Multiplying numbers is so easy compared to Multiplying Fractions. The fraction is represented as the division of the whole. The fraction is in the form of \u201cx\/y\u201d where \u201cx\u201d is the numerator and \u201cy\u201d is the denominator. One can apply the fraction concept to real-time examples easily after reading the entire concept here. If you have an apple and you made it into 4 equal parts, then it can represent as \\(\\frac { 1 }{ 4 } \\). Or else if it cut into 7 pieces then it can represented as \\(\\frac { 1 }{ 7 } \\).<\/p>\n
We have provided simple steps to multiply fractions and find the solution of multiplying fractions. It is easy to find out the solution using the below procedure. Multiplying fractions can be defined as the product of a fraction with another fraction or with the variables or with an integer. Follow the below process to multiply fractions<\/p>\n
Example:
\n1. Multiply \\(\\frac { 2 }{ 3 } \\) \u00d7 \\(\\frac { 1 }{ 5 } \\)<\/p>\n
Solution:
\nGiven that \\(\\frac { 2 }{ 3 } \\) \u00d7 \\(\\frac { 1 }{ 5 } \\)
\nTo multiply the above fractions, firstly multiply the numerators
\n2 \u00d7 1 = 2
\nmultiply the denominators
\n3 \u00d7 5 = 15
\nNow, simplify the fraction, we get \\(\\frac { 2 }{ 15 } \\)
\nIf \\(\\frac { x }{ y } \\) and \\(\\frac { m }{ n } \\) are the multiplicand and multiplier, then the output is \\(\\frac { xm }{ yn } \\)
\nProduct of Fraction = Product of Numerator\/Product of Denominator<\/p>\n
A fraction consists of two parts. One is the numerator and another one is the denominator. If \\(\\frac { a }{ b } \\) is a fraction, then the two parts are a and b where a is the numerator and b is the denominator. Or else if \\(\\frac { 3 }{ 4 } \\) is a fraction, then the two parts are 3 and 4 where 3 is the numerator and 4 is the denominator.<\/p>\n
Mainly, there are three types of fractions considered. They are proper fractions, improper fractions, and mixed fractions.
\nProper fractions: A fraction is said to be a proper fraction when the numerator of a fraction is less than the denominator.
\nExamples: \\(\\frac { 1 }{ 4 } \\), \\(\\frac { 5 }{ 6 } \\), \\(\\frac { 7 }{ 11 } \\)
\nImproper fractions: A fraction is said to be an improper fraction when the numerator is greater than the denominator.
\nExamples: \\(\\frac { 5 }{ 4 } \\), \\(\\frac { 7 }{ 6 } \\), \\(\\frac { 13 }{ 11 } \\)
\nMixed Fraction: A fraction is said to be a mixed fraction when we write the improper fraction in the combination of a whole number and a fraction.
\nExamples: 1 \\(\\frac { 5 }{ 4 } \\), 3 \\(\\frac { 9 }{ 6 } \\), 2 \\(\\frac { 6 }{ 7 } \\)<\/p>\n
Also, Read:<\/p>\n
Generally, the multiplication of fractions can be finished by multiplying numerators with numerators and multiplying denominators with denominators. To make the fractional multiplication simpler, we can reduce the fraction by canceling the common factors. By canceling out the common factors from the given factor, it becomes easier to find the exact output.<\/p>\n
Example: \\(\\frac { 9 }{ 4 } \\) and \\(\\frac { 2 }{ 3 } \\)
\n\\(\\frac { 9 }{ 4 } \\) can written as \\(\\frac { 3 \u00d7 3 }{ 2\u00d72 } \\)
\n\\(\\frac { 3 \u00d7 3 }{ 2\u00d72 } \\) \u00d7 \\(\\frac { 2 }{ 3 } \\) = \\(\\frac { 3 }{ 2 } \\)
\nIf there is no common factors, then the numerators and denominators are multiplied directly.<\/p>\n
There are different types of Fraction Multiplication available. They are<\/p>\n
In Multiplication of Fractional Number by a Whole Number, we multiply the numerator with the numerator and the denominator remains the same. Before you multiply, reduce the fraction to the lowest terms. Check out different problems on the Multiplication of Fractional Number by a Whole Number below.<\/p>\n
1. Multiply 2 \\(\\frac { 2 }{ 3 } \\) by 9<\/p>\n
Solution:
\nGiven that multiply 2 \\(\\frac { 2 }{ 3 } \\) by 9.
\nFirstly, convert given mixed fraction 2 \\(\\frac { 2 }{ 3 } \\) to fraction.
\n2 \\(\\frac { 2 }{ 3 } \\) = \\(\\frac { 8 }{ 3 } \\)
\nNow, multiply \\(\\frac { 8 }{ 3 } \\) by 9.
\nMultiply the numerator of the fractional number by the whole number. The denominator remains the same.
\n8 \u00d7 9 = 72.
\nSo, the fraction is \\(\\frac { 72 }{ 3 } \\)
\nSimplify the fraction to get the final answer.
