Common Core Math

Worksheet on Multiplication of Fractions is here. Get important questions involved in Fractions Multiplication. Refer to the various rules, methods, formulae of Fractions Multiplication. Follow questions regarding proper, improper, mixed fractions and how they work when multiplying them. Solved examples in Multiplying Fractions Worksheet will help you to get a piece of detailed information and also helps you to score better marks in the exam.

Problem 1:

Gita has eight marbles. She gave \(\frac { 1 }{ 4 } \) of them to her younger brother. How many marbles did her brother get?

Problem 2:

Mr. Gupta puts 3\(\frac { 1 }{ 4 } \) litres of petrol in his car. If he uses \(\frac { 1 }{ 3 } \) of it. How many litres of petrol did he use?

Problem 3:

Neha spends 3\(\frac { 3 }{ 5 } \) hours a day in morning exercises. How many hours does she spend in morning exercises in one week?

Problem 4:

One plum cake weighs \(\frac { 3 }{ 4 } \) kg. If Mr. Ramesh buys five such cakes, how many kilograms of cakes did he buy?

Problem 5:

The cost of one kilogram apples is Rupees 25\(\frac { 1 }{ 2 } \). What is the cost of 1\(\frac { 1 }{ 2 } \) kilogram apples?

Problem 6:

The thickness of the Mathematics book of Class – IV is 1\(\frac { 1 }{ 4 } \) cm. What will be the thickness of a pile of 16 such books?

Problem 7:

Milk is sold at Rs 16\(\frac { 3 }{ 4 } \) per litre, find the cost of 6\(\frac { 2 }{ 5 } \) litre of milk?

Problem 8:

Find the area of the rectangular park which is 41\(\frac { 2 }{ 3 } \) long and 18\(\frac { 3 }{ 5 } \) m board?

Problem 9.
If the cost of 5\(\frac { 2 }{ 5 } \) litres of milk is 236\(\frac { 1 }{ 4 } \), find the cost per litre?

Problem 10:

Margaret has 2\(\frac { 1 }{ 3 } \) cups of sugar. She is using 1\(\frac { 1 }{ 4 } \) cups to make cookies. How much sugar will she have left?

Problem 11:

Russell spent \(\frac { 1 }{ 3 } \) of his allowance to go to movies. He wants to buy a new video game that will cost him another \(\frac { 1 }{ 2 } \) of his allowance. If he buys the game. How much of his allowance will he have spent?

Problem 12:

Sam has 3\(\frac { 1 }{ 8 } \) acres of land. He planted potatoes on 2\(\frac { 2 }{ 3 } \) of the land. He wants to plant corn. How much land does he have left to plant the corn?

Problem 13:

I bought 80 pounds of spaghetti to share equally between 7 families. About how many pounds of spaghetti will each family receive?

Problem 14:

I have 70 feet of rope that I need to share equally between 11 people. About how many feet of rope will each person receive?

Problem 15:

Mom made pizza. There is only \(\frac { 1 }{ 4 } \) of the pizza left. Mom and her friend Sally are going to share the remaining pizza evenly. How much of pizza will they each get?

Place value is nothing but the position or place of a digit in the decimal number. In a number, every digit has someplace. The positions of digits in number starts from one’s place. The order of place value of digits of a number of right to left is units, tens, hundreds, thousands, ten thousand’s, and so on. Generally, a number is formed by grouping digits together.

Place, Place Value and Face Value Definitions

In a number, every digit has a fixed position known as the digit place. And each digit has a value depending on its place called the place value of the digit. Face value of a digit for any place in the value of the digit itself.

Place Value of a digit = (face value of the digit) x (value of the place)

Place Value Table

Place value chart is helpful to ensure that the digits are in the correct places. Place value tells us how much each digit stands for. The place value table is mentioned here.

Properties of Place Value

• The place value of every one-digit number is the same as the face value.

The place value and face value of 1, 2, 3, 4, 5, 6, 7, 8, and 9 are 1, 2, 3, 4, 5, 6, 7, 8, and 9. The place value of 0 is always 0. It may present at any place in the number, its value is always zero.

Example:

(i) In the numbers 105, 270, 1025 the place of value 0 is 0.

(ii) The place of 1 in 251 is 1, 7 in 8567 is 7.

• In a two-digit number, the place value of the ten-place digit is equal to 10 times of the digit.

Example:

(i) The place value of 6 in 67 is 6 x 10 = 60

(ii) The place value of 2 in 526 is 2 x 10 = 20

• In the number 567, the digit 7 is at one’s place, the digit 6 is at ten’s place and the digit 5 is at the hundred’s place.

So, the place value of 7 is 7, 6 is 6 x 10 = 60, and 5 is 5 x 100 = 500

Thus, for the place value of a digit, the digit is multiplied by the place value of 1 it has to be that place.

Example:

In the number 286,

The place value of 6 is 6 x 1 = 6

The place value of 8 is 8 x 10 = 80

The place value of 2 is 2 x 100 = 200

• Now it is the general law that the digit possesses its place value as the product of the digit and place value of one to be at that position.

Examples:

(i) In the number 3578,

The place value of 8 is 8 x 1 = 8 because 8 is at the unit’s place.

The place value of 7 is 7 x 10 = 70 because 7 is at ten’s place.

The place value of 5 is 5 x 100 = 500 because 5 is at hundred’s place

The place value of 3 is 3 x 1000 = 3000 because 3 is at thousand’s place.

(ii) In the number 58762, the place value of each digit is as follows

2 is 2 x 1 = 2

6 is 6 x 10 = 60

7 is 7 x 100 = 700

8 is 8 x 1000 = 8000

5 is 5 x 10000 = 50000

(iii) Find the place value of digits 30589

Also, check out

• Decimal Place Value Chart
• Place Value Chart

Example Questions on Place Value

Example 1:

Write the place value of the given numbers.

(i) 5 in 38956

(ii) 2 in 2587

(iii) 6 in 6845321

Solution:

(i) The given number is 38956

The place value of 5 in 38956 is 5 x 10 = 50. Because 5 is at tens place.

(ii) The given number is 2587

The place value of 2 in 2587 is 2 x 1000 = 2000. Because 2 is at thousands place.

