: Modeling Real Life<\/strong><\/p>\n Example<\/strong> Explanation: Show and Grow<\/strong><\/p>\n Question 14. Explanation: Question 15. Explanation: Question 16. Explanation: Question 17. Explanation: Write the fraction as a multiple of a unit fraction.<\/p>\n Question 1. Explanation: Question 2. Explanation: Question 3. Explanation: Question 4. Explanation: Question 5. Explanation: Question 6. Explanation: Question 7. Explanation: Question 8. Explanantion: Question 9. Explanation: Question 10 Explanation: Question 11. Explanation: Question 12. Explanation: Question 13. Explanation : Question 14. Explanation: Question 15. Draw a model for each expression. Then write a multiplication expression to represent each model. The multiplication expression is \\(\\frac{2}{6}\\) +\\(\\frac{2}{6}\\) +\\(\\frac{2}{6}\\) + Explanation: Structure<\/strong> Explanation: Think and Grow: Multiples of Fractions<\/strong><\/p>\n A multiple of any fraction can be written as a multiple of a unit fraction with a like denominator. Write the product as a multiple of a unit fraction. Then find the product.<\/p>\n Question 1. Explanation: Question 2. Explanation: Question 3. Explanation: Apply and Grow: Practice<\/strong><\/p>\n Write the product as a multiple of a unit fraction. Then \ufb01nd the product.<\/p>\n Question 4. Explanation: Question 5. Explanation: Question 6. Explanation: Question 7. Explanation: Question 8. Explanation: Question 9. Explanation: Number Sense<\/strong> Question 10. Explanation: Question 11. Explanation: Question 12. Explanation: Question 13. Explanation: Question 14. Think and Grow: Modeling Real Life<\/strong><\/p>\n A bird keeper uses a \\(\\frac{1}{3}\\) cup scoop to feed 3 birds. He feeds each bird \\(\\frac{2}{3}\\) cup of birdseed. How many times does he fill the scoop? Explanation : Question 15. Explanation: Question 16. Explanation: Question 17. Explanation: Write the product as a multiple of a unit fraction. Then find the product.<\/p>\n Question 1. Explanation: Question 2. Explanation: Question 3. Explanation: Question 4. Explanation: Question 5. Explanation: Question 6. Explanation: Question 7. Explanation: Question 8. Explanation: Question 9. Answer: Explanation: Question 10. Explanation: Question 11. Answer: Explanation: Review & Refresh<\/strong><\/p>\n Find the product.<\/p>\n Question 12. Explanation: Question 13. Explanation: Question 14. Explanation: Explore and Grow<\/strong><\/p>\n Use models to help you complete the table. What do you notice about each expression and its product? We notice that each expression can be written as the product as a multiple of a unit fraction, Think and Grow: Multiply Whole Numbers and Fractions<\/strong><\/p>\n You can \ufb01nd the product of a whole number and a fraction by multiplying the numerator by the whole number. Explanation: Show and Grow<\/p>\n Multiply.<\/p>\n Question 1. Question 2. Explanation: Question 3. Explanation: Apply and Grow: Practice<\/strong><\/p>\n Multiply.<\/p>\n Question 4. Explanation : Question 5. Explanation: Question 6. Explanation: Question 7. Explanation: Question 8. Explanation: Question 9. Explanation : Compare.<\/p>\n Question 10. Explanation: Question 11. Answer: Explanation: Question 12. Explanation: Question 13. Explanation: Question 14. Explanation: Think and Grow: Modeling Real Life<\/strong><\/p>\n Example<\/strong> Explanation: Show and Grow<\/strong><\/p>\n Question 15. Explanation: Question 16. Explanation: Now we divide \\(\\frac{18}{5}\\) we get the value as 3.6,means between 3 and 4 whole numbers our answer will lie.<\/p>\n Question 17. Explanation: Multiply<\/p>\n Question 1. Question 2. Explanation: Question 3. Explanation: Question 4. Explanation: Question 5. Explanation: Question 6. Explanation: Question 7. Explanation: Question 8. Explanation: Question 9. Explanation: Compare.<\/p>\n Question 10. Explanation: Question 11. Explanation: Question 12. Answer: Explanation: Question 13. Explanation: Question 14. Explanation: Question 15. Explanation: Question 16. Answer: Explanation: Review & Refresh<\/strong><\/p>\n Divide<\/p>\n Question 17. Explanation: Question 18. Explanation: Explanation: Explore and Grow<\/strong><\/p>\n Use models to help you complete the table. Structure<\/strong> Answer: Explanation: You can \ufb01nd the product of a whole number and a mixed number by writing the mixed number as a fraction or by using the Distributive Property Show and Grow<\/strong><\/p>\n Multiply<\/p>\n Question 1. Question 2. Explanation:\n
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<\/a>Lesson 9.1 Understand Multiples of Unit Fractions<\/h3>\n
\nReasoning<\/strong>
\nHow can you rewrite the equation using multiplication? Explain.
\nAnswer:
\nLet us take the fraction as \\(\\frac{3}{5}\\) we draw a model using fractions as below
\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-1-1.bmp\")
![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-2-2.bmp\")
\nAddition equation to represent \\(\\frac{3}{5}\\)\u00a0 model is \\(\\frac{3}{5}\\) = \\(\\frac{1}{5}\\) +
\n\\(\\frac{1}{5}\\) +\\(\\frac{1}{5}\\) to rewrite the equation using multiplication,
\nWe write the equation as \\(\\frac{3}{5}\\) = \\(\\frac{1}{5}\\) +\\(\\frac{1}{5}\\) +
\n\\(\\frac{1}{5}\\) = 3 X \\(\\frac{1}{5}\\) as the fraction \\(\\frac{3}{5}\\)
\nrepresents 3 parts that are each \\(\\frac{1}{5}\\) of the whole.<\/p>\n
\nExample<\/strong>
\nWrite \\(\\frac{5}{8}\\) as a multiple of a unit fraction.
\nThe fraction \\(\\frac{5}{8}\\) represents 5 parts that are each \\(\\frac{1}{8}\\) of the whole.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-500.png\")
\nAnswer:
\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-3-2.bmp\")
<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-1.png\")
\nAnswer:
\n\\(\\frac{2}{3}\\) = \\(\\frac{1}{3}\\) +\\(\\frac{1}{3}\\)
\n=\u00a0 2 X \\(\\frac{1}{3}\\).<\/p>\n
\nWe write \\(\\frac{2}{3}\\) in addition equation as \\(\\frac{2}{3}\\) =\\(\\frac{1}{3}\\) +
\n\\(\\frac{1}{3}\\) and multiplication as fraction \\(\\frac{2}{3}\\) represents 2 parts that are each
\n\\(\\frac{1}{3}\\) of the whole, \\(\\frac{2}{3}\\) =2 X \\(\\frac{1}{3}\\).<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-2.png\")
\nAnswer:
\n\\(\\frac{4}{8}\\) = \\(\\frac{1}{8}\\) +\\(\\frac{1}{8}\\) + \\(\\frac{1}{8}\\) +
\n\\(\\frac{1}{8}\\) = 4 X \\(\\frac{1}{8}\\).
\nExplanation:
\nWe write \\(\\frac{4}{8}\\) in addition equation as \\(\\frac{4}{8}\\) = \\(\\frac{1}{8}\\) +
\n\\(\\frac{1}{8}\\)\u00a0 + \\(\\frac{1}{8}\\) +\\(\\frac{1}{8}\\) and multiplication as
\nfraction \\(\\frac{4}{8}\\) represents 4 parts that are each \\(\\frac{1}{8}\\) of the whole,
\n\\(\\frac{4}{8}\\) =4 X \\(\\frac{1}{8}\\).<\/p>\n
\n\\(\\frac{6}{5}\\)
\nAnswer:
\n\\(\\frac{6}{5}\\) = \\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\) +\\(\\frac{1}{5}\\)+
\n\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\) = 6 X \\(\\frac{1}{5}\\).<\/p>\n
\nWe write \\(\\frac{6}{5}\\) in addition equation as \\(\\frac{6}{5}\\)= \\(\\frac{1}{5}\\)+
\n\\(\\frac{1}{5}\\) +\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+
\n\\(\\frac{1}{5}\\) and multiplication as fraction \\(\\frac{6}{5}\\) represents 6 parts
\nthat are \\(\\frac{1}{5}\\) of the whole \\(\\frac{6}{5}\\) = 6 X \\(\\frac{1}{5}\\).<\/p>\n
\n\\(\\frac{7}{100}\\)
\nAnswer:
\n\\(\\frac{7}{100}\\) = \\(\\frac{1}{100}\\) + \\(\\frac{1}{100}\\) + \\(\\frac{1}{100}\\) +
\n\\(\\frac{1}{100}\\)+ \\(\\frac{1}{100}\\)+ \\(\\frac{1}{100}\\)+ \\(\\frac{1}{100}\\)
\n= 7 X \\(\\frac{1}{100}\\).<\/p>\n
\nWe write \\(\\frac{7}{100}\\) in addition equation as \\(\\frac{7}{100}\\)= \\(\\frac{1}{100}\\) +
\n\\(\\frac{1}{100}\\) + \\(\\frac{1}{100}\\) + \\(\\frac{1}{100}\\)+ \\(\\frac{1}{100}\\)+
\n\\(\\frac{1}{100}\\)+ \\(\\frac{1}{100}\\) and multiplication as fraction \\(\\frac{7}{100}\\) represents
\n7 parts that are \\(\\frac{1}{100}\\) of the whole, \\(\\frac{7}{100}\\)= 7 X \\(\\frac{1}{100}\\).<\/p>\n
\n\\(\\frac{2}{6}\\)
\nAnswer:
\n\\(\\frac{2}{6}\\) = \\(\\frac{1}{6}\\) + \\(\\frac{1}{6}\\)
\n= 2 X \\(\\frac{1}{6}\\).<\/p>\n
\nWe write \\(\\frac{2}{6}\\) in addition equation as \\(\\frac{2}{6}\\)= \\(\\frac{1}{6}\\) +
\n\\(\\frac{1}{6}\\) and multiplication as fraction \\(\\frac{2}{6}\\) represents 2 parts that are
\n\\(\\frac{1}{6}\\) of the whole,\\(\\frac{2}{6}\\) = 2 X \\(\\frac{1}{6}\\).<\/p>\n
\n\\(\\frac{6}{8}\\)
\nAnswer:
\n\\(\\frac{6}{8}\\) = \\(\\frac{1}{8}\\) + \\(\\frac{1}{8}\\) + \\(\\frac{1}{8}\\)+
\n\\(\\frac{1}{8}\\)+ \\(\\frac{1}{8}\\)+ \\(\\frac{1}{8}\\) = 6 X \\(\\frac{1}{8}\\).<\/p>\n
\nWe write \\(\\frac{6}{8}\\) in addition equation as \\(\\frac{6}{8}\\) = \\(\\frac{1}{8}\\) +
\n\\(\\frac{1}{8}\\) + \\(\\frac{1}{8}\\)+ \\(\\frac{1}{8}\\)+ \\(\\frac{1}{8}\\)+
\n\\(\\frac{1}{8}\\) and multiplication as fraction \\(\\frac{6}{8}\\) represents 6 parts that are
\n\\(\\frac{1}{8}\\) of the whole, \\(\\frac{6}{8}\\) =6 X \\(\\frac{1}{8}\\).<\/p>\n
\n\\(\\frac{5}{4}\\)
\nAnswer:
\n\\(\\frac{5}{4}\\) = \\(\\frac{1}{4}\\) + \\(\\frac{1}{4}\\) +\\(\\frac{1}{4}\\) +
\n\\(\\frac{1}{4}\\) +\\(\\frac{1}{4}\\) = 5 X \\(\\frac{1}{4}\\).<\/p>\n
\nWe write \\(\\frac{5}{4}\\) in addition equation as \\(\\frac{5}{4}\\)=\\(\\frac{1}{4}\\) +
\n\\(\\frac{1}{4}\\) +\\(\\frac{1}{4}\\) +\\(\\frac{1}{4}\\) + \\(\\frac{1}{4}\\)
\nand multiplication as fraction \\(\\frac{5}{4}\\) represents 5 parts that are \\(\\frac{1}{4}\\)
\nof the whole, \\(\\frac{5}{4}\\) = 5 X \\(\\frac{1}{4}\\).<\/p>\n
\n\\(\\frac{3}{12}\\)
\nAnswer:
\n\\(\\frac{3}{12}\\)= \\(\\frac{1}{12}\\) + \\(\\frac{1}{12}\\) +\\(\\frac{1}{12}\\) <\/span>=
\n3 X \\(\\frac{1}{12}\\)<\/span><\/p>\n
\nWe write \\(\\frac{3}{12}\\) in addition equation as \\(\\frac{3}{12}\\)= \\(\\frac{1}{12}\\) +
\n\\(\\frac{1}{12}\\) + \\(\\frac{1}{12}\\) and multiplication as fraction \\(\\frac{3}{12}\\)
\nrepresents 3 parts that are \\(\\frac{1}{12}\\) of the whole, \\(\\frac{3}{12}\\) =
\n3 X \\(\\frac{1}{12}\\).<\/p>\n
\n<\/span>\\(\\frac{8}{100}\\)
\nAnswer:
\n\\(\\frac{8}{100}\\) = \\(\\frac{1}{100}\\) + \\(\\frac{1}{100}\\)+\\(\\frac{1}{100}\\)+
\n\\(\\frac{1}{100}\\)+\\(\\frac{1}{100}\\)+\\(\\frac{1}{100}\\)+\\(\\frac{1}{100}\\)+
\n\\(\\frac{1}{100}\\) = 8 X \\(\\frac{1}{100}\\).<\/p>\n
\nWe write \\(\\frac{8}{100}\\) in addition equation as \\(\\frac{8}{100}\\) =
\n\\(\\frac{1}{100}\\) + \\(\\frac{1}{100}\\)+\\(\\frac{1}{100}\\)+
\n\\(\\frac{1}{100}\\)+\\(\\frac{1}{100}\\)+ \\(\\frac{1}{100}\\)+
\n\\(\\frac{1}{100}\\)+\\(\\frac{1}{100}\\) and multiplication as fraction
\n\\(\\frac{8}{100}\\) represents 8 parts that are \\(\\frac{1}{100}\\) of the whole,
\n\\(\\frac{8}{100}\\)= 8 X \\(\\frac{1}{100}\\).<\/p>\n
\n\\(\\frac{7}{10}\\)
\nAnswer:
\n\\(\\frac{7}{10}\\) = \\(\\frac{1}{10}\\) +\\(\\frac{1}{10}\\) +\\(\\frac{1}{10}\\) +
\n\\(\\frac{1}{10}\\) +\\(\\frac{1}{10}\\) +\\(\\frac{1}{10}\\) +\\(\\frac{1}{10}\\)
\n= 7 X \\(\\frac{1}{10}\\).<\/p>\n
\nWe write \\(\\frac{7}{10}\\) in addition equation as \\(\\frac{7}{10}\\) = \\(\\frac{1}{10}\\) +
\n\\(\\frac{1}{10}\\) +\\(\\frac{1}{10}\\) +\\(\\frac{1}{10}\\) +\\(\\frac{1}{10}\\) +
\n\\(\\frac{1}{10}\\) +\\(\\frac{1}{10}\\) and multiplication as fraction \\(\\frac{7}{10}\\)
\nrepresents 7 parts that are \\(\\frac{1}{10}\\) of the whole,\\(\\frac{7}{10}\\) = 7 X \\(\\frac{1}{10}\\).<\/p>\n
\nStructure<\/strong>
\nWhen a fraction is written as a multiple of a unit fraction, what is the relationship between the numerator of the
\nfraction and the number that is multiplied by the unit fraction?