\n\\(\\frac { 72 }{ 3 } \\) = 24.<\/p>\n
The final answer is 24.<\/p>\n
(ii) Multiply \\(\\frac { 3 }{ 4 } \\) by 6<\/p>\n
Solution:
\nGiven that multiply \\(\\frac { 3 }{ 4 } \\) by 6
\nmultiply \\(\\frac { 3 }{ 4 } \\) by 6.
\nMultiply the numerator of the fractional number by the whole number. The denominator remains the same.
\n3 \u00d7 6 = 18.
\nSo, the fraction is \\(\\frac { 18 }{ 4 } \\)
\nSimplify the fraction to get the final answer.
\n\\(\\frac { 18 }{ 4 } \\) = \\(\\frac { 9 }{ 2 } \\).<\/p>\n
The final answer is \\(\\frac { 9 }{ 2 } \\).<\/p>\n
(iii) Multiply 3 \\(\\frac { 3 }{ 2 } \\) by 6<\/p>\n
Solution:
\nGiven that multiply 3 \\(\\frac { 3 }{ 2 } \\)\u00a0by 6.
\nFirstly, convert given mixed fraction 3 \\(\\frac { 3 }{ 2 } \\)\u00a0to fraction.
\n3 \\(\\frac { 3 }{ 2 } \\) = \\(\\frac { 9 }{ 2 } \\)
\nNow, multiply \\(\\frac { 9 }{ 2 } \\) by 6.
\nMultiply the numerator of the fractional number by the whole number. The denominator remains the same.
\n9 \u00d7 6 = 54.
\nSo, the fraction is \\(\\frac { 54 }{ 2 } \\)
\nSimplify the fraction to get the final answer.
\n\\(\\frac { 54 }{ 2 } \\) = 27.<\/p>\n
The final answer is 27.<\/p>\n
Multiplying Fraction with Another Fraction is explained with the below examples.<\/p>\n
(i). Multiply \\(\\frac { 3 }{ 5 } \\) by \\(\\frac { 6 }{ 5 } \\)<\/p>\n
Solution:
\nGiven that Multiply \\(\\frac { 3 }{ 5 } \\) by \\(\\frac { 6 }{ 5 } \\).
\nFirstly, multiply the numerators with numerators.
\n3 \u00d7 6 = 18.
\nNext, multiply the denominators with denominators.
\n5 \u00d7 5 = 25.
\nFinally, write the fraction in the simplest form.
\n\\(\\frac { 18 }{ 25 } \\)<\/p>\n
The final answer is \\(\\frac { 18 }{ 25 } \\)<\/p>\n
(ii) Multiply \\(\\frac { 3 }{ 4 } \\) by \\(\\frac { 7 }{ 2 } \\)<\/p>\n
Solution:
\nGiven that Multiply \\(\\frac { 3 }{ 4 } \\) by \\(\\frac { 7 }{ 2 } \\).
\nFirstly, multiply the numerators with numerators.
\n3 \u00d7 7 = 21.
\nNext, multiply the denominators with denominators.
\n4 \u00d7 2 = 8.
\nFinally, write the fraction in the simplest form.
\n\\(\\frac { 21 }{ 8 } \\)<\/p>\n
The final answer is \\(\\frac { 21 }{ 8 } \\).<\/p>\n
(iii) Multiply \\(\\frac { 2 }{ 3 } \\), \\(\\frac { 2 }{ 5 } \\), and \\(\\frac { 2 }{ 7 } \\)<\/p>\n
Solution:
\nGiven that Multiply \\(\\frac { 2 }{ 3 } \\), \\(\\frac { 2 }{ 5 } \\), and \\(\\frac { 2 }{ 7 } \\).
\nFirstly, multiply the numerators with numerators.
\n2 \u00d7 2 \u00d7 2 = 8.
\nNext, multiply the denominators with denominators.
\n3 \u00d7 5 \u00d7 7 = 105.
\nFinally, write the fraction in the simplest form.
\n\\(\\frac { 8 }{ 105 } \\)<\/p>\n
The final answer is \\(\\frac { 8 }{ 105 } \\).<\/p>\n
To find the multiplication of a mixed number with another mixed number, we need to change the mixed fractions to fractions and multiply them.<\/p>\n
(i) Multiply 3 \\(\\frac { 2 }{ 5 } \\) and 2 \\(\\frac { 3 }{ 7 } \\)<\/p>\n
Solution:
\nGiven that multiply 3 \\(\\frac { 2 }{ 5 } \\) and 2 \\(\\frac { 3 }{ 7 } \\).
\nFirstly, convert given mixed fractions 3 \\(\\frac { 2 }{ 5 } \\) and 2 \\(\\frac { 3 }{ 7 } \\) to fractions.