(iii) The given number is 6845321

The place value of 6 in 6845321 is 6 x 1000000 = 60,00,000. Because 6 is at ten lakhs place.

Example 2:

Write the place value of a highlighted digit in the given numbers

(i) 2589

(ii) 67525

(iii) 2515963

Solution:

(i) The given number is 2589

The place value of highlighted 8 in 2589 is 8 x 10 = 80 as it is located at the tens position.

(ii) The given number is 67525

The place value of highlighted digit 5 in 67525 is 5 x 100 = 500 as it is located at the hundred’s position.

(iii) The given number is 2515963

The place value of highlighted digit 1 in 2515963 is 1 x 10000 = 10000 as it is located at the ten thousand’s position.

Example 3:

Circle the following.

(i) Digit at the hundreds place in 5289.

(ii) Digit at the lakhs place in 2563891

(iii) Digit at the units place in 5280

Solution:

(i) In the number 5289,

9 is at units place, 8 is at tens place, 2 is at hundreds place and 5 is at thousand’s place

So, Digit at the hundreds place in 5289 is 2.

(ii) In the number 2563891,

1 is at units place, 9 is at tens place, 8 is at hundreds place, 3 is at thousand’s place, 6 is at ten thousand’s place, 5 is at lakhs place, 2 is at ten lakhs place.

Therefore, Digit at the lakhs place in 2563891 is 5.

(iii) In the number 5280,

0 is at the unit’s place, 8 is at the ten’s place, 2 is at the hundred’s place and 5 is at the thousand’s place.

Hence, the digit at the units place in 5280 is 0.

Example 4:

Find the place value of 5 in the given numbers.

(i) 6,00,521

(ii) 5,23,168

(iii) 2,05,387

Solution:

(i) The given number is 6,00,521

The place value of 5 is 5 x 100 = 500.

(ii) The given number is 5,23,168

The place value of 5 is 5 x 10,000 = 50,000.

(iii) The given number is 2,05,387

The place value of 5 is 5 x 1000 = 5000.

FAQs on Place Value

1. Write the differences between place value and face value?

Place value means the position of a particular digit in the number but face value represents the exact value of a digit in that number. For example in the number 2556, the place value of 2 is thousands but the face value is 2.

2. Define place value with an example?

The place value is the position of a digit in a number. The place values of digits are represented as ones, tens, hundreds, thousands, ten thousand, and so on. The example is the place value of 8 in 589 is 8 tens i.e 80.

Access Worksheet on Division of Fractions here to get acquainted with various problems on Division of Fractions. Refer to Fractions Division’s step-by-step procedure to solve the problems. Follow the study material and guidance to solve various questions and answers. Know the important methods, rules, and formulae of Dividing Fractions. Try to solve the Dividing Fractions Word Problems Worksheet available on your own to test your knowledge of the concept. We have provided detailed solutions to all the Dividing Fractions Problems available.

Dividing Fractions Word Problems Worksheets with Answers

Problem 1:

Jiya thought it would be nice to include \(\frac { 2 }{ 21 } \) of a pound of chocolate in each of the holiday gift bags she made for her friends and family. How many holiday gift bags could jiya make with \(\frac { 2 }{ 3 } \) of a pound of chocolate?

Problem 2:

Lithi has \(\frac { 1 }{ 5 } \) of a bag of dog food left. She is splitting it between her 3 dogs evenly. What fraction of the original bag does each dog get?

Problem 3:

John has \(\frac { 1 }{ 4 } \) of a gallon of saltwater that he is using for an experiment. He needs to evenly separate the saltwater into 3 separate beakers. How much salt water will be in each beaker?

Problem 4:

David has a board that measures 4ft in length. The board is going to be cut into \(\frac { 1 }{ 4 } \) ft pieces. How many pieces will David split the board into?

Problem 5:

Jasmine has \(\frac { 1 }{ 4 } \) hour left to finish 4 math problems on the test. How much time does she have to spend on each problem?

Problem 6:

Sandya finished \(\frac { 1 }{ 3 } \) of her homework problems. Which fraction is equivalent to what Sandya finished?

Problem 7:

Berlin has 9 cups of sugar. If this is \(\frac { 3 }{ 4 } \) of the number he needs to make a cake, how many cups does he need?

Problem 8:

Mahathi is working on projects that require 3\(\frac { 1 }{ 2 } \) yards of ribbon per project. Mahathi has 28 yards of ribbon. What is the greatest number of projects that Mahathi can complete with this ribbon?

Problem 9:

Arjun made 40 cookies for the upcoming bake sale. He made \(\frac { 3 }{ 5 } \) of the cookies of chocolate chip and \(\frac { 1 }{ 4 } \) of them peanut butter. How many chocolate chip and peanut butter cookies are there in together?

Problem 10:

Gillian took 6\(\frac { 1 }{ 2 } \) hours to build a dog house. If she worked for 1\(\frac { 3 }{ 4 } \) hours each night. How many nights did it take?

Problem 11:

A class consists of 40 students. Of them \(\frac { 2 }{ 5 } \) of the fraction are boys. Find the number of girls present in the class?

Problem 12:

John had Php 960. He spent \(\frac { 1 }{ 3 } \) of his money on food. How many were left to him?

Problem 13:

Efren had 480 apples for sale. He sold \(\frac { 3 }{ 5 } \) of them. How many were left?

Problem 14:

Rose and Mary were filling the class-raised garden bed with soil. Rose shoveled in \(\frac { 1 }{ 3 } \) of a cubic yard, and Mary shoveled in \(\frac { 1 }{ 2 } \) of a cubic yard. How much of the soil did they put into the garden bed altogether?

Problem 15:

Carl’s invited Otto over to his house. Carl’s liked to share with his guests, so he got out his chocolate stash from last Halloween. He still had \(\frac { 4 }{ 5 } \) of a pound of chocolate. Carl’s asked Otto how much chocolate he would like. Otto said that he would like \(\frac { 1 }{ 3 } \) of a pound of chocolate. Carl’s obliged. How much chocolate does Carl’s have left?