\nAnswer:
\nWhen a fraction is written as a multiple of a unit fraction, the relationship between the numerator of the fraction
\nand the number that is multiplied by the unit fraction, is the whole number times the unit fraction.<\/p>\n
\nwritten as a multiple of a unit fraction the number will be always the whole number (whole number of times the unit fraction)
\nand is multiplied by unit fraction. For example \\(\\frac{3}{8}\\) we write it as 3 X \\(\\frac{1}{8}\\)
\nhere it is 3 and this 3 is multiplied by unit fraction.<\/p>\n
\nWrite the mixed number as a multiple of a unit fraction.<\/p>\n
\n1\\(\\frac{1}{8}\\)
\nAnswer:
\n1\\(\\frac{1}{8}\\) = \\(\\frac{9}{8}\\) = \\(\\frac{1}{8}\\)+\\(\\frac{1}{8}\\)+
\n\\(\\frac{1}{8}\\)+\\(\\frac{1}{8}\\)+\\(\\frac{1}{8}\\)+\\(\\frac{1}{8}\\)+
\n\\(\\frac{1}{8}\\)+\\(\\frac{1}{8}\\)+\\(\\frac{1}{8}\\)= 9 X \\(\\frac{1}{8}\\) .<\/p>\n
\nFirst we convert a mixed number to an improper fraction, It is to multiply the bottom number 8 by the
\n“regular” number 1, add in the top number 1, and then put this on top of the original bottom number as 9 by 8.
\n1\\(\\frac{1}{8}\\) = 1+\\(\\frac{1}{8}\\) = \\(\\frac{9}{8}\\)
\nWe write \\(\\frac{9}{8}\\) in addition equation as \\(\\frac{9}{8}\\)= \\(\\frac{1}{8}\\)+
\n\\(\\frac{1}{8}\\)+\\(\\frac{1}{8}\\)+\\(\\frac{1}{8}\\)+\\(\\frac{1}{8}\\)+
\n\\(\\frac{1}{8}\\)+\\(\\frac{1}{8}\\)+\\(\\frac{1}{8}\\) +\\(\\frac{1}{8}\\)
\nand multiplication as fraction \\(\\frac{9}{8}\\) represents 9 parts that are \\(\\frac{1}{10}\\)
\nof the whole, \\(\\frac{9}{8}\\) = 9 X \\(\\frac{1}{8}\\).<\/p>\n
\n3\\(\\frac{4}{5}\\)
\nAnswer:
\n3\\(\\frac{4}{5}\\) = \\(\\frac{19}{5}\\)=\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+
\n\\(\\frac{1}{5}\\) +\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+
\n\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+
\n\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+
\n\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+
\n\\(\\frac{1}{5}\\)= 19 X \\(\\frac{1}{5}\\).<\/p>\n
\nFirst we convert a mixed number to an improper fraction, It is to multiply the bottom number 5 by the “regular”
\nnumber 3, add in the top number 4, and then put this on top of the original bottom number as 19 by 5.
\n3\\(\\frac{4}{5}\\)=3+\\(\\frac{4}{5}\\) = \\(\\frac{19}{5}\\)
\nWe write \\(\\frac{19}{5}\\) in addition equation as \\(\\frac{19}{5}\\) = \\(\\frac{1}{5}\\)+
\n\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\) +\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+
\n\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+
\n\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+
\n\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+
\n\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\) and multiplication as fraction \\(\\frac{19}{5}\\)
\nrepresents 19 parts that are \\(\\frac{1}{5}\\) of the whole,\\(\\frac{19}{5}\\)= 19 X \\(\\frac{1}{5}\\).<\/p>\n
\nA juice stand worker uses \\(\\frac{1}{2}\\) of an orange to garnish each drink.
\nThe worker has \\(\\frac{7}{12}\\) of an orange left. How many more drinks can the worker garnish?
\nWrite the fraction of orange left as a multiple of \\(\\frac{1}{12}\\).
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-3.png\")
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-501.png\")
\nAnswer:
\nThe worker can garnish \\(\\frac{1}{12}\\) more drinks,
\n\\(\\frac{7}{12}\\) minus \\(\\frac{1}{2}\\) means \\(\\frac{7}{12}\\) – \\(\\frac{1}{2}\\)
\n= \\(\\frac{1}{12}\\), Orange left is 7 X \\(\\frac{1}{12}\\).
\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-6-1.bmp\")
<\/p>\n
\nGiven a juice stand worker uses \\(\\frac{1}{2}\\) of an orange to garnish each drink.
\nThe worker has \\(\\frac{7}{12}\\) of an orange left. So the worker can garnish more \\(\\frac{7}{12}\\)
\nminus \\(\\frac{1}{2}\\) means \\(\\frac{7}{12}\\) – \\(\\frac{1}{2}\\) = \\(\\frac{1}{12}\\),
\nGiven \\(\\frac{7}{12}\\) of an orange is left , to write orange left as a multiple of \\(\\frac{1}{12}\\)
\nwe have orange left as \\(\\frac{7}{12}\\) so write it as 7 parts that are \\(\\frac{1}{12}\\) of the whole,
\n\\(\\frac{7}{12}\\)= 7 X \\(\\frac{1}{12}\\).<\/p>\n
\nA piece of rope is \\(\\frac{8}{5}\\) meters long. You cut the rope into \\(\\frac{1}{5}\\) meter long pieces.
\nHow many pieces do you cut?
\nAnswer:
\n8 pieces I have cut.<\/p>\n
\nGiven a piece of rope is \\(\\frac{8}{5}\\) meters long and it has been cut into \\(\\frac{1}{5}\\)
\nmeter long pieces, therefore pieces of rope cut is \\(\\frac{8}{5}\\) divided by \\(\\frac{1}{5}\\)
\n= \\(\\frac{8}{5}\\) X latex]\\frac{5}{1}[\/latex] = 8.<\/p>\n
\nA restaurant serves \\(\\frac{4}{10}\\) of a meatloaf to 4 customers. Each customer receives
\nthe same amount of meatloaf. What fraction of the meatloaf does each customer receive?
\nAnswer:
\nThe fraction of the meatloaf each customer receives is \\(\\frac{1}{10}\\)<\/p>\n
\nGiven a restaurant serves \\(\\frac{4}{10}\\) of a meatloaf to 4 customers and each customer receives the same
\namount of meatloaf so fraction of the meatloaf each customer receives is\u00a0 \\(\\frac{4}{10}\\)\u00a0 divided by 4 =
\n\\(\\frac{4}{10}\\) x \\(\\frac{1}{4}\\) = \\(\\frac{1}{10}\\).<\/p>\n
\nYou use 3\\(\\frac{3}{4}\\) pounds of trail mix to make treat bags. You put \\(\\frac{1}{4}\\)
\npound of trail mix into each bag. How many treat bags do you make?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-4.png\")
\nAnswer:
\nTotal number of treat bags made are 15<\/p>\n
\nI use 3\\(\\frac{3}{4}\\) pounds of trail mix to make treat bags, We convert a mixed number to an
\nimproper fraction,It is to multiply the bottom number 4 by the “regular” number 3, add in the top number 3,
\nand then put this on top of the original bottom number as 15 by 4, it becomes \\(\\frac{15}{4}\\),Each bag i kept
\n\\(\\frac{1}{4}\\) pound of trail mix so total number of treat bags required to make are \\(\\frac{15}{4}\\)
\ndivided by \\(\\frac{1}{4}\\)=\\(\\frac{15}{4}\\) X \\(\\frac{4}{1}\\)=15 treat bags.<\/p>\n
\nDIG DEEPER!<\/strong>
\nYou walk from home to school and then back home again each day for 5 days. Altogether, you walk \\(\\frac{10}{8}\\) miles. What is the distance from your home to school? Explain.