\n3 \\(\\frac { 2 }{ 5 } \\) = \\(\\frac { 17 }{ 5 } \\)
\n2 \\(\\frac { 3 }{ 7 } \\) = \\(\\frac { 17 }{ 7 } \\)
\nNow, multiply \\(\\frac { 17 }{ 5 } \\) by \\(\\frac { 17 }{ 7 } \\).
\nFirstly, multiply the numerators with numerators.
\n17 \u00d7 17 = 289.
\nNext, multiply the denominators with denominators.
\n5 \u00d7 7 = 35.
\nFinally, write the fraction in the simplest form.
\n\\(\\frac { 289 }{ 35 } \\)<\/p>\n
The final answer is \\(\\frac { 289 }{ 35 } \\).<\/p>\n
(ii) Multiply 2 \\(\\frac { 4 }{ 3 } \\) and 1 \\(\\frac { 6 }{ 5 } \\)<\/p>\n
Solution:
\nGiven that multiply 2 \\(\\frac { 4 }{ 3 } \\) and 1 \\(\\frac { 6 }{ 5 } \\).
\nFirstly, convert given mixed fractions 2 \\(\\frac { 4 }{ 3 } \\) and 1 \\(\\frac { 6 }{ 5 } \\) to fractions.
\n2 \\(\\frac { 4 }{ 3 } \\) = \\(\\frac { 10 }{ 3 } \\)
\n1 \\(\\frac { 6 }{ 5 } \\) = \\(\\frac { 11 }{ 5 } \\)
\nNow, multiply \\(\\frac { 10 }{ 3 } \\) by \\(\\frac { 11 }{ 5 } \\).
\nFirstly, multiply the numerators with numerators.
\n10 \u00d7 11 = 110.
\nNext, multiply the denominators with denominators.
\n5 \u00d7 3 = 15.
\nFinally, write the fraction in the simplest form.
\n\\(\\frac { 110 }{ 15 } \\) = \\(\\frac { 22 }{ 3 } \\)<\/p>\n
The final answer is \\(\\frac { 22 }{ 3 } \\).<\/p>\n
(i) Multiply 4 \\(\\frac { 2 }{ 9 } \\) and 5 \\(\\frac { 1 }{ 4 } \\)<\/p>\n
Solution:
\nGiven that multiply 4 \\(\\frac { 2 }{ 9 } \\) and 5 \\(\\frac { 1 }{ 4 } \\).
\nFirstly, convert given mixed fractions 4 \\(\\frac { 2 }{ 9 } \\) and 5 \\(\\frac { 1 }{ 4 } \\) to fractions.
\n4 \\(\\frac { 2 }{ 9 } \\) = \\(\\frac { 38 }{ 9 } \\)
\n5 \\(\\frac { 1 }{ 4 } \\) = \\(\\frac { 21 }{ 4 } \\)
\nNow, multiply\\(\\frac { 38 }{ 9 } \\) by \\(\\frac { 21 }{ 4 } \\).
\nFirstly, multiply the numerators with numerators.
\n38 \u00d7 21 = 798.
\nNext, multiply the denominators with denominators.
\n9 \u00d7 4 = 36.
\nFinally, write the fraction in the simplest form.
\n\\(\\frac { 798 }{ 36 } \\)<\/p>\n
The final answer is \\(\\frac { 798 }{ 36 } \\).<\/p>\n
I. Find the product
\n(i) \\(\\frac { 5 }{ 4 } \\) \u00d7 1
\n(ii) \\(\\frac { 3 }{ 5 } \\) \u00d7 6
\n(iii) \\(\\frac { 10 }{ 15 } \\) \u00d7 7
\n(iv) \\(\\frac { 2 }{ 3 } \\) \u00d7 0
\n(v) \\(\\frac { 1 }{ 4 } \\) \u00d7 \\(\\frac { 2 }{ 7 } \\)
\n(vi) 2\\(\\frac { 9 }{ 13 } \\) \u00d7 4
\n(vii) \\(\\frac { 1 }{ 6 } \\) \u00d7 \\(\\frac { 7 }{ 1 } \\)
\n(viii) \\(\\frac { 1 }{ 4 } \\) \u00d7 \\(\\frac { 8 }{ 6 } \\) \u00d7 \\(\\frac { 3 }{ 10 } \\)
\n(ix) \\(\\frac { 5 }{ 16 } \\) \u00d7 \\(\\frac { 11 }{ 23 } \\)
\n(x) \\(\\frac { 1 }{ 2 } \\) of 50
\n(xi) \\(\\frac { 1 }{ 3 } \\) of 90
\n(xii) \\(\\frac { 5 }{ 6 } \\) of \\(\\frac { 9 }{ 12 } \\)<\/p>\n
(i) \\(\\frac { 5 }{ 4 } \\) \u00d7 1
\nSolution:
\nGiven that \\(\\frac { 5 }{ 4 } \\) \u00d7 1
\nNow, multiply \\(\\frac { 5 }{ 4 } \\) by 1.
\nMultiply the numerator of the fractional number by the whole number. The denominator remains the same.
\n5 \u00d7 1 = 5.