Worksheet on Fractions is here. Know the step-by-step procedure to solve fraction problems. Refer to addition, subtraction, multiplication, and division of fractions to know the different model problems. Follow different terminology and rules to solve fraction problems. Various methods, rules, formulae involved in fractions operations are here. Go through the below sections to know more about the fractions.

Solved Problems on Simplifying Fractions

Problem 1:

Sameer has read three-fifth of the 75 pages of his book. How many more pages he needs to read to complete the book?

Problem 2:

Ravi had Rs.675. He gave \(\frac { 13 }{ 15 } \) of the amount to Sam. Sam spent \(\frac { 9 }{ 15 } \) of the amount given to him. How much money is Sam left with?

Problem 3:

Jagadish spends \(\frac { 3 }{ 5 } \) of his income on rent and \(\frac { 1 }{ 4 } \) of remainder amount on grocery. He saves the remaining amount.

a) What fraction of income does he save?

b) If he saves Rs.1029 per month, what is his monthly income?

Problem 4:

A baby rabbit was born \(\frac { 3 }{ 4 } \) of a month early. When it was born, its weight was \(\frac { 7 }{ 8 } \) kilogram. The weight at birth was \(\frac { 9 }{ 10 } \) kilogram less than the average weight of a newborn rabbit. What is the average weight of a newborn rabbit?

Problem 5:

In the zoo, \(\frac { 3 }{ 8 } \) of the staff are male. \(\frac { 7 }{ 12 } \) of the staff works part-time at the zoo. What is the fraction of the staff that is female?

Problem 6:

The lions in the zoo are fed three times a day. During the morning feeding, \(\frac { 2 }{ 15 } \) tons of meat is fed. During the afternoon feeding, the weight of the meat will be \(\frac { 1 }{ 15 } \) ton meat fed during the morning. If the total weight of the meat in a day is \(\frac { 1 }{ 2 } \) ton, how much is fed during the feeding at night?

Problem 7:

The monkey nursery is open two times a day: \(\frac { 2 }{ 3 } \) hours at noon and \(\frac { 5 }{ 12 } \) hours in the afternoon. How much time is the monkey nursery open everyday?

Problem 8:

An octopus weighed \(\frac { 5 }{ 6 } \) kilogram. After two weeks, its weight was increased by \(\frac { 3 }{ 10 } \) kilogram. But afterwards, it lost \(\frac { 1 }{ 5 } \) kilogram in weight as it was sick. What was the current weight?

Problem 9:

Two types of fish can be found in a small tank that is 5\(\frac { 1 }{ 7 } \) feet long. A blue fish is \(\frac { 2 }{ 15 } \) feet long and an orange fish is \(\frac { 7 }{ 10 } \) feet long. How much longer is the orange fish?

Problem 10:

Ila read 25 pages of a book containing 100 pages. Lalitha read \(\frac { 2 }{ 5 } \) of the same book. Who read less?

Problem 11:

Javed was given \(\frac { 5 }{ 7 } \) of a basket of apples. What fraction of apples are left in the basket?

Problem 12:

Reena was given 1\(\frac { 1 }{ 2 } \) piece of cake and Meena was given 1\(\frac { 1 }{ 3 } \) piece of cake. Find total amount was given to both of them?

Problem 13:

Bailey’s restaurant bought 6\(\frac { 1 }{ 3 } \) pounds of onions. The restaurant bought 8 times as much potatoes as onion. How many pounds of potatoes did the restaurant buy?

Problem 14:

Betsy has \(\frac { 2 }{ 5 } \) of a cup of powdered sugar. He sprinkles \(\frac { 3 }{ 4 } \) of the powdered sugar onto a plate of brownies. How much sugar does Betsy sprinkle on the brownies?

Problem 15:

At Goshen High School, \(\frac { 1 }{ 2 } \) of the students play a sport. Of the students who play a sport, \(\frac { 1 }{ 2 } \) play football. What fraction of the students play football?

Get detailed information regarding the division of fractions here. Check all the important terms, formulae, and the usage of fractions division. Refer step by step procedure to solve the fraction division problems. Know the various methods to solve proper, improper, mixed fractions, etc. Follow the complete guide to know the day-to-day usage of fractions division problems. Go through the below sections to follow the importance and problems of division on fractions.

Division of Fractions – Introduction

Dividing the fractions also involves various methods and also a lengthy process. First of all, you have to know the difference between proper, improper, and mixed fractions. Once you come to know the difference, then you can easily analyze the method to solve them. As we have seen, for the multiplication, we have to make the fractions equivalent.

In the same way, the division of fractions requires the equivalent fractions to solve them. First, make sure you make the fractions equivalent and then follow all the steps in dividing the fractions. Generally, fraction division in the direct method requires more effort. Hence, we are providing an alternative method here.

How to Divide Fractions?

Division of fractions can be done by multiplying the fractions by writing the reciprocal of one of fraction numbers or by reversing one of two fraction integers. Reciprocal of the fraction number or reverse of the fraction number means, if the fraction is \(\frac { a }{ b } \), then \(\frac { b }{ a } \) is its reciprocal. Interchanging the position of numerator and denominator is nothing but reversing the fraction. Fractions division can be classified into 3 ways.

• Fractions division by a fraction
• Fractions division by a mixed fraction
• Fractions division by a whole number

Fractions Division by a Fraction

Fractions division can be done in three steps. For division, we convert into the multiplication of fractions and obtain the desired result. The three steps are as follows.

1. Convert the second fraction into its reciprocal and multiply it with the first fraction.
2.  Multiply the denominator and numerator of both the fractions.
3. Next, simplify the fraction numbers.

For example, suppose that \(\frac { a }{ b } \) is divided by the fraction \(\frac { c }{ d } \). We can solve the division as:

• \(\frac { a }{ b } \) ÷ \(\frac { c }{ d } \) = \(\frac { a }{ b } \) * \(\frac { d }{ c } \)
• \(\frac { a }{ b } \) ÷\(\frac { c }{ d } \) = \(\frac { a*d }{ b*c } \)
• \(\frac { a }{ b } \) ÷ \(\frac { c }{ d } \) = \(\frac { ad }{ bc } \)

As given above, we can divide the fractions in three ways. Further simplification has to be done to get the exact result.