\nAnswer:
\nThe distance from home to school is \\(\\frac{1}{8}\\) miles<\/p>\n
\nTotal number of miles walked is \\(\\frac{10}{8}\\) in 5 days that to from home to school and
\nthen back home again means it is twice a day , Let us take X as the distance from home to school is,
\nGiven 2X x 5=\\(\\frac{10}{8}\\) miles, X = Then each day number of miles walked is\u00a0 \\(\\frac{10}{8}\\)
\ndivided by 10 which is\u00a0 equal to\u00a0 \\(\\frac{10}{8}\\) x \\(\\frac{1}{10}\\) =\\(\\frac{1}{8}\\),
\nTherefore X = \\(\\frac{1}{8}\\) miles.<\/p>\n<\/a>Understand Multiples of Unit Fractions Homework & practice 9.1<\/h3>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-5.png\")
\nAnswer:
\n\\(\\frac{2}{12}\\)= \\(\\frac{1}{12}\\)+\\(\\frac{1}{12}\\) = 2 X \\(\\frac{1}{12}\\)<\/p>\n
\nWe write \\(\\frac{2}{12}\\) in addition equation as \\(\\frac{2}{12}\\)= \\(\\frac{1}{12}\\) +
\n\\(\\frac{1}{12}\\) and multiplication as fraction \\(\\frac{2}{12}\\) represents 2 parts that are
\n\\(\\frac{1}{12}\\) of the whole, \\(\\frac{2}{12}\\)= 2 X \\(\\frac{1}{12}\\).<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-6.png\")
\nAnswer:
\n\\(\\frac{5}{100}\\)= \\(\\frac{1}{100}\\)+\\(\\frac{1}{100}\\)+\\(\\frac{1}{100}\\)+
\n\\(\\frac{1}{100}\\)+\\(\\frac{1}{100}\\) = 5 X \\(\\frac{1}{100}\\).<\/p>\n
\nWe write \\(\\frac{5}{100}\\) in addition equation as \\(\\frac{5}{100}\\)= \\(\\frac{1}{100}\\)+
\n\\(\\frac{1}{100}\\)+\\(\\frac{1}{100}\\)+\\(\\frac{1}{100}\\)+\\(\\frac{1}{100}\\)
\nand multiplication as fraction \\(\\frac{5}{100}\\) represents 5 parts that are \\(\\frac{1}{100}\\) of the whole, \\(\\frac{5}{100}\\) = 5 X \\(\\frac{1}{100}\\).<\/p>\n
\n\\(\\frac{3}{6}\\)
\nAnswer:
\n\\(\\frac{3}{6}\\)=\\(\\frac{1}{6}\\)+\\(\\frac{1}{6}\\)+\\(\\frac{1}{6}\\)
\n= 3 X \\(\\frac{1}{6}\\).<\/p>\n
\nWe write \\(\\frac{3}{6}\\) in addition equation as \\(\\frac{3}{6}\\)=\\(\\frac{1}{6}\\)+
\n\\(\\frac{1}{6}\\)+\\(\\frac{1}{6}\\) and multiplication as fraction \\(\\frac{3}{6}\\)
\nrepresents 3 parts that are \\(\\frac{1}{6}\\) of the whole,\\(\\frac{3}{6}\\) = 3 X \\(\\frac{1}{6}\\).<\/p>\n
\n\\(\\frac{7}{10}\\)
\nAnswer:
\n\\(\\frac{7}{10}\\) =\\(\\frac{1}{10}\\)+\\(\\frac{1}{10}\\)+\\(\\frac{1}{10}\\)+
\n\\(\\frac{1}{10}\\)+\\(\\frac{1}{10}\\)+\\(\\frac{1}{10}\\)+\\(\\frac{1}{10}\\)
\n= 7 X \\(\\frac{1}{10}\\)<\/p>\n
\nWe write \\(\\frac{7}{10}\\) in addition equation as \\(\\frac{7}{10}\\)= \\(\\frac{1}{10}\\)+
\n\\(\\frac{1}{10}\\)+\\(\\frac{1}{10}\\)+\\(\\frac{1}{10}\\)+\\(\\frac{1}{10}\\)+
\n\\(\\frac{1}{10}\\)+\\(\\frac{1}{10}\\) and multiplication as \\(\\frac{7}{10}\\) represents
\n7 parts that are \\(\\frac{1}{10}\\) of the whole,\\(\\frac{7}{10}\\) = 7 X \\(\\frac{1}{10}\\).<\/p>\n
\n\\(\\frac{4}{5}\\)
\nAnswer:
\n\\(\\frac{4}{5}\\) = \\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+
\n\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\) = 4 X \\(\\frac{1}{5}\\).<\/p>\n
\nWe write \\(\\frac{4}{5}\\) in addition equation as \\(\\frac{4}{5}\\)=\\(\\frac{1}{5}\\)+
\n\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\)+\\(\\frac{1}{5}\\) and multiplication as \\(\\frac{4}{5}\\)
\nrepresents 4 parts that are \\(\\frac{1}{5}\\) of the whole,\\(\\frac{4}{5}\\)= 4 X \\(\\frac{1}{5}\\).<\/p>\n
\n\\(\\frac{9}{2}\\)
\nAnswer:
\n\\(\\frac{9}{2}\\) = \\(\\frac{1}{2}\\)+\\(\\frac{1}{2}\\)+\\(\\frac{1}{2}\\)+
\n\\(\\frac{1}{2}\\)+\\(\\frac{1}{2}\\)+\\(\\frac{1}{2}\\)+\\(\\frac{1}{2}\\)+
\n\\(\\frac{1}{2}\\)+\\(\\frac{1}{2}\\) = 9 X \\(\\frac{1}{2}\\).<\/p>\n
\nWe write \\(\\frac{9}{2}\\) in addition equation as \\(\\frac{9}{2}\\) = \\(\\frac{1}{2}\\)+
\n\\(\\frac{1}{2}\\)+\\(\\frac{1}{2}\\)+\\(\\frac{1}{2}\\)+\\(\\frac{1}{2}\\)+
\n\\(\\frac{1}{2}\\)+\\(\\frac{1}{2}\\)+\\(\\frac{1}{2}\\)+\\(\\frac{1}{2}\\)
\nand multiplication as \\(\\frac{9}{2}\\) represents 9 parts that are \\(\\frac{1}{2}\\) of the whole,
\n\\(\\frac{9}{2}\\)= 9 X \\(\\frac{1}{2}\\).<\/p>\n
\n\\(\\frac{8}{8}\\)
\nAnswer:
\n\\(\\frac{8}{8}\\)=1=\\(\\frac{1}{8}\\)+\\(\\frac{1}{8}\\)+\\(\\frac{1}{8}\\)+
\n\\(\\frac{1}{8}\\)+\\(\\frac{1}{8}\\)+\\(\\frac{1}{8}\\)+\\(\\frac{1}{8}\\)+
\n\\(\\frac{1}{8}\\) = \\(\\frac{8}{8}\\) = 8 X \\(\\frac{1}{8}\\).<\/p>\n
\n\\(\\frac{8}{8}\\)= 1 ,but we write the fraction as a addition of a unit fraction and multiple of a unit fraction,
\nWe write \\(\\frac{8}{8}\\) in addition equation as \\(\\frac{8}{8}\\) = \\(\\frac{1}{8}\\)+
\n\\(\\frac{1}{8}\\)+\\(\\frac{1}{8}\\)+\\(\\frac{1}{8}\\)+\\(\\frac{1}{8}\\)+
\n\\(\\frac{1}{8}\\)+\\(\\frac{1}{8}\\)+\\(\\frac{1}{8}\\) and multiplication as \\(\\frac{8}{8}\\)
\nrepresents 8 parts that are \\(\\frac{1}{8}\\) of the whole,\\(\\frac{8}{8}\\)= 8 X \\(\\frac{1}{8}\\).<\/p>\n
\n\\(\\frac{6}{3}\\)
\nAnswer:
\n\\(\\frac{6}{3}\\)=2,\\(\\frac{6}{3}\\)= \\(\\frac{1}{3}\\)+\\(\\frac{1}{3}\\)+
\n\\(\\frac{1}{3}\\)+\\(\\frac{1}{3}\\)+\\(\\frac{1}{3}\\)+\\(\\frac{1}{3}\\)
\n= 6 X \\(\\frac{1}{3}\\).<\/p>\n
\n\\(\\frac{6}{3}\\)= 2 ,but we write the fraction as a addition of a unit fraction and multiple of a unit fraction,
\nWe write \\(\\frac{6}{3}\\) in addition equation as \\(\\frac{6}{3}\\)= \\(\\frac{1}{3}\\)+
\n\\(\\frac{1}{3}\\)+\\(\\frac{1}{3}\\)+\\(\\frac{1}{3}\\)+\\(\\frac{1}{3}\\)+
\n\\(\\frac{1}{3}\\) and multiplication as \\(\\frac{6}{3}\\) represents 6 parts that are
\n\\(\\frac{1}{3}\\) of the whole,\\(\\frac{6}{3}\\)= 6 X \\(\\frac{1}{3}\\).<\/p>\n
\nLogic<\/strong>
\nWhat is Newton\u2019s fraction? Write the fraction as a multiple of a unit fraction.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-7.png\")
\nAnswer:
\nNewton’s fraction = \\(\\frac{9}{12}\\)=\\(\\frac{1}{12}\\) +\\(\\frac{1}{12}\\) +
\n\\(\\frac{1}{12}\\) +\\(\\frac{1}{12}\\) +\\(\\frac{1}{12}\\) +\\(\\frac{1}{12}\\) +
\n\\(\\frac{1}{12}\\) +\\(\\frac{1}{12}\\) +\\(\\frac{1}{12}\\) = 9 X \\(\\frac{1}{12}\\).<\/p>\n
\nGiven that Newton’s fraction as sum of 9 unit fractions and each unit fraction is one twelfth of a whole.
\nSo Newton’s fraction is \\(\\frac{9}{12}\\) we write \\(\\frac{9}{12}\\) in addition equation as
\n\\(\\frac{9}{12}\\)=\u00a0 \\(\\frac{1}{12}\\) +\\(\\frac{1}{12}\\) +\\(\\frac{1}{12}\\) +
\n\\(\\frac{1}{12}\\) +\\(\\frac{1}{12}\\) +\\(\\frac{1}{12}\\) +\\(\\frac{1}{12}\\) +
\n\\(\\frac{1}{12}\\) +\\(\\frac{1}{12}\\) and multiplication as \\(\\frac{9}{12}\\) represents 9 parts
\nthat are \\(\\frac{1}{12}\\) of the whole,\\(\\frac{9}{12}\\)= 9 X \\(\\frac{1}{12}\\).<\/p>\n
\nStructure<\/strong>
\nWrite a multiplication equation that represents the grapefruit halves.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-8.png\")
\nAnswer:
\n\\(\\frac{6}{2}\\)=\\(\\frac{1}{2}\\)+\\(\\frac{1}{2}\\)+\\(\\frac{1}{2}\\)+
\n\\(\\frac{1}{2}\\)+\\(\\frac{1}{2}\\)+\\(\\frac{1}{2}\\)
\n= 6 X \\(\\frac{1}{2}\\).<\/p>\n
\nGiven 6 number of grapefruit halves so there are total grapefruit as \\(\\frac{6}{2}\\) we write
\n\\(\\frac{6}{2}\\) in addition equation as \\(\\frac{6}{2}\\)=\\(\\frac{1}{2}\\)+
\n\\(\\frac{1}{2}\\)+\\(\\frac{1}{2}\\)+\\(\\frac{1}{2}\\)+\\(\\frac{1}{2}\\)+
\n\\(\\frac{1}{2}\\),so the multiplication equation is \\(\\frac{6}{2}\\) represents 6 parts that are
\n\\(\\frac{1}{2}\\) of the whole,\\(\\frac{6}{2}\\)= 6 X \\(\\frac{1}{2}\\).<\/p>\n
\nWhich One Doesn’t Belong?<\/strong>
\nWhich expression does not belong with the other three?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-9.png\")
\nAnswer:
\n4 X \\(\\frac{1}{5}\\) expression does not belong with the other three, as all the other expressions values results are same =\\(\\frac{5}{4}\\) only 4 X \\(\\frac{1}{5}\\) expression is not.<\/p>\n
\n1. 5 X \\(\\frac{1}{4}\\) = \\(\\frac{5}{4}\\)
\n2. \\(\\frac{1}{4}\\)+\\(\\frac{1}{4}\\)+\\(\\frac{1}{4}\\)+\\(\\frac{1}{4}\\)=
\n5 X \\(\\frac{1}{4}\\)= \\(\\frac{5}{4}\\)
\n3. \\(\\frac{5}{4}\\) =\\(\\frac{5}{4}\\)
\n4. 4 X \\(\\frac{1}{5}\\)= \\(\\frac{4}{5}\\)\u2260\u00a0 \\(\\frac{5}{4}\\)
\nSo in the above expressions only 4 X \\(\\frac{1}{5}\\)\u00a0 does not belong with the other three expressions.<\/p>\n
\nModeling Real Life<\/strong>
\nYou are making blueberry pancakes. You have \\(\\frac{6}{8}\\) cup of blueberries. You put \\(\\frac{1}{8}\\) cup of blueberries in each pancake. How many pancakes do you make?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-10.png\")
\nAnswer:
\n6 pancakes i can make.<\/p>\n
\nI have \\(\\frac{6}{8}\\) cup of blueberries and i can put \\(\\frac{1}{8}\\) cup of blueberries
\nin each pan cake so total number of pancakes made are \\(\\frac{6}{8}\\) divided by \\(\\frac{1}{8}\\) =
\n\\(\\frac{6}{8}\\) X \\(\\frac{8}{1}\\)= 6 pancakes.<\/p>\n
\nDIG DEEPER!<\/strong>
\nYou cut a loaf of zucchini bread into 20 equal slices. You and your friends eat \\(\\frac{3}{10}\\) of the slices.
\nYou want to put each leftover slice into its own bag. How many bags do you need?
\nAnswer:
\n14 bags are needed.<\/p>\n
\nGiven a loaf of zucchini bread is cut\u00a0 into 20 equal slices and i ,friend eat \\(\\frac{3}{10}\\) of the slices,
\nTotal number of slices of zucchini bread =20, Number of slices ate = \\(\\frac{3}{10}\\) means it says
\nout of 10 slices 3 were ate, so out of 20 slices\u00a0 2 x 3= 6 slices were eaten. Number of slices left = 20 – 6 =14 slices
\nand one bag contains only one slice. Therefore number of bags needed are 14.<\/p>\n
\nIs 46 a multiple of 45.
\nAnswer:
\nNo 46 is not a multiple of 45.<\/p>\n
\nA\u00a0multiple\u00a0is a\u00a0number that can be divided by another number a certain number of times without a remainder.
\n45 when divided by 46 a certain times will leave a remainder, So 46 is not a multiple of 45
\nor a factor\u00a0is\u00a0one of two or more numbers that divides a given number without a remainder.
\nAs factors of 45 are 1,3,5,9,15 and factors of 46 are 1,2,23, both do not have common factors so 46 is not a multiple of 45.<\/p>\n
\nIs 3 a factor of 75?
\nAnswer:
\nYes 3 is a factor of 75
\nExplanation:
\nWe know that a factor is one that divides a given number without a remainder and 75 when divided by 3
\nleaves no remainder, So 3 is a factor of 75.<\/p>\n<\/a>Lesson 9.2 Understand Multiples of Fractions<\/h3>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-11.png\")
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-12.png\")
\nAnswer:
\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-7-1.bmp\")
<\/p>\n
\n\\(\\frac{2}{6}\\) = 4 X \\(\\frac{2}{6}\\) =
\n\\(\\frac{1}{6}\\) +\\(\\frac{1}{6}\\)+ \\(\\frac{1}{6}\\) +\\(\\frac{1}{6}\\)+
\n\\(\\frac{1}{6}\\) +\\(\\frac{1}{6}\\)+ \\(\\frac{1}{6}\\) +\\(\\frac{1}{6}\\) =
\n8 X \\(\\frac{1}{6}\\).<\/p>\n
\n\\(\\frac{2}{6}\\) +\\(\\frac{2}{6}\\) +\\(\\frac{2}{6}\\) +\\(\\frac{2}{6}\\)
\nthe multiplication equation is\u00a0 4 parts that are \\(\\frac{2}{6}\\) of the whole as\u00a0 4 X \\(\\frac{2}{6}\\)
\n\\(\\frac{1}{6}\\) +\\(\\frac{1}{6}\\)+ \\(\\frac{1}{6}\\) +\\(\\frac{1}{6}\\)+
\n\\(\\frac{1}{6}\\) +\\(\\frac{1}{6}\\)+ \\(\\frac{1}{6}\\) +\\(\\frac{1}{6}\\) =
\n8 X \\(\\frac{1}{6}\\) the multiplication equation is 8 parts that are \\(\\frac{1}{6}\\) of the whole as
\n8 X \\(\\frac{1}{6}\\).<\/p>\n
\nCompare your expressions. How are they the same? How are they different?