\nSo, the fraction is \\(\\frac { 5 }{ 4 } \\)<\/p>\n
The final answer is \\(\\frac { 5 }{ 4 } \\).<\/p>\n
(ii) \\(\\frac { 3 }{ 5 } \\) \u00d7 6
\nSolution:
\nGiven that \\(\\frac { 3 }{ 5 } \\) \u00d7 6
\nmultiply \\(\\frac { 3 }{ 5 } \\) by 6
\nMultiply the numerator of the fractional number by the whole number. The denominator remains the same.
\n3 \u00d7 6 = 18.
\nSo, the fraction is \\(\\frac { 18 }{ 5 } \\)
\nSimplify the fraction to get the final answer.
\n\\(\\frac { 18 }{ 5 } \\).<\/p>\n
The final answer is \\(\\frac { 18 }{ 5 } \\).<\/p>\n
(iii) \\(\\frac { 10 }{ 15 } \\) \u00d7 7
\nSolution:
\nGiven that \\(\\frac { 10 }{ 15 } \\) \u00d7 7
\nmultiply \\(\\frac { 10 }{ 15 } \\) by 7
\nMultiply the numerator of the fractional number by the whole number. The denominator remains the same.
\n10 \u00d7 7 = 70.
\nSo, the fraction is \\(\\frac { 70 }{ 15 } \\)
\nSimplify the fraction to get the final answer.
\n\\(\\frac { 70 }{ 15 } \\) = \\(\\frac { 14 }{ 3 } \\).<\/p>\n
The final answer is \\(\\frac { 14 }{ 3 } \\).<\/p>\n
(iv) \\(\\frac { 2 }{ 3 } \\) \u00d7 0
\nSolution:
\nAny fraction that multiplies with 0 gives 0.
\nTherefore, the answer is 0.<\/p>\n
(v) \\(\\frac { 1 }{ 4 } \\) \u00d7 \\(\\frac { 2 }{ 7 } \\)
\nSolution:
\nGiven that Multiply \\(\\frac { 1 }{ 4 } \\) by \\(\\frac { 2 }{ 7 } \\).
\nFirstly, multiply the numerators with numerators.
\n1 \u00d7 2 = 2.
\nNext, multiply the denominators with denominators.
\n4 \u00d7 7 = 28.
\nFinally, write the fraction in the simplest form.
\n\\(\\frac { 2 }{ 28 } \\)
\nSimplify the fraction to get the final answer.
\n\\(\\frac { 1 }{ 14 } \\).<\/p>\n
The final answer is \\(\\frac { 1 }{ 14 } \\).<\/p>\n
(vi) 2\\(\\frac { 9 }{ 13 } \\) \u00d7 4
\nSolution:
\nGiven that multiply 2\\(\\frac { 9 }{ 13 } \\) \u00d7 4.
\nFirstly, convert given mixed fraction 2\\(\\frac { 9 }{ 13 } \\) to fraction.
\n2\\(\\frac { 9 }{ 13 } \\) = \\(\\frac { 35 }{ 13 } \\)
\nNow, multiply \\(\\frac { 35 }{ 13 } \\) by 4.
\nMultiply the numerator of the fractional number by the whole number. The denominator remains the same.
\n35 \u00d7 4 = 140.
\nSo, the fraction is \\(\\frac { 140 }{ 13 } \\)
\nSimplify the fraction to get the final answer.
\n\\(\\frac { 140 }{ 13 } \\).<\/p>\n
The final answer is \\(\\frac { 140 }{ 13 } \\).<\/p>\n
(vii) \\(\\frac { 1 }{ 6 } \\) \u00d7 \\(\\frac { 7 }{ 1 } \\)
\nSolution:
\nGiven that Multiply \\(\\frac { 1 }{ 6 } \\) \u00d7 \\(\\frac { 7 }{ 1 } \\).
\nFirstly, multiply the numerators with numerators.
\n1 \u00d7 7 = 7.
\nNext, multiply the denominators with denominators.
\n6 \u00d7 1 = 6.
\nFinally, write the fraction in the simplest form.
\n\\(\\frac { 7 }{ 6 } \\)
\nSimplify the fraction to get the final answer.
\n\\(\\frac { 7 }{ 6 } \\).<\/p>\n
The final answer is \\(\\frac { 7 }{ 6 } \\).<\/p>\n
(viii) \\(\\frac { 1 }{ 4 } \\) \u00d7 \\(\\frac { 8 }{ 6 } \\) \u00d7 \\(\\frac { 3 }{ 10 } \\)
\nSolution:
\nGiven that Multiply \\(\\frac { 1 }{ 4 } \\) \u00d7 \\(\\frac { 8 }{ 6 } \\) \u00d7 \\(\\frac { 3 }{ 10 } \\).
\nFirstly, multiply the numerators with numerators.
\n1 \u00d7 8 \u00d7 3 = 24.
\nNext, multiply the denominators with denominators.
\n4 \u00d7 6 \u00d7 10 = 240.