Fractions Division by a Whole Number

Fractions Division by a whole number is the easiest process. Follow the below steps to divide a whole number.

1. The whole number is nothing but the real numbers which include zero and all positive integers. All the whole numbers can be written as the fraction values if we give the denominator value as 1.
2. Find the reciprocal of the given number
3. Now, multiply the value of the fraction by a given fraction.
4. Then, simplify the equation to get its lowest terms.

Example:

Divide the fraction \(\frac { 6 }{ 5 } \) by 10?

Solution:

As given in the question,

The equation is \(\frac { 6 }{ 5 } \) by 10.

Step 1: Conversion into the whole number

As 10 is the whole number, we convert it into fractional value i.e., we write it as \(\frac { 10 }{ 1 } \)

Step 2: Find the reciprocal of the fraction

To find the reciprocal, we get \(\frac { 1 }{ 10 } \)

Step 3: Multiply both the fractions

Multiply the fractions, \(\frac { 6 }{ 5 } \) x \(\frac { 1 }{ 10 } \)

Step 4: Now, multiply the numertors and denominators of the fractions i.e., \(\frac { 6×1 }{ 15×10 } \)

Step 5: Simplify the equation

The resutant is  \(\frac { 3 }{ 25 } \)

Fractions Division by a Mixed Fraction

Fractions Division by a mixed fraction is almost similar to fractions division by fraction. The following are the steps to divide mixed fractions.

1. Conversion of mixed fraction into an improper fraction
2. Now, find the reciprocal of the improper fraction
3. Multiply the resultant fraction by the given fraction value.
4. Simplify the fractions.

Example:

Divide the fraction \(\frac { 2 }{ 5 } \) by 3\(\frac { 1 }{ 2 } \)?

Solution:

As given in the question,

The equation is \(\frac { 2 }{ 5 } \) by 3\(\frac { 1 }{ 2 } \)

Step 1: Conversion of mixed fraction into improper fraction

Convert, 3\(\frac { 1 }{ 2 } \), we get the result as 7/2

Step 2: Now, convert the reciprocal of the improper fraction, we get \(\frac { 2 }{ 7 } \)

Step 3: Multiply \(\frac { 2 }{ 5 } \) and \(\frac { 2 }{ 7 } \)

Step 4: Multiply the numertors and denominators of the fractions i.e., \(\frac { 2×2 }{ 5×7 } \)

Step 5: Simplify the fraction

the result value is \(\frac { 4 }{ 35 } \)

Fractions Division of Decimal Values

In the above sections, we have seen how to divide the fractions into three steps. Now, we see how to divide decimals with examples.

To convert the decimal values into natural numbers, we multiply both the numerator and denominator by 10.

Example:

Divide \(\frac { 0.5 }{ 0.2 } \)

Solution:

As given in the question,

The equation is \(\frac { 0.5 }{ 0.2 } \)

To divide the decimal values, convert the values into natural numbers by multiplying both numerator and denominator with 10.

Therefore, \(\frac { 0.5×10 }{ 0.2×10 } \)

We get the solution as, \(\frac { 5 }{ 2 } \) = 2.5

Also, we use the method of dividing fractions to solve the problem.

We can write 0.5 as \(\frac { 5 }{ 10 } \) and 0.2 as \(\frac { 2 }{ 10 } \)

Therefore, to find the solution of \(\frac { 5÷10 }{ 2÷10 } \)

Take the reciprocal of the second fraction i.e., \(\frac { 10 }{ 2 } \)

= \(\frac { 5*10 }{ 10*2 } \)

= \(\frac { 50 }{ 20 } \)

= \(\frac { 5 }{ 2 } \)

= 2.5

Dividing Fractions Examples

Problem 1: Lucy has \(\frac { 1 }{ 5 } \) of a bag of dog food left. She is splitting it between her 3 dogs evenly. What fraction of the original bag does each dog get?

Solution:

As given in the question,

Amount of dog food left = \(\frac { 1 }{ 5 } \)

No of dogs = 3

The fraction of the original bag each dog gets = \(\frac { 1/5 }{ 3 } \)

= \(\frac { 1 }{ 5 } \) x \(\frac { 1 }{ 3 } \)

= \(\frac { 1 }{ 15 } \) of the bag each dog gets.

Thus the final solution is \(\frac { 1 }{ 15 } \)

Problem 2: AJ has \(\frac { 1 }{ 4 } \) of a gallon of saltwater that he is using for an experiment. He needs to evenly separate the saltwater into separate beakers. How much salt water will be in each beaker?

Solution:

As given in the question,

Amount of salt water he is using for an experiment = \(\frac { 1 }{ 4 } \)

No of beakers = 3

Amount of salt water in each beaker = \(\frac { 1/4 }{ 3 } \)

= \(\frac { 1 }{ 4 } \) x \(\frac { 1 }{ 3 } \)

= \(\frac { 1 }{ 12 } \)

Therefore, \(\frac { 1 }{ 12 } \) gallons of salt water will be in each beaker.

Problem 3: Devin has a board that measures 4 ft in length. The board is going to be cut into \(\frac { 1 }{ 4 } \) ft pieces. How many pieces will Devin split the board into?

Solution:

As given in the question,

Length of the board = 4 ft

No of pieces the board is going to be cut = \(\frac { 1 }{ 4 } \)

No of pieces Devin split the board = 4 ÷ \(\frac { 1 }{ 4 } \)

= \(\frac { 4 }{ 1 } \) x \(\frac { 4 }{ 1 } \)

= \(\frac { 16 }{ 1 } \)

Hence, the final solution is 16 pieces.

Therefore, Devin will split the board into 16 pieces.

Have you ever wondered why certain numbers divide evenly into a number while others will not? Divisibility Rules or Tests will help you determine whether the given number actually divides the other number without actually dividing. Maths may not be easy for some of us and to help you we have listed the guidelines on whether a Number is Divisible by 6 or not. Check out Solved Examples for testing whether a number is divisible by 6 or not.