\nSame means the result of both expressions is same = \\(\\frac{8}{6}\\)
\nDifferent means in one expression we take value of \\(\\frac{2}{6}\\) 4 times and in another
\nexpression we take \\(\\frac{1}{6}\\) 8 times.<\/p>\n
\nSame means \\(\\frac{2}{6}\\) +\\(\\frac{2}{6}\\) +\\(\\frac{2}{6}\\) +\\(\\frac{2}{6}\\) =
\n4 X \\(\\frac{2}{6}\\) = \\(\\frac{8}{6}\\) and \\(\\frac{1}{6}\\) +\\(\\frac{1}{6}\\)+
\n\\(\\frac{1}{6}\\) +\\(\\frac{1}{6}\\)+\\(\\frac{1}{6}\\) +\\(\\frac{1}{6}\\)+
\n\\(\\frac{1}{6}\\) +\\(\\frac{1}{6}\\) = 8 X \\(\\frac{1}{6}\\) =\\(\\frac{8}{6}\\) ,
\nboth have results similar as \\(\\frac{8}{6}\\), Different means here we are taking expressions as addition values of\u00a0 \\(\\frac{2}{6}\\) by 4 times and in other expression we are taking addition values of \\(\\frac{1}{6}\\) by 8 times.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-13.png\")
\nAnswer:
\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-8.bmp\")
<\/p>\n
\n<\/strong>Explanation:
\nTo write 2 X \\(\\frac{3}{5}\\) multiple of unit fraction first we write \\(\\frac{3}{5}\\) as multiple of
\n3 X \\(\\frac{1}{5}\\) then we multiply it by 2 as 2 X 3 X \\(\\frac{1}{5}\\)=6 X \\(\\frac{1}{5}\\).
\n
\nShow and Grow<\/strong><\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-14.png\")
\nAnswer:
\n2 X \\(\\frac{4}{5}\\) = 2 X 4 X \\(\\frac{1}{5}\\) = 8 X \\(\\frac{1}{5}\\) = \\(\\frac{8}{5}\\).<\/p>\n
\nFirst we write \\(\\frac{4}{5}\\)\u00a0 as \u00a0\\(\\frac{1}{5}\\) + \\(\\frac{1}{5}\\) +
\n\\(\\frac{1}{5}\\) + \\(\\frac{1}{5}\\) = 4 X \\(\\frac{1}{5}\\) then multiply it by 2
\nwhich is\u00a0 2 X 4 X \\(\\frac{1}{5}\\) = 8 X \\(\\frac{1}{5}\\) = \\(\\frac{8}{5}\\).<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-15.png\")
\nAnswer:
\n3 X \\(\\frac{2}{10}\\) = 3 X 2 X \u00a0\\(\\frac{1}{10}\\) = 6 X \\(\\frac{1}{10}\\) =\\(\\frac{6}{10}\\).<\/p>\n
\nFirst we write \\(\\frac{2}{10}\\) as \\(\\frac{1}{10}\\) +\\(\\frac{1}{10}\\) = 2 X \\(\\frac{1}{10}\\)
\nthen multiply it by 3 which is 3 X 2 X \\(\\frac{1}{10}\\) = 6 X \\(\\frac{1}{10}\\) =\\(\\frac{6}{10}\\).<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-16.png\")
\nAnswer:
\n4 X \\(\\frac{3}{2}\\) = 4 X 3 X \\(\\frac{1}{2}\\) = 12 X \\(\\frac{1}{2}\\) = \\(\\frac{12}{2}\\) = 6.<\/p>\n
\nFirst we write \\(\\frac{3}{2}\\) as \\(\\frac{1}{2}\\) +\\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\) = 3 X \\(\\frac{1}{2}\\) then we multiply it by 4 which is 4 X 3 X \\(\\frac{1}{2}\\)= 12 X \\(\\frac{1}{2}\\)= \\(\\frac{12}{2}\\)=6.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-17.png\")
\nAnswer:
\n5 X \\(\\frac{2}{3}\\) = 5 X 2 X \\(\\frac{1}{3}\\) = 10 X \\(\\frac{1}{3}\\)=
\n\\(\\frac{10}{3}\\).<\/p>\n
\nFirst we write \\(\\frac{2}{3}\\) as \\(\\frac{1}{3}\\)+\\(\\frac{1}{3}\\)=
\n2 X \\(\\frac{1}{3}\\) then multiply it by 5 which is 5 X 2 X \\(\\frac{1}{3}\\)=
\n10 X \\(\\frac{1}{3}\\)= \\(\\frac{10}{3}\\).<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-18.png\")
\nAnswer:
\n6 X \\(\\frac{5}{8}\\)= 6 X 5 X \\(\\frac{1}{8}\\)= 30 X \\(\\frac{1}{8}\\) =
\n\\(\\frac{30}{8}\\).<\/p>\n
\nFirst we write \\(\\frac{5}{8}\\) as \\(\\frac{1}{8}\\)+ \\(\\frac{1}{8}\\)+
\n\\(\\frac{1}{8}\\) + \\(\\frac{1}{8}\\)+ \\(\\frac{1}{8}\\) = 5 X \\(\\frac{1}{8}\\)
\nthen multiply it by 6 which is 6 X 5 X \\(\\frac{1}{8}\\)=30 X \\(\\frac{1}{8}\\)= \\(\\frac{30}{8}\\).<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-19.png\")
\nAnswer:
\n9 X \\(\\frac{7}{4}\\) = 9 X 7 X\\(\\frac{1}{4}\\)= 63 X \\(\\frac{1}{4}\\) =
\n\\(\\frac{63}{4}\\).<\/p>\n
\nFirst we write \\(\\frac{7}{4}\\) as \\(\\frac{1}{4}\\)+\\(\\frac{1}{4}\\)+
\n\\(\\frac{1}{4}\\)+ \\(\\frac{1}{4}\\)+\\(\\frac{1}{4}\\)+\\(\\frac{1}{4}\\)+
\n\\(\\frac{1}{4}\\) = 7 x \\(\\frac{1}{4}\\)
\nthen we multiply it by 9 which is 9 X 7 X \\(\\frac{1}{4}\\)= 63 X \\(\\frac{1}{4}\\) =
\n\\(\\frac{63}{4}\\).<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-20.png\")
\nAnswer:
\n7 X \\(\\frac{4}{12}\\)=7 X 4 X \\(\\frac{1}{12}\\)= 28 X \\(\\frac{1}{12}\\)=
\n\\(\\frac{28}{12}\\) also 7 X \\(\\frac{4}{12}\\)= 7 X \u00a0\\(\\frac{1}{3}\\)= \\(\\frac{7}{3}\\).<\/p>\n
\nFirst we write \\(\\frac{4}{12}\\) as \\(\\frac{1}{12}\\)+ \\(\\frac{1}{12}\\)+
\n\\(\\frac{1}{12}\\)+\\(\\frac{1}{12}\\)= 4 X \\(\\frac{1}{12}\\) then we multiply it by 7
\nwhich is 7 X 4 X \\(\\frac{1}{12}\\)= 28 X \\(\\frac{1}{12}\\)=\\(\\frac{28}{12}\\)
\nwe can also simplify 7 X \\(\\frac{4}{12}\\) as 4,12 can be divided by 4 we can also write
\n7 X \\(\\frac{4}{12}\\) as 7 X \u00a0\\(\\frac{1}{3}\\)= \\(\\frac{7}{3}\\).<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-21.png\")
\nAnswer:
\n\\(\\frac{9}{6}\\) X 8 = 9 X \\(\\frac{1}{6}\\) X 8 = 72 X \\(\\frac{1}{6}\\) =
\n\\(\\frac{72}{6}\\) =12.<\/p>\n
\nFirst we write \\(\\frac{9}{6}\\) as \\(\\frac{1}{6}\\) +\\(\\frac{1}{6}\\) +
\n\\(\\frac{1}{6}\\) + \\(\\frac{1}{6}\\) +\\(\\frac{1}{6}\\) +\\(\\frac{1}{6}\\) +
\n\\(\\frac{1}{6}\\) + \\(\\frac{1}{6}\\) +\\(\\frac{1}{6}\\) =9 X \\(\\frac{1}{6}\\)
\nthen we multiply it by 8 which is 9 X 8 X \\(\\frac{1}{6}\\) = 72 X \\(\\frac{1}{6}\\) =
\n\\(\\frac{72}{6}\\)\u00a0 further as 6 can divide 72 and leaving no remainder we write \\(\\frac{72}{6}\\) =12.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-22.png\")
\nAnswer:
\n10 X \\(\\frac{20}{100}\\) = 10 X \\(\\frac{2}{10}\\)=2 X 10 X \\(\\frac{1}{10}\\)=
\n20 \\(\\frac{1}{10}\\)=\\(\\frac{20}{10}\\)=2.<\/p>\n
\nFirst we write \\(\\frac{20}{100}\\) = \\(\\frac{2}{10}\\) as \\(\\frac{1}{10}\\) +
\n\\(\\frac{1}{10}\\) = 2 X \\(\\frac{1}{10}\\) then multiply it by 10 which is
\n2 X 10 X \\(\\frac{1}{10}\\)= 20 X \\(\\frac{1}{10}\\)=\\(\\frac{20}{10}\\)
\nand 10 can divide 20 leaving no remainder further we can write \\(\\frac{20}{10}\\) as 2.<\/p>\n
\nFind the unknown number.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-23.png\")
\nAnswer:
\nThe unknown number is 2.<\/p>\n
\n___ X \\(\\frac{8}{10}\\) = \\(\\frac{16}{10}\\)= to get the unknown number we take it as P,
\nP X \\(\\frac{8}{10}\\) = \\(\\frac{16}{10}\\) means P = \\(\\frac{16}{10}\\) X
\n\\(\\frac{10}{8}\\)\u00a0 we get 2 , so P=2.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-24.png\")
\nAnswer:
\nThe unknown number is 5.<\/p>\n
\nLet us take unknown letter as P so 4 X \\(\\frac{P}{2}\\) = \\(\\frac{20}{2}\\) ,
\n4 X P= 2 X \\(\\frac{20}{2}\\) to get value of P we take 4 to other side ,
\nTherefore P=20 X \\(\\frac{1}{4}\\) = 5, so the unknown number is 5.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-25.png\")
\nAnswer:
\nThe unknown number is 100.<\/p>\n
\nLet us take unknown number as P given 3 X \\(\\frac{9}{P}\\) = \\(\\frac{27}{100}\\) ,
\n27 X[ latex]\\frac{1}{P}[\/latex] = \\(\\frac{27}{100}\\), Therefore P= 27 X \\(\\frac{100}{27}\\)=100.<\/p>\n
\nReasoning<\/strong>
\nWithout calculating, would you plot the product of 5 and \\(\\frac{3}{6}\\) to the left or to the right of 5 on a number line? Explain.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-26.png\")
\nAnswer:
\nYes , without calculating we can plot 5 and \\(\\frac{3}{6}\\) to the left of 5
\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-9.bmp\")
<\/p>\n
\n5 X \\(\\frac{3}{6}\\)= 5 X\u00a0 \\(\\frac{1}{2}\\) since the denominator of each given fraction is 2
\ndivide the space between every pairs of two consecutive integers (on the number line) in 2 equal parts each part
\nso obtained will represent the fraction \\(\\frac{1}{2}\\) , so on the number line we move 5 parts on the
\nright-side of zero as shown in the figure.
\n<\/span><\/p>\n
\nPatterns<\/strong>
\nDescribe and complete the pattern.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-27.png\")
\nAnswer:
\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-10.bmp\")
\nExplanation:
\nWe first write the expressions as multiple of unit fraction and find the product so
\n1. 3 X \\(\\frac{1}{5}\\) can be written as\u00a0 product of 3 X 1 X\u00a0 \\(\\frac{1}{5}\\)=
\n3 X \\(\\frac{1}{5}\\) = \\(\\frac{3}{5}\\)
\n2. 3 X \\(\\frac{2}{5}\\)\u00a0 can be written as product of\u00a0 3 X 2 X \\(\\frac{1}{5}\\) =
\n6 X \\(\\frac{1}{5}\\) = \\(\\frac{6}{5}\\)
\n3. 3 X \\(\\frac{3}{5}\\) can be written as product of 3 X 3 X \\(\\frac{1}{5}\\) =
\n9 X \\(\\frac{1}{5}\\) = \\(\\frac{9}{5}\\)
\n4. 3 X \\(\\frac{4}{5}\\) can be written as product of\u00a0 3 X 4 X \\(\\frac{1}{5}\\) =
\n12 X \\(\\frac{1}{5}\\) = \\(\\frac{12}{5}\\)
\n5. 3 X \\(\\frac{5}{5}\\) can be written as product of 3 X 5 X \\(\\frac{1}{5}\\) =
\n15 X \\(\\frac{1}{5}\\) = \\(\\frac{15}{5}\\) further can be simplified as 15,5 goes in 5,
\nso dividing by 5 we get \\(\\frac{15}{5}\\) =\u00a0 3.<\/p>\n
\nThree birds each need \\(\\frac{2}{3}\\) cup of birdseed, so find 3 \u00d7 \\(\\frac{2}{3}\\).