\nFinally, write the fraction in the simplest form.
\n\\(\\frac { 24 }{ 240 } \\)
\nSimplify the fraction to get the final answer.
\n\\(\\frac { 1 }{ 10 } \\).<\/p>\n
The final answer is \\(\\frac { 1 }{ 10 } \\).<\/p>\n
(ix) \\(\\frac { 5 }{ 16 } \\) \u00d7 \\(\\frac { 11 }{ 23 } \\)
\nSolution:
\nGiven that Multiply \\(\\frac { 5 }{ 16 } \\) \u00d7 \\(\\frac { 11 }{ 23 } \\).
\nFirstly, multiply the numerators with numerators.
\n5 \u00d7 11 = 55.
\nNext, multiply the denominators with denominators.
\n16 \u00d7 23 = 368.
\nFinally, write the fraction in the simplest form.
\n\\(\\frac { 55 }{ 368 } \\)
\nSimplify the fraction to get the final answer.
\n\\(\\frac { 55 }{ 368 } \\).<\/p>\n
The final answer is \\(\\frac { 55 }{ 368 } \\).<\/p>\n
(x) \\(\\frac { 1 }{ 2 } \\) of 50
\nSolution:
\nGiven that \\(\\frac { 1 }{ 2 } \\) of 50
\nmultiply \\(\\frac { 1 }{ 2 } \\) by 50
\nMultiply the numerator of the fractional number by the whole number. The denominator remains the same.
\n1 \u00d7 50 = 50.
\nSo, the fraction is \\(\\frac { 50 }{ 2 } \\)
\nSimplify the fraction to get the final answer.
\n\\(\\frac { 50 }{ 2 } \\) = 25.<\/p>\n
The final answer is 25.<\/p>\n
(xi) \\(\\frac { 1 }{ 3 } \\) of 90<\/p>\n
Solution:
\nGiven that \\(\\frac { 1 }{ 3 } \\) of 90
\nmultiply \\(\\frac { 1 }{ 3 } \\) by 90
\nMultiply the numerator of the fractional number by the whole number. The denominator remains the same.
\n1 \u00d7 90 = 90.
\nSo, the fraction is \\(\\frac { 90 }{ 3 } \\)
\nSimplify the fraction to get the final answer.
\n\\(\\frac { 90 }{ 3 } \\) = 30.<\/p>\n
The final answer is 30.<\/p>\n
II. Multiply and write the product in the lowest terms.<\/p>\n
(i) \\(\\frac { 1 }{ 2 } \\) \u00d7 60
\n(ii) \\(\\frac { 1 }{ 3 } \\) \u00d7 18
\n(iii) \\(\\frac { 2 }{ 5 } \\) \u00d7 25
\n(iv) \\(\\frac { 4 }{ 3 } \\) \u00d7 0
\n(v) \\(\\frac { 7 }{ 29 } \\) \u00d7 1
\n(vi) 6 \u00d7 \\(\\frac { 7 }{ 36 } \\)
\n(vii) \\(\\frac { 5 }{ 34 } \\) \u00d7 \\(\\frac { 34 }{ 8 } \\)
\n(viii) \\(\\frac { 12 }{ 25 } \\) \u00d7 \\(\\frac { 5 }{ 6 } \\)
\n(ix) \\(\\frac { 6 }{ 14 } \\) \u00d7 \\(\\frac { 56 }{ 7 } \\)
\n(x) \\(\\frac { 1 }{ 3 } \\) \u00d7 \\(\\frac { 4 }{ 5 } \\) \u00d7 \\(\\frac { 5 }{ 8 } \\)
\n(xi) \\(\\frac { 6 }{ 3 } \\) \u00d7 \\(\\frac { 1 }{ 2 } \\) \u00d7 \\(\\frac { 3 }{ 3 } \\)
\n(xii) 3\\(\\frac { 8 }{ 5 } \\) \u00d7 \\(\\frac { 5 }{ 4 } \\)<\/p>\n
(i) \\(\\frac { 1 }{ 2 } \\) \u00d7 60
\nSolution:
\nGiven that \\(\\frac { 1 }{ 2 } \\) \u00d7 60
\nNow, multiply \\(\\frac { 1 }{ 2 } \\) by 60.
\nMultiply the numerator of the fractional number by the whole number. The denominator remains the same.
\n1 \u00d7 60 = 60.
\nSo, the fraction is \\(\\frac { 60 }{ 2 } \\)
\nSimplify the fraction to get the final answer.
\n\\(\\frac { 60 }{ 2 } \\) = 30.<\/p>\n
The final answer is 30.<\/p>\n
(ii) \\(\\frac { 1 }{ 3 } \\) \u00d7 18
\nSolution:
\nGiven that \\(\\frac { 1 }{ 3 } \\) \u00d7 18
\nNow, multiply \\(\\frac { 1 }{ 3 } \\) by 18.
\nMultiply the numerator of the fractional number by the whole number. The denominator remains the same.