Divisibility Rule of 6 – Definition

A number is divisible by 6 if it is divisible by both 2 and 3. To know whether a number is divisible by 6 one needs to know both the Divisibility Rules of 2 and 3 in advance.

How to Check whether a Number is Divisible by 6 or not?

Go through the below Divisibility Guidelines of 6 to know whether a number is divisible by 6 or not. To know if a number is divisible by 6 it has to meet two conditions in prior and they are along the lines

• It has to be divisible by 2 i.e. the last digit in the number should be even.
• It has to be divisible by  3 i.e. the sum of digits must be a multiple of 3.

If both the conditions are met then the given number is also a multiple of 6 and divisible by 6.

Solved Examples on Divisibility Tests for 6

Find whether the following numbers are divisible by 6 or not

1. 48

Solution:

Given Number is 48

To check whether it is divisible by 6 or not it has to meet two conditions

48 is divisible by 2 since the units digit of the number i.e. 8 is divisible by 2

48 is divisible by 3 since the sum of digits is a multiple of 3 i.e. 4+8 = 12 is divisible by 3

Therefore, 48 is divisible by both 2 and 3

Thus, 48 is divisible by 6.

2. 258

Solution:

Given Number is 258

258 is divisible by 2 since the units digit of the number i.e. 6 is divisible by 2

258 is divisible by 3 since the sum of digits is divisible by 3 i.e. 2+5+8 = 15 is divisible by 3

Since 258 is divisible by both 2, 3 it is also divisible by 6

3. 154

Solution:

Given Number is 154

154 is divisible by 2 since the units digit of the number i.e. 4 is divisible by 2

154 is not divisible by 3 as the sum of the digits is not divisible by 3 i.e. 1+5+4 = 10

10 is not divisible by 3

Since the given number is not divisible by 3 the given number is not divisible by 6.

4. 243

Solution:

Given Number is 243

243 is not divisible by 2 since the units digit of the number is not divisible by 2 i.e. 3 is not divisible by 2

243 is divisible by 3 since the sum of digits is a multiple of 3 i.e. 2+4+3 = 9 and 9 is divisible by 3

Since the given number is not divisible by 2 it is not divisible by 6

Therefore, 243 is not divisible by 6.

Complex Number is a combination of both Real and Imaginary Numbers. In other words, Complex Numbers are defined as the numbers that are in the form of x+iy where x, y are real numbers and i =√-1.

z = x+iy here x is the real part of the Complex Number and is denoted by Re Z and y is called the Imaginary Part and is denoted as Im Z. In the later sections, you will find What is a Complex Number and Properties of Complex Numbers. We tried explaining each and every Property of Complex Number in detail with Proofs.

What are Complex Numbers?

If x, y ∈ R, then ordered pair (x, y) = x + iy is called a complex number. It is denoted by z. Where x is the real part and is denoted as Re(z) and y is the imaginary part of the complex number and represented as Im(z).

(i) If Re(z) = x = 0, then the number z is a purely imaginary number

(ii) If Im(z) = y = 0 then the number z is a purely real number.

Properties of Complex Numbers

1. If x, y are two real numbers and x+iy =0 then x = 0 and y = 0

Proof:

Since, x + iy = 0 = 0 + i0, thus by the definition of equality of two complex numbers we can say that, x = 0 and y = 0.

2. If x, y, p, q are real and x + iy = p + iq then x = p and y = q

Proof:

Given x + iy = p + iq

rearranging the equation we get x − p = -i(y − q)

⇒ (x − p)² = i² (y − q)²

⇒ (x − p)² + (y − q)² = 0 (We know i² = -1)……..(1)

Since x, y, p, q are real, and (x − p)² and (y − q)² are both non-negative. Equation (1) is satisfied if each square is separately zero.

Thus we can write the equation as follows

(x − p)² = 0 or x = p and (y − q)² = 0 or y = q.

3. Similar to real numbers, the set of complex numbers also satisfy the commutative, associative, and distributive laws

Proof:

If z₁, z₂ and z₃ be three complex numbers then,

z₁ + z₂ = z₂ + z₁ (commutative law of addition) and z₁. z₂ = z₂. z₁ (commutative law of multiplication)

(z₁ + z₂) + z₃ = z₁ + (z₂ + z₃) (associative law of addition) and (z₁. z₂) z3 = z₁ (z₂. z₃) (associative law of multiplication)

z₁(z₂ + z₃) = z₁ z₂ + z₁ z₃ (distributive law)

4. Sum and Product of Two Conjugate Complex Quantities are both Real.

Proof:

Consider z = x + iy is a complex number where x, y are real.

Then, the conjugate of z is = x − iy.

Now, z + \(\overline {z}\)= x + iy + x − iy = 2x, is real.

and z. \(\overline {z}\) = (x + iy)(x − iy) = x² − i²y² = x² + y² is also real.

5. For two complex quantities z₁ and z₂,  |z₁+ z₂| ≤ |z₁ | + |z₂ |

Proof:

Let z₁ = r₁(cosθ₁ + isinθ₁ ) and z₂ = r₂(cosθ₂ + isinθ₂ ).

Hence |z₁ | = r₁ and |z₂ | = r₂

Now

z₁ + z₂ = r₁(cosθ₁isinθ₁) + r₂(cosθ₂ + isinθ₂)

= (r₁(cosθ₁+ r₂cosθ₂ )+ i(r₁sinθ₁+ r₂sinθ₂)

Hence |z₁+ z₂ | = √(r₁cosθ₁+ r₂cosθ₂)₂ + (r₁sinθ₁+ r₂sinθ₂)₂

= √r₁2(cos₂θ₁+ sin2₁) + r₂2(cos2θ₂+ sin2θ₂) + 2r₁r₂ (cosθ₁ cosθ₂+ sinθ₁ sinθ₂)

= √r1₂ + r2₂ + 2r₁r₂cos (θ₁– θ₂)

Now, |cos(θ₁– θ₂)| ≤ 1

Hence |z₁+ z₂| ≤ √r1₂ + r2₂ + 2r₁r₂ or |z₁+ z₂ | ≤ |z₁| + |z₂ |

6. If the sum of two complex numbers is real and the product of two complex numbers is also real then the complex numbers are conjugate to each other.