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-28.png\")
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-29.png\")
\nAnswer:
\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-11.bmp\")
<\/p>\n
\nGiven A bird keeper uses a \\(\\frac{1}{3}\\) cup scoop to feed 3 birds each bird he feeds
\n\\(\\frac{2}{3}\\) cup of birdseed, Three birds each need \\(\\frac{2}{3}\\) cup of birdseed
\nso the bird keeper fills the scoop as 3 X \\(\\frac{2}{3}\\) = 3 X _____P______ X \\(\\frac{1}{3}\\) here
\nP is the\u00a0 number of times the bird keeper fills the cup scoop.
\n3 X 2 X \\(\\frac{1}{3}\\) =\u00a0 3 X P X \\(\\frac{1}{3}\\) , when we equate both sides,
\nwe get 3 X 2 = 3 X P , therefore P = 2.
\nShow and Grow<\/strong><\/p>\n
\nA chef makes 4 servings of honey1oatmeal. She uses a \\(\\frac{1}{2}\\) tablespoon measuring spoon to measure \\(\\frac{3}{2}\\) tablespoons of honey for each serving. How many times does she fill the measuring spoon?
\nAnswer:
\n3 times the chef fill the measuring spoon.<\/p>\n
\nChef uses a \\(\\frac{1}{2}\\) table spoon as measuring spoon, To measure honey for each serving
\nshe needed for each serving is \\(\\frac{3}{2}\\) , so 4 X \\(\\frac{3}{2}\\) ,
\nLet us take P as number of times of measuring spoon , Given 4 X \\(\\frac{3}{2}\\) =
\n4 X _P_<\/span> X \\(\\frac{1}{2}\\), 4 X ___3___<\/span> X \\(\\frac{1}{2}\\)= 4 X _P_<\/span> X \\(\\frac{1}{2}\\) ,
\nwe equate both sides\u00a0 we get value of P as 3 , therefore 3 times the chef fill the measuring spoon.<\/p>\n
\nYou have 7 magnetic blocks that are each \\(\\frac{9}{100}\\) meter long. You connect the ends of the blocks to make a snake. What fraction of a meter is the block snake?
\nAnswer:
\n\\(\\frac{63}{100}\\) meter is the block snake.<\/p>\n
\nGiven 7 magnetic blocks and each are \\(\\frac{9}{100}\\) meter long. After connecting the ends
\nof the blocks to make a snake is 7 X \\(\\frac{9}{100}\\) = 7 X 9 X \\(\\frac{1}{100}\\) =
\n63 X \\(\\frac{1}{100}\\) = \\(\\frac{63}{100}\\) meter.<\/p>\n
\nYour friend roller-skates \\(\\frac{15}{10}\\) miles each day for 5 days. How many miles does your friend roller-skate in all?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-30.png\")
\nAnswer:
\nMy friend roller skate \\(\\frac{15}{2}\\) miles in all.<\/p>\n
\nGiven friend roller-skates \\(\\frac{15}{10}\\) miles each day means \\(\\frac{3}{2}\\) miles
\neach day so for 5 days it is 5 X \\(\\frac{3}{2}\\) = 5 X 3 X \\(\\frac{1}{2}\\) =
\n15 X \\(\\frac{1}{2}\\) = \\(\\frac{15}{2}\\) miles.<\/p>\n<\/a>Understand Multiples of Fractions Homework & Practice 9.2<\/h3>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-31.png\")
\nAnswer:
\n2 X \\(\\frac{2}{3}\\) = 2 X 2 X \\(\\frac{1}{3}\\) = 4 X (\\(\\frac{1}{3}\\)) =
\n\\(\\frac{4}{3}\\)<\/p>\n
\nTo write the product as a multiple of a unit fraction we write it \\(\\frac{2}{3}\\)
\nas 2 X \\(\\frac{1}{3}\\) and multiply by 2 = 2 X 2 X \\(\\frac{1}{3}\\) =
\n4 X \\(\\frac{1}{3}\\) = \\(\\frac{4}{3}\\)<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-32.png\")
\nAnswer:
\n3 X \\(\\frac{5}{8}\\) = 3 X 5 X \\(\\frac{1}{8}\\) = 15 X (\\(\\frac{1}{8}\\)) =
\n\\(\\frac{15}{8}\\).<\/p>\n
\nTo write the product as a multiple of a unit fraction we write it \\(\\frac{5}{8}\\) as
\n5 X \\(\\frac{1}{8}\\) and multiply by 3 = 3 X 5 X \\(\\frac{1}{8}\\) = 15 X \\(\\frac{1}{8}\\)
\n= \\(\\frac{15}{8}\\)<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-33.png\")
\nAnswer:
\n4 X \\(\\frac{8}{2}\\) = 4 X 8 X \\(\\frac{1}{2}\\) = 32 X (\\(\\frac{1}{2}\\)) =
\n\\(\\frac{32}{2}\\) =16.<\/p>\n
\nTo write the product as a multiple of a unit fraction we write it \\(\\frac{8}{2}\\) as
\n8 X \\(\\frac{1}{2}\\) and multiply by 4 = 4 X 8 X \\(\\frac{1}{2}\\) =
\n32 X \\(\\frac{1}{2}\\) = \\(\\frac{32}{2}\\) = 16.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-34.png\")
\nAnswer:
\n5 X \\(\\frac{9}{10}\\) = 5 X 9 X \\(\\frac{1}{10}\\) = 45 X (\\(\\frac{1}{10}\\)) =
\n\\(\\frac{45}{10}\\) = \\(\\frac{9}{2}\\)<\/p>\n
\nTo write the product as a multiple of a unit fraction we write it \\(\\frac{9}{10}\\) as
\n9 X \\(\\frac{1}{10}\\) and multiply by 5 = 5 X 9 X \\(\\frac{1}{10}\\) =
\n45 X \\(\\frac{1}{10}\\) = \\(\\frac{45}{10}\\) = \\(\\frac{9}{2}\\).<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-35.png\")
\nAnswer:
\n8 X \\(\\frac{6}{5}\\) = 8 X 6 X \\(\\frac{1}{5}\\) = 48X (\\(\\frac{1}{5}\\)) =
\n\\(\\frac{48}{5}\\)<\/p>\n
\nTo write the product as a multiple of a unit fraction we write it \\(\\frac{6}{5}\\) as
\n6 X \\(\\frac{1}{5}\\) and multiply by 8 = 8 X 6 X \\(\\frac{1}{5}\\) =
\n48 X \\(\\frac{1}{5}\\) = \\(\\frac{48}{5}\\).<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-36.png\")
\nAnswer:
\n10 X \\(\\frac{2}{4}\\) = 10 X 2 X \\(\\frac{1}{4}\\) = 20 X (\\(\\frac{1}{4}\\)) =
\n\\(\\frac{20}{4}\\) = \\(\\frac{10}{2}\\).<\/p>\n
\nTo write the product as a multiple of a unit fraction we write it \\(\\frac{2}{4}\\) as 2 X \\(\\frac{1}{4}\\)
\nand multiply by 10 = 2 X 10 X \\(\\frac{1}{4}\\) = 20 X \\(\\frac{1}{4}\\) = \\(\\frac{20}{4}\\) =
\n\\(\\frac{10}{2}\\).<\/p>\n
\nNumber Sense<\/strong>
\nWhich expression are equivalent to ![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-37.png\")
?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-38.png\")
\nAnswer:
\nThe expressions equivalent to 4 X \\(\\frac{7}{8}\\) are\u00a0 (4 X 7) x \\(\\frac{1}{8}\\) ,
\n\\(\\frac{28}{8}\\),\\(\\frac{7}{8}\\)+\\(\\frac{7}{8}\\)+\\(\\frac{7}{8}\\) +
\n\\(\\frac{7}{8}\\).<\/p>\n
\nWe have the value of expression of 4 X \\(\\frac{7}{8}\\) as \\(\\frac{28}{8}\\) So
\n1.(4 X 7) x \\(\\frac{1}{8}\\)= \\(\\frac{28}{8}\\)
\n2. \\(\\frac{28}{8}\\)=\\(\\frac{28}{8}\\)
\n3. 4 X 7 \u2260 \\(\\frac{28}{8}\\)
\n4. \\(\\frac{32}{7}\\) \u2260 \\(\\frac{28}{8}\\)
\n5. \\(\\frac{7}{8}\\)+\\(\\frac{7}{8}\\)+\\(\\frac{7}{8}\\)+\\(\\frac{7}{8}\\) =
\n\\(\\frac{28}{8}\\), Therefore expressions 1,2,5 are equivalent to \\(\\frac{28}{8}\\).
\nThe expressions equivalent to 4 X \\(\\frac{7}{8}\\) are\u00a0 (4 X 7) x \\(\\frac{1}{8}\\) , \\(\\frac{28}{8}\\),\\(\\frac{7}{8}\\)+\\(\\frac{7}{8}\\)+\\(\\frac{7}{8}\\)+\\(\\frac{7}{8}\\)<\/p>\n
\nWhich is greater, ![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-39.png\")
? Explain.
\nAnswer:
\n6 X \\(\\frac{6}{2}\\) is greater<\/p>\n
\n6 X \\(\\frac{6}{2}\\)= 6 X 6 X \\(\\frac{1}{2}\\)=36 X \\(\\frac{1}{2}\\)=
\n\\(\\frac{36}{2}\\) and 5 X \\(\\frac{7}{2}\\) =5 X 7 X \\(\\frac{1}{2}\\)=
\n35 X \\(\\frac{1}{2}\\), Now comparing both sides 36 X \\(\\frac{1}{2}\\) and
\n35 X \\(\\frac{1}{2}\\) we see 36 X \\(\\frac{1}{2}\\) > 35 X \\(\\frac{1}{2}\\)
\nso 6 X \\(\\frac{6}{2}\\) is greater.<\/p>\n
\nStructure<\/strong>
\nYour friend fills a \\(\\frac{3}{4}\\) – cup measuring cup with rice 2 times.
\nWrite an equation to show how much rice she uses.<\/p>\n
\nFriend uses \\(\\frac{3}{2}\\) cups.<\/p>\n
\nFriend fills a \\(\\frac{3}{4}\\) – cup with rice 2 times, so she uses 2 X \\(\\frac{3}{4}\\) =
\n2 X 3 x \\(\\frac{1}{4}\\) = 6 X \\(\\frac{1}{4}\\)= \\(\\frac{6}{4}\\)=
\n\\(\\frac{3}{2}\\).<\/p>\n
\nModeling Real Life<\/strong>
\nYou are making a tornado in each of 2 bottles. Each bottle needs to contain \\(\\frac{20}{4}\\) cups of water.
\nYou only have a \\(\\frac{1}{4}\\) – cup measuring cup. How many times do you need to fill the measuring cup?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-39.1.png\")
\nAnswer:
\nTo make a tornado we require 40 cups of water.<\/p>\n
\nEach bottle needs \\(\\frac{20}{4}\\) cups of water and have a \\(\\frac{1}{4}\\) – cup
\nmeasuring cup, Now we take P as number of times for filling so \\(\\frac{20}{4}\\) =
\nP X \\(\\frac{1}{4}\\), 20 X \\(\\frac{1}{4}\\)=P X \\(\\frac{1}{4}\\),
\nEquating both sides we get\u00a0 P = 20,\u00a0 so it is 20 times to fill the measuring cups of water
\nfor one bottle, Given that to make a tornado we require 2 bottles, 2 X 20 cups of water = 40 cups of water.<\/p>\n
\nDIG DEEPER!<\/strong>
\nYou and your friend are each selling 12 coupon books. So far, you have sold \\(\\frac{2}{6}\\)
\nof your books. Your friend has sold 3 times as many as you. What fraction of your friend\u2019s coupon books has she sold?<\/p>\n
\nWe will get the fraction as whole 1 so friend has sold all the 12 coupon books.<\/p>\n
\nSo far i sold \\(\\frac{2}{6}\\) books out of 12 coupon books. Lets us take P number of books,
\ni have sold P out of 12 coupon books, P= 12 X \\(\\frac{2}{6}\\) =12 X 2 X \\(\\frac{1}{6}\\) =
\n24 X \\(\\frac{1}{6}\\) = \\(\\frac{24}{6}\\) =4 , So i have sold 4 coupon books,
\nGiven friend has sold 3 times as many as I, Means 3 X 4 =12 means friend has sold all the coupon books<\/p>\n
\n12 \u00d7 47 = ___
\nAnswer:
\n12 X 47 = 564<\/p>\n
\nWhen 12 is multiplied by 47 we get the product as 564.<\/p>\n
\n35 \u00d7 31 = ___
\nAnswer:
\n35 X 31 =1,085<\/p>\n
\nWhen 35 is multiplied by 31 we get the product as 1,085.<\/p>\n
\n58 \u00d7 49 = ___
\nAnswer:
\n58 X 49 = 2,842<\/p>\n
\nWhen 58 is multiplied by 49 we get the product as 2,842.<\/p>\n<\/a>Lesson 9.3 Multiply Whole Numbers and Fractions<\/h3>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-40.png\")
\nConstruct Arguments<\/strong>
\nExplain how to \ufb01nd the product of a whole number and a fraction without using models.