\n1 \u00d7 18 = 18.
\nSo, the fraction is \\(\\frac { 18 }{ 3 } \\)
\nSimplify the fraction to get the final answer.
\n\\(\\frac { 18 }{ 3 } \\) = 6.<\/p>\n
The final answer is 6.<\/p>\n
(iii) \\(\\frac { 2 }{ 5 } \\) \u00d7 25
\nSolution:
\nGiven that \\(\\frac { 2 }{ 5 } \\) \u00d7 25
\nNow, multiply \\(\\frac { 2 }{ 5 } \\) by 25.
\nMultiply the numerator of the fractional number by the whole number. The denominator remains the same.
\n2 \u00d7 25 = 50.
\nSo, the fraction is \\(\\frac { 50 }{ 5 } \\)
\nSimplify the fraction to get the final answer.
\n\\(\\frac { 50 }{ 5 } \\) = 10.<\/p>\n
The final answer is 10.<\/p>\n
(iv) \\(\\frac { 4 }{ 3 } \\) \u00d7 0
\nSolution:
\nAny fraction that multiplies with 0 gives 0.
\nTherefore, the answer is 0.<\/p>\n
(v) \\(\\frac { 7 }{ 29 } \\) \u00d7 1
\nSolution:
\nAny fraction that multiplies with 1 gives the same output.
\nTherefore, the answer is \\(\\frac { 7 }{ 29 } \\).<\/p>\n
(vi) 6 \u00d7 \\(\\frac { 7 }{ 36 } \\)
\nSolution:
\nGiven that 6 \u00d7 \\(\\frac { 7 }{ 36 } \\)
\nNow, multiply 6 by \\(\\frac { 7 }{ 36 } \\).
\nMultiply the numerator of the fractional number by the whole number. The denominator remains the same.
\n6 \u00d7 7 = 42.
\nSo, the fraction is \\(\\frac { 42 }{ 36 } \\)
\nSimplify the fraction to get the final answer.
\n\\(\\frac { 42 }{ 36 } \\) = \\(\\frac { 21 }{ 18 } \\).<\/p>\n
The final answer is \\(\\frac { 21 }{ 18 } \\).<\/p>\n
(vii) \\(\\frac { 5 }{ 34 } \\) \u00d7 \\(\\frac { 34 }{ 8 } \\)
\nSolution:
\nGiven that Multiply \\(\\frac { 5 }{ 34 } \\) \u00d7 \\(\\frac { 34 }{ 8 } \\).
\nFirstly, multiply the numerators with numerators.
\n5 \u00d7 34 = 170.
\nNext, multiply the denominators with denominators.
\n34 \u00d7 8 = 272.
\nFinally, write the fraction in the simplest form.
\n\\(\\frac { 170 }{ 272 } \\)
\nSimplify the fraction to get the final answer.
\n\\(\\frac { 5 }{ 8 } \\).<\/p>\n
The final answer is \\(\\frac { 5 }{ 8 } \\).<\/p>\n
(viii) \\(\\frac { 12 }{ 25 } \\) \u00d7 \\(\\frac { 5 }{ 6 } \\)
\nSolution:
\nGiven that Multiply \\(\\frac { 12 }{ 25 } \\) \u00d7 \\(\\frac { 5 }{ 6 } \\).
\nFirstly, multiply the numerators with numerators.
\n12 \u00d7 5 = 60.
\nNext, multiply the denominators with denominators.
\n25 \u00d7 6 = 150.
\nFinally, write the fraction in the simplest form.
\n\\(\\frac { 60 }{ 150 } \\)
\nSimplify the fraction to get the final answer.
\n\\(\\frac { 60 }{ 150 } \\) = \\(\\frac { 2 }{ 5 } \\).<\/p>\n
The final answer is \\(\\frac { 2 }{ 5 } \\).<\/p>\n
(ix) \\(\\frac { 6 }{ 14 } \\) \u00d7 \\(\\frac { 56 }{ 7 } \\)
\nSolution:
\nGiven that Multiply \\(\\frac { 6 }{ 14 } \\) \u00d7 \\(\\frac { 56 }{ 7 } \\).
\nFirstly, multiply the numerators with numerators.
\n6 \u00d7 56 = 336.
\nNext, multiply the denominators with denominators.
\n14 \u00d7 7 = 98.
\nFinally, write the fraction in the simplest form.
\n\\(\\frac { 336 }{ 98 } \\)
\nSimplify the fraction to get the final answer.
\n\\(\\frac { 336 }{ 98 } \\) = 168.<\/p>\n
The final answer is 168.<\/p>\n
(x) \\(\\frac { 1 }{ 3 } \\) \u00d7 \\(\\frac { 4 }{ 5 } \\) \u00d7 \\(\\frac { 5 }{ 8 } \\)
\nSolution:
\nGiven that Multiply \\(\\frac { 1 }{ 3 } \\) \u00d7 \\(\\frac { 4 }{ 5 } \\) \u00d7 \\(\\frac { 5 }{ 8 } \\).