Proof:

Let us consider z₁ = a + ib and z₂ = c + id are two complex quantities (a, b, c, d and real and b ≠ 0, d ≠0).

As per the property,

z₁ + z₂ = a+ ib + c + id = (a + c) + i(b + d) is real.

Therefore, b + d = 0

⇒ d = -b

and,

z₁.z₂ = (a + ib)(c + id) = (a + ib)(c +id) = (ac – bd) + i(ad + bc) is real.

Therefore, ad + bc = 0

⇒ -ab + bc = 0, (Since, d = -b)

⇒ b(c – a) = 0

⇒ c = a (Since, b ≠ 0)

Hence, z₂ = c + id = a + i(-b) = a – ib

Thus, we can say that z₁ and z₂ are conjugate to each other.

Are you looking for help regarding the Units of Time Conversion i.e. from Hours to Minutes? You have come the right way and we will guide you all throughout on How to Convert from Hours to Minutes. Check out the basic definitions of hours, minutes, hrs to min conversion table, the procedure for hours to mins conversion, etc. Have a glance at the Solved Examples on Hours to Minutes Conversions and understand how to solve related problems easily. You can also check out our Math Conversion Chart to learn more about length, mass, capacity conversions along with Time Conversions.

Hours & Minutes Definitions

Hour(hr)

An Hour is a Unit of Time Conventionally defined as 1/24th of a day or 60 Minutes. The Hour is the SI unit of time accepted for the Metric System. Hours can be abbreviated as hr. As per the conversion base, 1 hr = 60 Minutes or 3600 Seconds.

Minutes(min)

A Minute is a period of time conventionally equal to 1/60 of an hour or 60 seconds. The Minute is the SI unit of time accepted for the Metric System. Minutes can be abbreviated as min. According to the Conversion Base, 1 Min = 60 Seconds.

Hours to Minutes Conversion Chart | Hrs to Mins Conversion Table

Below is the list of hours converted to minutes. Refer to them and have an idea of How many minutes are there in a Particular Hour.

How to Convert Hours to Minutes?

To convert hours measurement to minutes multiply time by the conversion ratio. Use the simple formula listed below to change between Hours to Minutes easily as a part of your conversions.

We know 1 hour = 60 minutes

Time in Minutes is equal to hours multiplied by 60.

Therefore, the Hours to Minutes Conversion Formula is given as

Now that you know the formula to Convert Between Hours to Minutes simply substitute the given hrs value and calculate the minutes in no time. To understand more about hr to min Conversions check out a few worked out examples provided by us in the below modules and know how to convert Hours to Minutes easily and quickly.

Read Similar Articles

• Conversion of Hours into Seconds
• Conversion of Minutes into Seconds
• Conversion of Minutes into Hours

Solved Examples on Conversion of Hours into Minutes

1. Convert 12 hrs to min?

Solution:

We know 1 hr = 60 minutes

The formula to convert from hrs to mins is given as follows

min = hours *60

min = 12*60

= 720

Therefore, 12 hrs converted to mins is 720 mins.

2. Convert 6 hrs 30 mins to minutes?

Solution:

Given 6hrs 30 mins

We know 1 hr = 60 minutes

6hrs 30 minutes = 6*60+30

= 360+30

= 390 minutes

Therefore, 6 hrs 30 mins converted to mins is 390 minutes.

3. Convert 8 hrs 42 mins to mins?

Solution:

We know 1 hr = 60 mins

8hrs 42 mins = 8*60+42

=480+42

= 512 mins

Therefore, 8 hrs 42 mins to 512 mins.

FAQs on Converting Hours to Minutes

1. What is the formula for converting hours to minutes?

The formula for converting hours to minutes is Minutes = Hours*60

2. How many minutes are there in 1 hour?

There are 60 minutes in an hour.

3. How to convert hr to mins?

Since there are 60 mins in an hour to convert from hrs to mins multiply with 60.

Worried about how to find the Arc Length? Don’t Panic as we will guide you completely in this and help you with the definition of Arc Length, Formula and Proof for Length of the Arc explained in detail. Check out the step by step explanation provided for determining the Arc Length. Also, refer to the solved examples for calculating the length of the arc and solve related problems in no time.

In general, Arc Length is nothing but the distance along the curved line making the arc. Remember that Arc Length is greater than the Straight Line Distance present between the Endpoints. Know about Denotations in the Arc Length Formula in the later sections.

Prove that the radian measure of any angle at the centre of a circle is equal to the ratio of the arc subtending that angle at the centre to the radius of the circle?

Let, us consider XOY to be a given angle. Now, with Centre O and any radius \(\overline {O L} \) draw a circle. Consider the circle drawn intersects \(\overline {O X} \) and \(\overline {O Y} \) at Points L and M respectively.

From the figure, it is clear that Arc LM subtends ∠LOM at Centre O. Now, take an Arc LN of length equal to the radius of the circle and join \(\overline {O N} \).
From definition, ∠LON = 1 radian.

We know the ratio of two arcs in a circle is equal to the ratio of the angles subtended by the arcs at the center of the circle,

Therefore, ∠LOM/∠LON = Arc LM/Arc LN
or, ∠LOM/1 radian = Arc LM/Radius \(\overline {O L} \)
or, ∠LOM = Arc LM/Radius OL × 1 radian = Arc LM/ Radius \(\overline {O L} \) radian.
Thus, circular measures of ∠LOM is Arc LM/Radius \(\overline {O L} \)
Let us consider θ be the circular measure of ∠LOM, Arc LM = s and Radius of the circle = \(\overline {O L} \) = r then,
θ = s/r, [i.e. theta equals s over r]

or, s = r θ, [i.e. s r theta formula]

Denotations in the Arc Length Formula

• s is the Arc Length
• r is the Radius of the Circle
• θ is the Central Angle of the Arc

Formulas to Measure the Arc Length

Solved Examples on Arc Length using the Formula s = rθ

1. Calculate the Length of the Arc if the radius of the circle is 9 cm and θ = 45°?

Solution:

We know the formula to Calculate the Arc Length s = rθ

Substituting the given input values r = 9 cm, θ =45° we get

Arc Length = 9*45°

= 9*0.785398(since 45° in radians =0.785398)

= 7.06 cm

Therefore, Arc Length is 7.06 cm

2. What would be the length of the arc formed by 65° of a circle having a diameter of 14 cm?

Solution:

From the given data

θ =65°

Diameter of the Circle = 14 cm

Radius of the Circle = \(\frac { d }{ 2 } \)

= \(\frac { 14 }{ 2 } \)

= 7 cm

We know the formula to calculate the Arc Length s = rθ

= 7*65°

= 7*1.13446

= 7.94 cm

Therefore, Arc Length is 7.94cm

Temperature is written in terms of Celsius, Fahrenheit, Kelvin. Temperature can be converted from one unit to another using certain formulas. Of all the Temperature Conversions Celsius to Fahrenheit Conversion is the most commonly used. To help you understand we have provided the formula for °C to °F Conversion, the procedure to convert from Celsius to Fahrenheit in the later modules.

Both Celsius and Fahrenheit have different freezing and boiling points of water and follow the varied unit differences between each scale. Check out Solved Examples on Celsius to Fahrenheit Temperature Conversion for a better understanding of the concept.

Celsius to Fahrenheit Conversion Formula

Conversion from Celsius to Fahrenheit can be mathematically expressed using the formula

F = \(\frac { 9 }{ 5 } \)*C+32

Where F is the Temperature in Fahrenheit

C is the Temperature in Celsius

How to Convert Celsius to Fahrenheit(°C to °F)?

Check out the quick and easiest way to perform Celsius to Fahrenheit Conversion. They are along the lines

• To convert from Celsius to Fahrenheit firstly multiply the value of the celsius degrees by 9.
• Later divide the product with 5.
• Add 32 to the result obtained in the earlier step.
• That’s the required Fahrenheit Value and place °F symbol next to it.

Celsius to Fahrenheit Conversion Table

Relation between °C and °F

The Relation between Celsius and Fahrenheit is direct. Celsius is directly proportional to Fahrenheit and it implies

• If the Temperature in Celsius increases then the Fahrenheit Equivalent Temperature also increases.
• If the Temperature in Celsius decreases then the Fahrenheit Equivalent Temperature also decreases.

Both the Scales of Temperature have their own measurements. In Fahrenheit Scale 32 °F is the freezing point of water and 212 °F is the boiling point of water. However, in Celsius Scale 0 °C is the Freezing Point of water and 100 °C is the boiling point of water.

Solved Examples on Celsius to Fahrenheit Conversion

1. Convert 40°C to °F?

Solution:

We know the formula to convert Celsius to Fahrenheit is

\(F=(\frac{9}{5}\times 1)+32\)

\(F= (\frac{9}{5}\times 40)+32\)

=104°F

Therefore 40°C converted to Fahrenheit is 104°F

2. What is 60°C in Fahrenheit?

Solution:

We know the formula to convert Celsius to Fahrenheit is

\(F=(\frac{9}{5}\times 1)+32\)

\(F=(\frac{9}{5}\times 60)+32\)

= 140°F

Therefore, 60°C in Fahrenheit is 140°F

FAQs on Celsius to Fahrenheit Conversion

1. What is the formula to convert from Celsius(°C) to Fahrenheit(°F)?

The Formula to Convert from Celsius to Fahrenheit is \(F=(\frac{9}{5}\times 1)+32\)

2. What is C equal to in F?

1 Degree in Centigrade is Equal to 33.8 Fahrenheit.

3. What are the different Temperature Conversions?

The three major temperature conversions are

• Conversion Between Celsius and Kelvin
• Conversion Between Fahrenheit and Kelvin
• Conversion Between Celsius and Fahrenheit

Greater than and Less than Symbols are used to compare any numbers. If a number is bigger than another symbol greater than symbol is used and when a number is less than the other number less than symbol is used. Refer to the entire article to learn about Greater than and Less than Symbols, Notations, and Tricks to remember them easily. Using Symbols will help you save time and space and users can understand them easily.

Greater than and Less than Symbols – Definition

Greater than and Less than Symbols denotes the inequality between two values. The symbol used to represent greater than is “>” and less than is “<“.

Greater than Sign

Greater than Symbol is placed between two values if the first value is greater than the second value. In Inequality, greater than symbol will always be pointed towards the greater value, and the symbol consisting of two equal length strokes connecting in an acute angle at the right.

For Example 8>5, here 8 is greater than 5

Less than Sign

Less than symbol is placed between two values when the first value is less than the second value. In Inequality, less than symbol will always be pointed towards the lesser value, and the symbol consisting of two equal length strokes connecting in an acute angle at the left.

For Example 10<15, here 10 is less than 15.

Greater than and Less than Symbols makes it easy for the readers to understand.

All Symbols – Summary

Below is the list of Inequality Symbols and their Notations. They are along the lines

Tricks to Remember Greater than and Less than Symbols

To remember Greater than and Less than Symbols two methods are used. They are as follows

• Alligator Method
• L Method

Alligator Method: We know an Alligator or Crocodile always wants to eat a larger number of fishes. Alligator Mouth Opens always opens towards the largest number. Consider the numbers on both sides represent the number of fishes.

For Example: 10>6

Alligator mouth opens towards 10 since it wants to et 10 fishes rather than 6 fishes. It means 6 <10

L Method: Letter L appears similar to the Less than Symbol “<“.

Example: 20<40

Also, Read: Greater or Less than and Equal to

Applications of Greater than and Less than Symbols

In Mathematics we always don’t end with equality. At times, you can even have greater than and less than symbols. The Statements can be expressed using a Mathematical Expression.

Example: Consider there are x number of students in a class and they are more than 50 students if 10 more joined the class then they are 50 students in the class. Expressing this statement in mathematical expression we get

x+10>50

Solving Inequalities is similar to solving equations. While dealing with Inequalities Problems you should pay attention to the inequality sign direction. Some of the tricks that don’t affect the direction of inequalities are as listed below

• Multiply or Divide the Inequalities on both the sides with the same Positive Number.
• Add or Subtract the same number on both sides of the Inequality Expression.