\nAnswer:
\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-12.bmp\")
![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-12-1.bmp\")
\nExplanation:<\/p>\n
\nThe product of a number and a counting number is a multiple of the number. We can find multiples
\nof unit fractions. To \ufb01nd the product of a whole number and a fraction without using models,
\nFirst we multiply the numerator by the whole number, then rewrite the expression as a multiple
\nof a unit fraction and denominator stays the same we get the product results.<\/p>\n
\nThe denominator stays the same.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-41.png\")
\nAnswer:
\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-13.bmp\")
<\/p>\n
\nTo find 4 X \\(\\frac{2}{3}\\)
\nMethod 1:\u00a0 Multiply the numerator by the whole number as 4 X 2 and divide by 3= \\(\\frac{8}{3}\\)
\nMethod 2 : Then writing the expression as a multiple of unit fraction \\(\\frac{2}{3}\\)=
\n4 X ( 2 X \\(\\frac{1}{3}\\) ) applying associative property of multiplication
\n(4 X 2) X \\(\\frac{1}{3}\\)= 8 X \\(\\frac{1}{3}\\)=\\(\\frac{8}{3}\\)<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-42.png\")
\nAnswer:
\n4 X \\(\\frac{1}{6}\\) = \\(\\frac{4}{6}\\) also equals to \\(\\frac{2}{3}\\)
\nExplanation :
\nAlready the expression is in multiple of unit fraction so 4 X \\(\\frac{1}{6}\\) = \\(\\frac{4}{6}\\) and further simplification it is equal to \\(\\frac{2}{3}\\)<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-43.png\")
\nAnswer:
\n3 X \\(\\frac{2}{4}\\) = 3 X \\(\\frac{1}{2}\\) = \\(\\frac{3}{2}\\).<\/p>\n
\n3 X \\(\\frac{2}{4}\\) can be simplified as 3 X \\(\\frac{1}{2}\\) now the expression is in
\nmultiple of unit fraction so\u00a0 3 X \\(\\frac{1}{2}\\) =\\(\\frac{3}{2}\\).<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-44.png\")
\nAnswer:
\n7 X \u00a0\\(\\frac{3}{2}\\) = 7 x 3 X \u00a0\\(\\frac{1}{2}\\) = 21 X \\(\\frac{1}{2}\\) =
\n\\(\\frac{21}{2}\\).<\/p>\n
\n7 X \\(\\frac{3}{2}\\)\u00a0 first we write the expression as multiple of unit fraction so
\n7 X ( 3 X \\(\\frac{1}{2}\\) ) applying associative property of multiplication
\n( 7 X\u00a0 3) X \\(\\frac{1}{2}\\) ) = 21 X \\(\\frac{1}{2}\\) = \\(\\frac{21}{2}\\)<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-45.png\")
\nAnswer:
\n2 X \\(\\frac{1}{5}\\) = \\(\\frac{2}{5}\\).<\/p>\n
\nAlready the expression 2 X \\(\\frac{1}{5}\\) is a multiple of unit fraction so we multiply
\nthe whole with the numerator and numerator is being same, 2 X \\(\\frac{1}{5}\\) =
\n\\(\\frac{2}{5}\\).<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-46.png\")
\nAnswer:
\n5 X \\(\\frac{3}{10}\\) = \\(\\frac{15}{10}\\)=\\(\\frac{3}{2}\\).<\/p>\n
\n5 X \\(\\frac{3}{10}\\), we write the expression as multiple of unit fraction so
\n5 X 3 X \\(\\frac{1}{10}\\)= 15 X \\(\\frac{1}{10}\\)= \\(\\frac{15}{10}\\)
\nfurther it can be simplified, as both numerator and denominator can be divided by 5 so
\n\\(\\frac{15}{10}\\)=\\(\\frac{3}{2}\\).<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-47.png\")
\nAnswer:
\n6 X \\(\\frac{7}{8}\\)= \\(\\frac{42}{8}\\)= \\(\\frac{21}{4}\\).<\/p>\n
\n6 X\u00a0 \\(\\frac{7}{8}\\), we write the expression as multiple of unit fraction so
\n6 X 7 X \\(\\frac{1}{8}\\) applying associative property of multiplication
\n6 X ( 7 X \\(\\frac{1}{8}\\) )= ( 6 X 7 ) X \\(\\frac{1}{8}\\)= 42 X \\(\\frac{1}{8}\\)=
\n\\(\\frac{42}{8}\\) and further also the fraction can be simplified, as both numerator and denominator
\ncan be divided by 2, making \\(\\frac{42}{8}\\) as \\(\\frac{21}{4}\\).<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-48.png\")
\nAnswer:
\n8 X \\(\\frac{9}{10}\\)= \\(\\frac{72}{10}\\)=\\(\\frac{36}{5}\\).<\/p>\n
\n8 X\u00a0 \\(\\frac{9}{10}\\), we write the expression as multiple of unit fraction
\nso 8 X 9 X \\(\\frac{1}{10}\\) applying associative property of multiplication
\n8 X ( 9 X \\(\\frac{1}{10}\\) )= (8 X 9 ) X \\(\\frac{1}{10}\\)=
\n72 X \\(\\frac{1}{10}\\)= \\(\\frac{72}{10}\\) and further also the fraction can be simplified,
\nas both numerator and denominator can be divided by 2, making \\(\\frac{72}{10}\\) as \\(\\frac{36}{5}\\).<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-49.png\")
\nAnswer:
\n3 X \\(\\frac{60}{100}\\) =\\(\\frac{180}{100}\\) =\\(\\frac{18}{10}\\).<\/p>\n
\n3 X\u00a0 \\(\\frac{60}{100}\\),\u00a0 we write the expression as multiple of unit fraction,
\nSo 3 X 60 X \\(\\frac{1}{100}\\) applying associative property of multiplication
\n3 X (60 X \\(\\frac{1}{100}\\) )= (3 X 60 ) X \\(\\frac{1}{100}\\)= 180 X \\(\\frac{1}{100}\\)=
\n\\(\\frac{180}{100}\\) and further also the fraction can be simplified,
\nas both numerator and denominator can be divided by 10, making \\(\\frac{180}{100}\\)
\nas \\(\\frac{18}{10}\\).<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-50.png\")
\nAnswer:
\n\\(\\frac{4}{2}\\) X 10 = 20.<\/p>\n
\n\\(\\frac{4}{2}\\) X 10 , we write the expression as multiple of unit fraction,
\nSo 4 X \\(\\frac{1}{2}\\) X 10= 40 X \\(\\frac{1}{2}\\)=\\(\\frac{40}{2}\\)
\nas the fraction can be further simplified as both numerator and denominator can be divided by 2, making it as 20.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-51.png\")
\nAnswer:
\n7 X \\(\\frac{2}{4}\\) =\\(\\frac{14}{4}\\) is smaller <\u00a0 5 X \\(\\frac{3}{4}\\)=
\n\\(\\frac{15}{4}\\).<\/p>\n
\n7 X \\(\\frac{2}{4}\\), First we write expression as a multiple of unit fraction
\n7 X 2 X \\(\\frac{1}{4}\\) =14 X \\(\\frac{1}{4}\\) = \\(\\frac{14}{4}\\)
\nNow 5 X \\(\\frac{3}{4}\\) is also written as a multiple of unit fraction 5 X 3 X \\(\\frac{1}{4}\\) =
\n15 X \\(\\frac{1}{4}\\) =\\(\\frac{15}{4}\\) comparing \\(\\frac{14}{4}\\) and
\n\\(\\frac{15}{4}\\) as the denominators are same same 4 and in numerators 15 is great than 14,
\nSo\u00a0 \\(\\frac{14}{4}\\)\u00a0 is less than or smaller or < \\(\\frac{15}{4}\\) ,
\n7 X \\(\\frac{2}{4}\\) is smaller < 5 X \\(\\frac{3}{4}\\)<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-52.png\")
<\/p>\n
\n4 X \\(\\frac{1}{8}\\) is greater than > 4 X \\(\\frac{1}{10}\\).<\/p>\n
\n4 X \\(\\frac{1}{8}\\) already the expression is in multiple of unit fraction,
\nwe write as \\(\\frac{4}{8}\\) and even the expression 4 X \\(\\frac{1}{10}\\)
\nis in multiple of unit fraction we write as \\(\\frac{4}{10}\\) because in order to compare
\nthe fractions we must first turn their different denominators into the same denominators to make
\ndenominators same we multiply 4 X \\(\\frac{1}{8}\\) by 10 \/10 the value will not change =
\n4 X 10 X \\(\\frac{1}{80}\\)=40 X \\(\\frac{1}{80}\\) =\u00a0 \\(\\frac{40}{80}\\)
\nnow other expression 4 X \\(\\frac{1}{10}\\) by 8\/8 so that the value = 4 X 8 X \\(\\frac{1}{80}\\) =
\n32 X \\(\\frac{1}{80}\\) now as denominator are same we can compare only numerators
\n\\(\\frac{40}{80}\\) with \\(\\frac{32}{80}\\) as 40 is greater than 32,
\nSo \u00a0\\(\\frac{4}{8}\\) is greater than > \\(\\frac{4}{10}\\) ,
\n4 X \\(\\frac{1}{8}\\) is greater than > 4 X \\(\\frac{1}{10}\\).<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-53.png\")
\nAnswer:
\n\\(\\frac{4}{3}\\) X 9 = 6 X \\(\\frac{6}{3}\\) both are equal.<\/p>\n
\nFirst we write expressions as a multiple of unit fraction \\(\\frac{4}{3}\\) X 9 =
\n9 X 4 X \\(\\frac{1}{3}\\) =36 X \\(\\frac{1}{3}\\) =\\(\\frac{36}{3}\\)
\nnow other expression\u00a0 6 X \\(\\frac{6}{3}\\) as = 6 X 6 X \\(\\frac{1}{3}\\) =
\n36 X \\(\\frac{1}{3}\\) = \\(\\frac{36}{3}\\) ,
\nAs denominator is same in the both expression we compare numerators and even
\nthe numerators are same in both the expression so given both products are equal .
\nTherefore \\(\\frac{4}{3}\\) X 9 =, is equal to 6 X \\(\\frac{6}{3}\\).<\/p>\n
\nYOU BE THE TEACHER<\/strong>
\nYour friend says the product of 6 and \\(\\frac{5}{8}\\) is \\(\\frac{5}{48}\\). Is your friend correct? Explain.
\nAnswer:
\nNo she is not correct as the product of\u00a0 6 X \\(\\frac{5}{8}\\) \u2260 \\(\\frac{5}{48}\\).<\/p>\n
\nWe write the expression as a product\u00a0 6 and \\(\\frac{5}{8}\\) = 6 X \\(\\frac{5}{8}\\)
\nto \ufb01nd the product of a whole number and a fraction we multiply the numerator by the whole number.
\nThe denominator stays the same. 6 X 5 X\u00a0 \\(\\frac{1}{8}\\) =30 X \\(\\frac{1}{8}\\) =
\n\\(\\frac{30}{8}\\) now comparing with \\(\\frac{5}{48}\\) as denominators are different in order
\nto compare the fractions we must first turn their different denominators into the same<\/em> denominators
\nto make denominators same we multiply \\(\\frac{30}{8}\\) with numerator and denominator
\nas 6= \\(\\frac{30}{8}\\) X \\(\\frac{6}{6}\\) we get \\(\\frac{180}{48}\\),
\nnow comparing with \\(\\frac{5}{48}\\) being denominators same, now numerators 180,5 both are
\nnot same so friend is not correct as the product of\u00a0 6 X \\(\\frac{5}{8}\\) \u2260 \\(\\frac{5}{48}\\).<\/p>\n
\nOpen-Ended<\/strong>
\nThe product of a whole number and a fraction is \\(\\frac{24}{10}\\). What could the two factors be?
\nAnswer:
\nThe product is given as \\(\\frac{24}{10}\\) and the two factors can be (1,24) or (2,12) or (3,8) or (4,6)
\nwith multiple of \\(\\frac{1}{10}\\).<\/p>\n
\nGiven the product of a whole number and a fraction is \\(\\frac{24}{10}\\) to find the two factors,
\nwe first write the product as whole with multiple of unit fraction,\\(\\frac{24}{10}\\),
\nwe write as 24 X \\(\\frac{1}{10}\\), now the whole part is 24 we find the factors for 24,
\ntwo more numbers that multiply to make 24 are 1 x 24 = 2 x 12 = 3 x 8 = 4 x 6 = 24.
\nThis means the factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24 so the two factors can be
\n(1,24) X \\(\\frac{1}{10}\\) or\u00a0 (2,12) X \u00a0\\(\\frac{1}{10}\\) or (3,8) X \\(\\frac{1}{10}\\)
\nor (4,6) X \\(\\frac{1}{10}\\) = 24 X \\(\\frac{1}{10}\\) = \\(\\frac{24}{10}\\).<\/p>\n
\nA short roller-coaster track is \\(\\frac{3}{10}\\) mile long. A longer roller-coaster track is about 4 times as long as the short track. About how long is the longer roller-coaster track?