\nFirstly, multiply the numerators with numerators.
\n1 \u00d7 4 \u00d7 5 = 20.
\nNext, multiply the denominators with denominators.
\n3 \u00d7 5 \u00d7 8 = 120.
\nFinally, write the fraction in the simplest form.
\n\\(\\frac { 20 }{ 120 } \\)
\nSimplify the fraction to get the final answer.
\n\\(\\frac { 20 }{ 120 } \\) = \\(\\frac { 1 }{ 6 } \\).<\/p>\n
The final answer is \\(\\frac { 1 }{ 6 } \\).<\/p>\n
(xi) \\(\\frac { 6 }{ 3 } \\) \u00d7 \\(\\frac { 1 }{ 2 } \\) \u00d7 \\(\\frac { 3 }{ 3 } \\)
\nSolution:
\nGiven that Multiply \\(\\frac { 6 }{ 3 } \\) \u00d7 \\(\\frac { 1 }{ 2 } \\) \u00d7 \\(\\frac { 3 }{ 3 } \\).
\nFirstly, multiply the numerators with numerators.
\n6 \u00d7 1 \u00d7 3 = 18.
\nNext, multiply the denominators with denominators.
\n3 \u00d7 2 \u00d7 3 = 18.
\nFinally, write the fraction in the simplest form.
\n\\(\\frac { 18 }{ 18 } \\)
\nSimplify the fraction to get the final answer.
\n\\(\\frac { 18 }{ 18 } \\) = 1.<\/p>\n
The final answer is 1.<\/p>\n
(xii) 3\\(\\frac { 8 }{ 5 } \\) \u00d7 \\(\\frac { 5 }{ 4 } \\)
\nSolution:
\nGiven that multiply 3\\(\\frac { 8 }{ 5 } \\) \u00d7 \\(\\frac { 5 }{ 4 } \\).
\nFirstly, convert given mixed fraction 3\\(\\frac { 8 }{ 5 } \\) to fraction.
\n3\\(\\frac { 8 }{ 5 } \\) = \\(\\frac { 23 }{ 5 } \\)
\nMultiply \\(\\frac { 23 }{ 5 } \\) \u00d7 \\(\\frac { 5 }{ 4 } \\).
\nFirstly, multiply the numerators with numerators.
\n23 \u00d7 5 = 115.
\nNext, multiply the denominators with denominators.
\n5 \u00d7 4 = 20.
\nFinally, write the fraction in the simplest form.
\n\\(\\frac { 115 }{ 20 } \\)
\nSimplify the fraction to get the final answer.
\n\\(\\frac { 115 }{ 20 } \\) = \\(\\frac { 23 }{ 4 } \\).<\/p>\n
The final answer is \\(\\frac { 23 }{ 4 } \\).<\/p>\n
III. Find the given quantity.<\/p>\n
(i) \\(\\frac { 1 }{ 6 } \\) of 48 kg apples
\nSolution:
\nGiven that \\(\\frac { 1 }{ 6 } \\) of 48 kg apples.
\n\\(\\frac { 1 }{ 6 } \\) \u00d7 48 kg
\n8 kg<\/p>\n
The answer is 8 kg.<\/p>\n
(ii) \\(\\frac { 1 }{ 7 } \\) of $280
\nSolution:
\nGiven that \\(\\frac { 1 }{ 7 } \\) of $280.
\n\\(\\frac { 1 }{ 7 } \\) \u00d7 $280
\n$40<\/p>\n
The answer is $40.<\/p>\n
(iii) \\(\\frac { 6 }{ 3 } \\) of 54 km
\nSolution:
\nGiven that \\(\\frac { 6 }{ 3 } \\) of 54 km.
\n\\(\\frac { 6 }{ 3 } \\) \u00d7 54 km
\n108 km<\/p>\n
The answer is 108 km.<\/p>\n
(iv) \\(\\frac { 2 }{ 8 } \\) of 40 chairs
\nSolution:
\nGiven that \\(\\frac { 2 }{ 8 } \\) of 40 chairs.
\n\\(\\frac { 2 }{ 8 } \\) \u00d7 40 chairs
\n10 chairs<\/p>\n
The answer is 10 chairs.<\/p>\n
1. 3\\(\\frac { 5 }{ 8 } \\) m of cloth is required to make a shirt. Sam wants to make 32 shirts, what length of cloth does he need?<\/p>\n
Solution:
\nGiven that 3\\(\\frac { 5 }{ 8 } \\) m of cloth is required to make a shirt.
\nSam wants to make 32 shirts.
\n3\\(\\frac { 5 }{ 8 } \\) m of 32.
\nFirstly, convert given mixed fraction 3\\(\\frac { 5 }{ 8 } \\) to fraction.
\n3\\(\\frac { 5 }{ 8 } \\) = \\(\\frac { 29 }{ 8 } \\)
\n\\(\\frac { 29 }{ 8 } \\) \u00d7 32
\nNow, multiply \\(\\frac { 29 }{ 8 } \\) by 32.
\nMultiply the numerator of the fractional number by the whole number. The denominator remains the same.
\n29 \u00d7 32 = 928.
\nSo, the fraction is \\(\\frac { 928 }{ 8 } \\)
\nSimplify the fraction to get the final answer.
\n\\(\\frac { 928 }{ 8 } \\) = 116.<\/p>\n
The final answer is 116.<\/p>\n
2. \\(\\frac { 5 }{ 2 } \\) cups of milk is required to make a cake of 1 kg. How many cups of milk is required to make a cake of \\(\\frac { 2 }{ 5 } \\) kg?<\/p>\n
Solution:
\nGiven that \\(\\frac { 5 }{ 2 } \\) cups of milk is required to make a cake of 1 kg.
\nTo make a cake of \\(\\frac { 2 }{ 5 } \\) kg, multiply \\(\\frac { 5 }{ 2 } \\) with \\(\\frac { 2 }{ 5 } \\).
\nFirstly, multiply the numerators with numerators.
\n2 \u00d7 5 = 10.
\nNext, multiply the denominators with denominators.
\n5 \u00d7 2 = 10.
\nFinally, write the fraction in the simplest form.
\n\\(\\frac { 10 }{ 10 } \\)
\nSimplify the fraction to get the final answer.
\n\\(\\frac { 10 }{ 10 } \\) = 1.<\/p>\n
The final answer is 1.<\/p>\n
3. Shelly bought \\(\\frac { 11 }{ 9 } \\) liters of juice. If the cost of 1-liter juice is $36, find the total cost of juice?<\/p>\n
Solution:
\nGiven that Shelly bought \\(\\frac { 11 }{ 9 } \\) liters of juice.
\nIf the cost of 1-liter juice is $36, multiply \\(\\frac { 11 }{ 9 } \\) with $36.
\n\\(\\frac { 11 }{ 9 } \\) \u00d7 $36 = $44.<\/p>\n
The final answer is $44.<\/p>\n
4. The weight of each bag is 7\\(\\frac { 1 }{ 9 } \\) Kg. What would be the weight of 36 such bags?<\/p>\n
Solution:
\nGiven that the weight of each bag is 7\\(\\frac { 1 }{ 9 } \\) Kg.
\nIf the weight of 36 such bags is 7\\(\\frac { 1 }{ 9 } \\) Kg \u00d7 36.
\nFirstly, convert given mixed fraction 7\\(\\frac { 1 }{ 9 } \\) to fraction.
\n7\\(\\frac { 1 }{ 9 } \\) = \\(\\frac { 64 }{ 9 } \\)
\nNow, multiply \\(\\frac { 64 }{ 9 } \\) by 36.
\nMultiply the numerator of the fractional number by the whole number. The denominator remains the same.
\n64 \u00d7 36 = 2304.
\nSo, the fraction is \\(\\frac { 2304 }{ 9 } \\)
\nSimplify the fraction to get the final answer.
\n\\(\\frac { 2304 }{ 9 } \\) = 256.<\/p>\n
The final answer is 256.<\/p>\n
5. Sam works for 1 \\(\\frac { 5 }{ 6 } \\) hours each day. For how much time will she work in a month if she works for 24 days in a month?<\/p>\n
Solution:
\nGiven that Sam works for 1 \\(\\frac { 5 }{ 6 } \\) hours each day.
\nIf she works for 24 days in a month, 1 \\(\\frac { 5 }{ 6 } \\) hours each day \u00d7 24
\nFirstly, convert given mixed fraction 1 \\(\\frac { 5 }{ 6 } \\) to fraction.
\n1 \\(\\frac { 5 }{ 6 } \\) = \\(\\frac { 11 }{ 6 } \\)
\nNow, multiply \\(\\frac { 11 }{ 6 } \\) by 24.
\nMultiply the numerator of the fractional number by the whole number. The denominator remains the same.
\n11 \u00d7 24 = 264.
\nSo, the fraction is \\(\\frac { 264 }{ 6 } \\)
\nSimplify the fraction to get the final answer.
\n\\(\\frac { 264 }{ 6 } \\) = 44.<\/p>\n
The final answer is 44.<\/p>\n","protected":false},"excerpt":{"rendered":"
Multiplying numbers is so easy compared to Multiplying Fractions. The fraction is represented as the division of the whole. The fraction is in the form of \u201cx\/y\u201d where \u201cx\u201d is the numerator and \u201cy\u201d is the denominator. One can apply the fraction concept to real-time examples easily after reading the entire concept here. If you … Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":65164,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[5],"tags":[],"jetpack_featured_media_url":"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/03\/Multiplying-Fractions.png","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/65156"}],"collection":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=65156"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/65156\/revisions"}],"predecessor-version":[{"id":92340,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/65156\/revisions\/92340"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/65164"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=65156"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=65156"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=65156"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}