\nMultiply the shorter roller-coaster track length by 4.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-54.png\")
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-54.1.png\")
\nSo, the longer roller-coaster track is about _\\(\\frac{12}{10}\\) _<\/span> miles long or \\(\\frac{6}{5}\\) miles long
\nAnswer:
\nThe longer roller-coaster track is about \\(\\frac{12}{10}\\) miles long or \\(\\frac{6}{5}\\).<\/p>\n
\nGiven a short roller-coaster track is \\(\\frac{3}{10}\\) mile long and longer roller-coaster
\ntrack is about 4 times as long as the short track to find how long is the longer roller-coaster track
\nwe multiply short roller-coaster track\u00a0 \\(\\frac{3}{10}\\) mile by 4, 4 X \\(\\frac{3}{10}\\)
\nnow we write expression as a multiple of unit fraction so 4 X 3 X \\(\\frac{1}{10}\\) =
\n12 X \\(\\frac{1}{10}\\) =\\(\\frac{12}{10}\\)\u00a0 as numerator and denominator
\ncan be further simplified as both can be divided by 2 making it as \\(\\frac{6}{5}\\).<\/p>\n
\nThe Renaissance Tower in Dallas, Texas is \\(\\frac{27}{100}\\) kilometer tall. The Burj Khalifa is about 3 times as tall as the Renaissance Tower. About how tall is the Burj Khalifa?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-55.png\")
\nAnswer:
\nThe Burj Khalifa is \\(\\frac{81}{100}\\) kilometers tall.<\/p>\n
\nGiven the Renaissance Tower in Dallas, Texas is \\(\\frac{27}{100}\\) kilometer tall and
\nThe Burj Khalifa is about 3 times as tall as the Renaissance Tower, To find how tall is the Burj Khalifa
\nwe multiply the Renaissance Tower in Dallas, Texas length by 3,
\n3 X \\(\\frac{27}{100}\\) we write expression as a multiple of unit fraction
\n3 X 27 X \\(\\frac{1}{100}\\) = 81 X \\(\\frac{1}{100}\\) =\\(\\frac{81}{100}\\),
\nSo the Burj Khalifa is \\(\\frac{81}{100}\\) kilometers tall.<\/p>\n
\nYou water 6 plants using \\(\\frac{3}{5}\\) liter of water for each. How many liters of water do you use?
\nBetween which two whole numbers does your answer lie?
\nAnswer:
\n\\(\\frac{18}{5}\\) liters of water is used, The answer will lie in between 3 and 4.<\/p>\n
\nGiven \\(\\frac{3}{5}\\) liter of water for each is watered, for 6 plants total number of liters of water
\nused is 6 X \\(\\frac{3}{5},now we write as multiple of unit fraction as 6 X 3 X [latex]\\frac{1}{5}\\) =
\n18 X \\(\\frac{1}{5}\\)= \\(\\frac{18}{5}\\) liters of water is used.<\/p>\n
\nDIG DEEPER!<\/strong>
\nYou have 6 cups of strawberries. You want to make 4 strawberry-banana smoothies and 4 strawberry-kiwi smoothies. Each smoothie needs \\(\\frac{2}{3}\\) cup of strawberries. Do you have enough? If not, how many more cups of strawberries do you need?
\nAnswer:
\nYes we have enough cups of strawberries, we dont require more cups of strawberries.<\/p>\n
\nGiven to make each smoothie we need \\(\\frac{2}{3}\\) cup of strawberries
\nfirst to make 4 strawberry-banana smoothies we need 4 X \\(\\frac{2}{3}\\) cup of strawberries
\n= 4 X 2 X \\(\\frac{1}{3}\\)= 8 X \\(\\frac{1}{3}\\) =\\(\\frac{8}{3}\\),
\nNow similarly for making 4 strawberry-kiwi smoothies we need 4 X \\(\\frac{2}{3}\\)
\ncup of strawberries = 4 X 2 X \\(\\frac{1}{3}\\)= 8 X \\(\\frac{1}{3}\\) =
\n\\(\\frac{8}{3}\\),Now total cups of strawberries requried to make smoothie is
\n\\(\\frac{8}{3}\\) + \\(\\frac{8}{3}\\) = 2 X \\(\\frac{8}{3}\\)=
\n2 X 8 X \\(\\frac{1}{3}\\)=16 X \\(\\frac{1}{3}\\)= \\(\\frac{16}{3}\\) totals cups
\nof strawberries required to make smoothies. Now we compare \\(\\frac{16}{3}\\) with 6,
\nTo compare first we make both denominators same so we multiply 6 with \\(\\frac{3}{3}\\)=
\n6 X \\(\\frac{3}{3}\\)= 6 X 3 X \\(\\frac{1}{3}\\)= 18 X \\(\\frac{1}{3}\\)=
\n\\(\\frac{18}{3}\\) as both the denominators are same we compare
\n\\(\\frac{16}{3}\\) and \\(\\frac{18}{3}\\) by seeing numerator
\n16 is less than 18 means we have enough cups of strawberries.<\/p>\n<\/a>Multiply Whole Numbers and Fractions Homework & practice 9.3<\/h3>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-56.png\")
\nAnswer:
\n2 X \\(\\frac{1}{4}\\) = \\(\\frac{2}{4}\\)=\\(\\frac{1}{2}\\)
\nExplanation:
\nAs the given expression is already a unit fraction we multiply it as 2 X \\(\\frac{1}{4} =
\n\\)\\(\\frac{2}{4}\\) and further both numerator and denominator can be divided by 2
\nmaking it as \\(\\frac{1}{2}\\)<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-57.png\")
\nAnswer:
\n3 X \\(\\frac{3}{5}\\)= \\(\\frac{9}{5}\\).<\/p>\n
\n3 X \\(\\frac{3}{5}\\) can be written as multiple of unit fraction as
\n3 X (3 X \\(\\frac{1}{5}\\)) applying associative property of multiplication
\n( 3 X 3 ) X \\(\\frac{1}{5}\\)= 9 X \\(\\frac{1}{5}\\) = \\(\\frac{9}{5}\\).<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-58.png\")
\nAnswer:
\n1 X \\(\\frac{6}{8}\\)= \\(\\frac{6}{8}\\)= \\(\\frac{3}{4}\\).<\/p>\n
\n1 X \\(\\frac{6}{8}\\) can be written as multiple of unit fraction as 1 X ( 6 X\u00a0 \\(\\frac{1}{8}\\))
\napplying associative property of multiplication ( 1 X 6 ) X \\(\\frac{1}{8}\\) = 6 X \\(\\frac{1}{8}\\)=
\n\\(\\frac{6}{8}\\) as numerator and denominator can be further simplified as both can be divided by 2
\nmaking as \\(\\frac{6}{8}\\)= \\(\\frac{3}{4}\\)X \\(\\frac{2}{2}\\)=\\(\\frac{3}{4}\\).<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-59.png\")
\nAnswer:
\n4 X \\(\\frac{10}{12}\\)= \\(\\frac{40}{12}\\)= \\(\\frac{10}{3}\\)<\/p>\n
\n4 X \\(\\frac{10}{12}\\) can be written as multiple of unit fraction as 4 X ( 10 X\u00a0 \\(\\frac{1}{12}\\))
\napplying associative property of multiplication ( 4 X 10 ) X \\(\\frac{1}{12}\\) = 40 X \\(\\frac{1}{12}\\)=
\n\\(\\frac{40}{12}\\) as numerator and denominator can be further simplified as both can be divided by 4
\nas \\(\\frac{40}{12}\\)= \\(\\frac{10}{3}\\) X \\(\\frac{4}{4}\\)=\\(\\frac{10}{3}\\) X 1 =
\n\\(\\frac{10}{3}\\).<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-60.png\")
\nAnswer:
\n7 X \\(\\frac{6}{10}\\) = \\(\\frac{42}{10}\\)= \\(\\frac{21}{5}\\)<\/p>\n
\n7 X \\(\\frac{6}{10}\\) can be written as multiple of unit fraction as 7 X ( 6 X\u00a0 \\(\\frac{1}{10}\\))
\napplying associative property of multiplication ( 7 X 6 ) X \\(\\frac{1}{10}\\) =
\n42 X \\(\\frac{1}{10}\\)= \\(\\frac{42}{10}\\) as numerator and denominator
\ncan be further simplified as both can be divided by 2 as \\(\\frac{42}{10}\\)=
\n\\(\\frac{21}{5}\\) X \\(\\frac{2}{2}\\)=\\(\\frac{21}{5}\\) X 1 = \\(\\frac{21}{5}\\).<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-61.png\")
\nAnswer:
\n\\(\\frac{4}{6}\\) X 5 =\\(\\frac{20}{6}\\) =\\(\\frac{10}{3}\\).<\/p>\n
\n\\(\\frac{4}{6}\\) X 5\u00a0 can be written as multiple of unit fraction as 5 X ( 4 X\u00a0 \\(\\frac{1}{6}\\))
\napplying associative property of multiplication ( 5 X 4 ) X \\(\\frac{1}{6}\\) =
\n20 X \\(\\frac{1}{6}\\)= \\(\\frac{20}{6}\\) as numerator and denominator
\ncan be further simplified as both can be divided by 2 as \\(\\frac{20}{6}\\) =
\n\\(\\frac{10}{3}\\) X \\(\\frac{2}{2}\\)=\\(\\frac{10}{3}\\) X 1 =\\(\\frac{10}{3}\\).<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-62.png\")
\nAnswer:
\n8 X \\(\\frac{5}{2}\\) = \\(\\frac{40}{2}\\) =20.<\/p>\n
\n8 X \\(\\frac{5}{2}\\) can be written as multiple of unit fraction as
\n8 X ( 5 X\u00a0 \\(\\frac{1}{2}\\)) applying associative property of multiplication
\n( 8 X 5 ) X \\(\\frac{1}{2}\\) = 40 X \\(\\frac{1}{2}\\) = \\(\\frac{40}{2}\\)
\nfurther it can be simplified as \\(\\frac{40}{2}\\)=20<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-63.png\")
\nAnswer:
\n\\(\\frac{70}{100}\\) X 6 = \\(\\frac{420}{100}\\) = \\(\\frac{42}{10}\\).<\/p>\n
\n\\(\\frac{70}{100}\\) X 6\u00a0 can be written as multiple of unit fraction as
\n6 X ( 70 X\u00a0 \\(\\frac{1}{100}\\)) applying associative property of multiplication
\n( 6 X 70 ) X \\(\\frac{1}{100}\\) = 420 X \\(\\frac{1}{100}\\)= \\(\\frac{420}{100}\\)
\nas numerator and denominator can be further simplified as both can be divided by 10 as \\(\\frac{420}{100}\\)= \\(\\frac{42}{10}\\) X \\(\\frac{10}{10}\\)=\\(\\frac{42}{10}\\) X 1 =\\(\\frac{42}{10}\\).<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-64.png\")
\nAnswer:
\n10 X \\(\\frac{9}{3}\\)=\\(\\frac{90}{3}\\)=30.<\/p>\n
\n10 X \\(\\frac{9}{3}\\) can be written as multiple of unit fraction as
\n10 X ( 9 X\u00a0 \\(\\frac{1}{3}\\)) applying associative property of multiplication
\n( 10 X 9 ) X \\(\\frac{1}{3}\\) = 90 X \\(\\frac{1}{3}\\)= \\(\\frac{90}{3}\\)
\nfurther it can be simplified\u00a0 because 90 can be divided by 3 without leaving remainder making
\n\\(\\frac{90}{3}\\) as 30.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-65.png\")
\nAnswer:
\n2 X \\(\\frac{4}{2}\\) = 8 X \\(\\frac{1}{2}\\).<\/p>\n
\n2 X \\(\\frac{4}{2}\\) we write as multiple of unit fraction 2 X 4 X \\(\\frac{1}{2}\\) =
\n8 X \\(\\frac{1}{2}\\) = \u00a0\\(\\frac{8}{2}\\) and
\n8 X \\(\\frac{1}{2}\\) is already multiple of unit fraction = latex]\\frac{8}{2}[\/latex]
\nnow we can compare both sides\u00a0 as the denominators are same and numerators are same
\nboth the expressions are equal 2 X \\(\\frac{4}{2}\\) = 8 X \\(\\frac{1}{2}\\).<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-66.png\")
\nAnswer:
\n9 X \\(\\frac{1}{5}\\) > \\(\\frac{9}{12}\\)<\/p>\n
\n9 X \\(\\frac{1}{5}\\) already it is multiple of unit fraction we write it as \\(\\frac{9}{5}\\)
\nand 9 X \\(\\frac{1}{12}\\) is also a multiple of unit fraction we write it as \\(\\frac{9}{12}\\)
\nnow comparing first we make both denominators same so the multiples of 5 are 5,10,15,20,25,30,35,40,45,50,55,60,65
\nand multiples of 12 are 12,24,36,48,60,72 so the least common multiple of both 5 and 12 is 60 ,
\nSo to get denominator 60 we multiply top and bottom by 12 for \\(\\frac{9}{5}\\) =
\n\\(\\frac{9}{5}\\) X \\(\\frac{12}{12}\\)= \\(\\frac{108}{60}\\) ,
\nSo to get denominator 60 we multiply top and bottom by 5 for \\(\\frac{9}{12}\\)=
\n\\(\\frac{9}{12}\\) X \\(\\frac{5}{5}\\)= \\(\\frac{45}{60}\\)
\nNow comparing \\(\\frac{108}{60}\\) with \\(\\frac{45}{60}\\)\u00a0 as both denominator are same,
\nAs we see numerator it is clear that 108 is more than 45 so \\(\\frac{108}{60}\\) > \\(\\frac{45}{60}\\) ,
\n9 X \\(\\frac{1}{5}\\) > \\(\\frac{9}{12}\\).<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-67.png\")
<\/p>\n
\n\\(\\frac{6}{10}\\)X 4 < 9 X \\(\\frac{3}{10}\\).<\/p>\n
\n\\(\\frac{6}{10}\\)X 4 we write as multiple of unit fraction 4 X 6 X \\(\\frac{1}{10}\\)=
\n24 X \\(\\frac{1}{10}\\) =\\(\\frac{24}{10}\\) and 9 X \\(\\frac{3}{10}\\) as
\n9 X 3 X \\(\\frac{1}{10}\\)= 27 X \\(\\frac{1}{10}\\)=\\(\\frac{27}{10}\\),
\nWe can compare both as denominators of both are 10 we compare numerators as 24 with 27
\nas 27 is great,\\(\\frac{24}{10}\\) < \\(\\frac{27}{10}\\),
\n\\(\\frac{6}{10}\\) X 4 < 9 X \\(\\frac{3}{10}\\).<\/p>\n
\nWriting<\/strong>
\nExplain one way to multiply a whole number by a fraction.
\nAnswer:
\nFirst we write fraction as multiple of unit fraction then applying associative property of multiplication
\nwe multiply the whole numbers first then with the unit fraction,later writing product.<\/p>\n
\nLet us take the whole number as 2 and fraction as \\(\\frac{3}{5}\\),Here first we write fraction as
\nmultiple of unit fraction as 2 X 3 X \\(\\frac{1}{5}\\) now applying associative property of multiplication,
\nwe multiply the whole numbers first then with the unit fraction,
\n6 X \\(\\frac{1}{5}\\) as \\(\\frac{6}{5}\\).<\/p>\n
\nNumber Sense<\/strong>
\nBetween which two whole numbers does the product of 10 and \\(\\frac{5}{6}\\) lie ?
\nAnswer:
\nIn between 8 and 9 whole numbers the product of 10 and \\(\\frac{5}{6}\\) lies.<\/p>\n
\n10 X \\(\\frac{5}{6}\\) we first write it as multiple of unit fraction as
\n10 X ( 5 X \\(\\frac{1}{6}\\)) applying associative property of multiplication,
\nWe write (10 X 5) X \\(\\frac{1}{6}\\)= 50 X \\(\\frac{1}{6}\\) = \\(\\frac{50}{6}\\)
\nif we divide \\(\\frac{50}{6}\\))\u00a0 we get 8.333 which is in between 8 and 9 whole numbers.<\/p>\n
\nModeling Real Life<\/strong>
\nA seamstress makes fabric dog collars. An extra small dog collar is \\(\\frac{1}{3}\\) yard long.
\nA large dog collar is 2 times as long as the extra small dog collar. How long is the large dog collar?
\nAnswer:
\nThe large dog collar is \\(\\frac{2}{3}\\) yards long.<\/p>\n
\nGiven the extra small dog collar is \\(\\frac{1}{3}\\) yard long and a large dog collar is
\n2 times as long as the extra small dog collar, so the large dog collar = 2 X \\(\\frac{1}{3}\\)
\nas the fraction is multiple of unit fraction we write as \\(\\frac{2}{3}\\) ,
\ntherefore the large dog collar is \\(\\frac{2}{3}\\) yards long.<\/p>\n
\nDIG DEEPER!<\/strong>
\nNewton has 16 baseball cards. Descartes has \\(\\frac{1}{4}\\) as many cards as Newton, and your friend has \\(\\frac{1}{2}\\) as many cards as Descartes. How many baseball cards do Newton, Descartes, and your friend have in all?
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-68.png\")
<\/p>\n
\nNewton has 16 baseball cards, Descartes has 4 baseball cards and my friend has 2 baseball cards,
\nover all there are total 22 baseball cards.<\/p>\n
\nGiven Newton has 16 baseball cards and Descartes has \\(\\frac{1}{4}\\) as many cards as
\nNewton so\\(\\frac{1}{4}\\) of 16 = 16 X \\(\\frac{1}{4}\\) cards\u00a0 it is already
\nas multiple of unit fraction we can write as \\(\\frac{16}{4}\\) further can be simplified
\nbecause 16 can be divide by 4 so we get as 4 means Descartes has 4 cards.Now my friend has
\n\\(\\frac{1}{2}\\) as many cards as Descartes So Descartes has 4 cards means my friend has
\n\\(\\frac{1}{2}\\) out of 4= 4 X \\(\\frac{1}{2}\\)\u00a0 as it is already a multiple of unit fracrtion,
\nwe take it as \\(\\frac{4}{2}\\) further we can simplify as 4 is divisiblle by 2 we get 2 cards.
\nNewton has 16 baseball cards,Descartes has 4 baseball cards and my friend has 2 baseball cards,
\nover all there are total 22 baseball cards.<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-69.png\")
\nAnswer:
\n= 19.<\/p>\n
\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-14-1.bmp\")
<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-70.png\")
\nAnswer:
\n=81 with 4 as remainder.<\/p>\n
\nStep 1:Start by setting it up with the divisor 7 on the left side and the dividend 571 on the right side,
\n
\nStep 2: The divisor (7) does not\u00a0 goes into the first digit of the dividend (5), So we take second digit also , The divisor (7) goes into the two digits of the dividend (57) by 8 time(s),there fore put 8 on the top
\n8
\n
\nStep 3: Multiply the divisor by the result in the previous step. Therefore, put 8 on top (7 x 9 = 56) and write that answer below the dividend.
\n8
\n
\n56
\nStep 4: Subtract the result in the previous step from the two digits of the dividend (57 -56 = 1) and write the answer below.
\n8
\n
\n\u00a056<\/span>
\n1
\nStep 5: Move down the 3rd digit of the dividend (1)
\n8
\n
\n\u00a056<\/span>
\n11
\nStep 6:The divisor (7) goes into the bottom number (11),\u00a0 time(s). Therefore, put 1 on top:
\n81
\n
\n\u00a0 \u00a0 \u00a056<\/span>
\n11
\nStep 7 : Multiply the divisor by the result in the previous step (7 x 1 = 7) and write that answer at the bottom:
\n81
\n
\n\u00a0 \u00a0 \u00a056<\/span>
\n11
\n07
\nStep 8 : Subtract the result in the previous step from the number written above it. (11 – 7 = 04) and write the answer at the bottom
\n81
\n
\n\u00a056<\/span>
\n11
\n \u00a0 \u00a0 07<\/span>
\n4
\nWe stop here as 4 is less than 7 and further we get in decimals , So =81 with 4 as remainder
\nQuestion 19.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-71.png\")
\nAnswer:
\n= 184 with 3 as remainder.<\/p>\n
\nStep 1:Start by setting it up with the divisor 5 on the left side and the dividend 923 on the right side,
\n
\nStep 2: The divisor (5)\u00a0 \u00a0goes into the first digit of the dividend (9)\u00a0 by 8 time there fore put 1 on the top
\n1
\n
\nStep 3: Multiply the divisor by the result in the previous step\u00a0 (5 x 1 = 5) and write that answer below the dividend.
\n1
\n
\n5
\nStep 4: Subtract the result in the previous step from the first digit of the dividend (9 -5 = 4) and write the answer below.
\n1
\n
\n \u00a0 \u00a05
\n<\/span>\u00a0 \u00a0 4
\nStep 5: Move down the 2nd digit of the dividend (2),like below
\n1
\n
\n \u00a0 \u00a05
\n<\/span>\u00a0 \u00a0 \u00a042
\nStep 6:The divisor (5) goes into the bottom number (40),\u00a0 8 time(s). Therefore, put 8 on top:
\n18
\n
\n \u00a0 \u00a05
\n<\/span>\u00a0 \u00a0 \u00a042
\nStep 7 : Multiply the divisor by the result in the previous step (5 x 8 = 40) and write that answer at the bottom:
\n18
\n
\n \u00a0 \u00a05
\n<\/span>\u00a0 \u00a0 \u00a042
\n40
\nStep 8: Subtract the result in the previous step from the number written above it. (42 – 40 = 04) and write the answer at the bottom
\n18
\n
\n \u00a0 \u00a05
\n<\/span>\u00a0 \u00a0 \u00a042
\n\u00a0 \u00a0 \u00a040\u00a0 \u00a0<\/span>
\n2
\nStep 9 :Move down the 3nd digit of the dividend (3),like below
\n18
\n
\n \u00a0 \u00a05
\n<\/span>\u00a0 \u00a0 \u00a042
\n\u00a0 \u00a0 \u00a040\u00a0 \u00a0<\/span>
\n23
\nStep 10 : The divisor (5) goes into the bottom number (20),\u00a0 4 time(s). Therefore, put 4 on top:
\n184
\n
\n\u00a0 \u00a0 \u00a05
\n<\/span>\u00a0 \u00a0 \u00a042
\n\u00a0 \u00a0 \u00a040\u00a0 \u00a0<\/span>
\n23
\n20
\nStep 11 : Subtract the result in the previous step from the number written above it. (23 – 20 = 03) and write the answer at the bottom
\n184
\n
\n\u00a0 \u00a0 \u00a05
\n<\/span>\u00a0 \u00a0 \u00a042
\n\u00a0 \u00a0 \u00a040\u00a0 \u00a0<\/span>
\n23
\n \u00a0 \u00a0 \u00a020
\n<\/span>\u00a0 \u00a0 \u00a0 \u00a003
\nWe stop here as 3 is less than 5 and further we get in decimals , So = 184 with 3 as remainder.<\/p>\n<\/a>Lesson 9.4 Multiply Whole Numbers and Mixed Numbers<\/h3>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-72.png\")
<\/p>\n
\nHow does the Distributive Property relate to your models? Explain.<\/p>\n
\n![\"\"](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/9-Multiply-Whole-Numbers-and-Fractions-15-3.bmp\")
<\/p>\n
\nAccording to the distributive property, multiplying the sum of two or more addends by a number
\nwill give the same result as multiplying each addend individually by the number and then adding the products together.
\nWe use distribute property while relating the models first we draw each multiplying addend individually and
\nthen add the products together to give the result.
\nExample : 2 X 1 \\(\\frac{3}{8}\\) using the distributive property we write
\n2 X 1 \\(\\frac{3}{8}\\) as 2 X ( 1 + \\(\\frac{3}{8}\\) )here first we draw model of
\n2 X 1 then we draw model of 2 X \\(\\frac{3}{8}\\) then we add the products together as
\n2 + \\(\\frac{6}{8}\\)= 2 + \\(\\frac{3}{4}\\)=\\(\\frac{11}{4}\\).
\nThink and Grow: Multiply Whole Numbers and Mixed Numbers<\/strong><\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-73.png\")
\nOne Way:<\/strong> Write the mixed number as a fraction, then multiply.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-74.png\")
\nAnother Way:<\/strong> Use the Distributive Property.
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-75.png\")
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-76.png\")
\nAnswer:
\n3 X 1 \\(\\frac{1}{2}\\) = \\(\\frac{9}{2}\\)
\nExplanation:
\nFirst we write the mixed number as a fraction then multiply, so 1 \\(\\frac{1}{2}\\) =
\n1+ \\(\\frac{1}{2}\\) = 2 x 1+1 by 2=\u00a0 \\(\\frac{3}{2}\\) now we multiply it with the whole ,
\n3 X \\(\\frac{3}{2}\\) now we write in unit fraction and multiply\u00a0 3 X 3 X \\(\\frac{1}{2}\\)=
\n9 X\u00a0 \\(\\frac{1}{2}\\)= \\(\\frac{9}{2}\\).<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-77.png\")
\nAnswer:
\n = \\(\\frac{27}{4}\\)=6 \\(\\frac{3}{4}\\)
\nExplanation:
\nFirst we write the mixed number as a fraction then multiply, so 2 \\(\\frac{1}{4}\\) =
\n2 + \\(\\frac{1}{4}\\)=(2 X 4 + 1) by 4 = \\(\\frac{9}{4}\\) now we multiply it with the whole,
\n3 X \\(\\frac{9}{4}\\) now we write in unit fraction and multiply\u00a0 3 X 9 X \\(\\frac{1}{4}\\) =
\n27 X \\(\\frac{1}{4}\\) = \\(\\frac{27}{4}\\), we can write the product as mixed fraction as
\n4<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00a0goes in\u00a06<\/span><\/span><\/span><\/span><\/span><\/span><\/span> times. 6 will be our whole number 4 X <\/span><\/span>6<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00a0is\u00a024<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00a0and we have\u00a03<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00a0left over (27<\/span><\/span>\u2212<\/span><\/span>24<\/span><\/span><\/span><\/span><\/span><\/span><\/span>),
\n3 will be our numerator and our denominator will stay the same 4= \\(\\frac{27}{4}\\)=
\n6 \\(\\frac{3}{4}\\).<\/p>\n
\n![\"Big](\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-9-Multiply-Whole-Numbers-and-Fractions-78.png\")
\nAnswer:
\n \\(\\frac{38}{12}\\)= 3 \\(\\frac{2}{12}\\).<\/p>\n
\nFirst we write the mixed number as a fraction then multiply, so 1 \\(\\frac{7}{12}\\)=
\n1 + \\(\\frac{7}{12}\\)= (1 X 12 + 7 ) by 12 = \\(\\frac{19}{12}\\)
\nnow we multiply it with the whole, 2 X \\(\\frac{19}{12}\\) now we write in unit fraction and
\nmultiply\u00a0 2 X 19 X \\(\\frac{1}{12}\\)= 38 X \\(\\frac{1}{12}\\) = \\(\\frac{38}{12}\\),
\nwe can write the product as mixed fraction as 12 goes in 3 times. 3 will be our whole number 12