Worked out Examples on Greater than and Less than Symbols

Question 1.

Diya has thirteen bananas and Manvi has twenty bananas. Find out who has more bananas?

Solution:

No. of Bananas Diya has = 13

No. of Bananas Manvi has = 20

Since 20>13

Thus, Manvi has more Bananas.

2. Dheeraj sleeps for thirty minutes and Manav sleeps for forty-five minutes every day in the afternoon. Find out who sleeps for less time?

Solution:

No. of Minutes Deeraj Sleeps = 30 min

No. of Minutes Manav Sleeps = 45 min

since 30<45

Dheeraj Sleeps for Less time compared to Manav.

FAQs on Greater than and Less than Symbols

1. What are the Different Inequality Symbols?

The different Inequality Symbols are

Greater than (>)
Less than (<)
Not equal to (≠)
Greater than or equal to (≥)
Less than or equal to (≤)

2. How to Remember Greater than and Less than Symbols?

You can use different methods like Alligator Method and L Method to remember the Greater than and Less than Symbols easily.

3. When can we use Greater than and Less than Symbols?

We can use Greater than and Less than Symbols to represent the Inequality Expressions. The Symbols used to denote greater than and less than are >, <.

Are you searching everywhere to find Word Problems on Division? If so, you have come the right way where you can find the complete list of Division Word Problems here. Practice using the Division Word Problems available here and test your level of understanding. For the sake of your convenience, we even listed Step by Step Solutions to all the Division Questions available. Have a glance at them and learn how to solve Word Problems on Division easily and quickly.

Examples of Word Problems Involving Division

1. There are 150 grade 4 students, in a school. The students are to be equally divided into 6 classes. How many students do we have in each class?

Solution:

No. of Grade 4 Students = 150

Since 150 Students are to be divided equally among 6 Classes we have the equation as such

= \(\frac { 150 }{ 6 } \)

= 25

Therefore, 6 Classes will have 25 Students each if 150 students divided equally.

2. Mary made 323 cupcakes. She packed 5 cupcakes into each box. How many boxes of cupcakes did she pack? How many cupcakes were left unpacked?

Solution:

No. of Cupcakes mary made = 323

She packed 5 Cupcakes into each box = 5

No. of boxes of cupcakes she packed =\(\frac { 323}{ 5 } \)

= 64 remainder 3

Therefore, 3 cupcakes are left unpacked.

3. If 9000 kg of wheat is packed in 85 bags, how much wheat will each bag contain?

Solution:

Since 85 bags contain wheat of 9000kg

Therefore, 1 bag contains wheat (9000 ÷ 85) kg

= 105kg

Each bag contains 105kg.

4. 85 people have been invited to a banquet. The caterer is arranging tables. Each table can seat 10 people. How many tables are needed?

Solution:

Since 85 people have been invited to a banquet and 10 people can be seated in  1 table

No. of Tables needed = 85 ÷ 10

Quotient = 8

Remainder = 5

80 People can be organized in 8 Tables and 5 People will be left. So the Caterer has to arrange one more table so that the 5 People can sit.

Thus, the total number of tables needed = 8+1

= 9

5. How many hours are there in 1800 minutes? 

Solution:

We know 1 hr = 60 minutes

To know how many hours are there in 1800 minutes we have to divide by 60 minutes

= 1800 ÷ 60

= 30 hours

Therefore, there are 30 hours in 1800 minutes.

6. A bus can hold 96 passengers. If there are 8 rows of seats on the bus, how many seats are in each row?

Solution:

The capacity of the bus that it can hold = 96 Passengers

No. of Rows in the Bus = 8

No. of Seats in each row = Capacity of Bus ÷ No. of Rows

= 96 ÷ 8

= 12

Therefore, there are 12 seats in each row.

7. $5,800 is distributed equally among 20 men. How much money will each person get?

Solution:

From the given data

Money received by 20 men = $5,800

Money received by 1 man = $5,800 ÷ 20

=

Thus $290 is received by each man when a sum of $5800 is distributed equally among 20 men.

8. Tarun had 56 apples. He divides all apples evenly among 7 friends. How many apples did Tarun give to each of his friends?

Solution:

Tarun had 56 apples

He divided all apples evenly among 7 friends

No. of Apples Tarun gave to each friend = Total Apples Tarun had ÷ No. of Friends he equally distributed the Apples among

= 56 ÷ 7

= 8

Therefore, Tarun gave 8 Apples each to his 7 friends on distributing 56 apples equally.

9. Nandy needs 6 lemons to make a glass of orange juice. If Nandy has 252 oranges, how many glasses of orange juice can she make?

Solution:

No. of Lemons Nandy need to make an Orange Juice = 6

Total No. of Oranges Nandy has = 252

To find out how many glasses of orange juice Nandy can make simply divide the total number of oranges she has with the. of lemons needed to make an orange juice.

= 252÷6

= 42

Therefore, Nandy can make 42 glasses of Orange Juice.

10. In your classes you counted 130 hands. How many students were in the class?

Solution:

No. of Hands Counted = 130

Each student has 2 hands

To find how many students were in the class simply divide the total no. of hands counted by the no. of hands each student has i.e. 130÷2 = 65

Therefore, there were 65 students in the Class.

A cuboid is a three-dimensional shape having three axes. It has 3 faces which are convex polyhedrons, 12 edges, 12 vertices. Find the different formulas of the cuboid like perimeter, total surface area, lateral surface area, base surface area, and diagonal in the following sections of this page. One can also find the cuboid definition, properties, and solved example questions here.

Cuboid Definition

The cuboid is a closed three-dimensional geometric figure having 6 rectangular regions. Each rectangular region is called the face. The point of intersection of three edges in the cuboid is called the vertices or corners. The sides of all rectangular faces are called the edges of the cuboid. Some of the examples for the objects in the cuboid shape are matchbox, shoebox, bricks, matrices.

The shape of the cuboid is shown here.

Faces, Edges, Vertices of the Cuboid

The cuboid is made up of 6 rectangular faces, 12 edges, 8 corners. The faces, edges, and corners for the above-mentioned cuboid image are as follows:

• The six faces are ABCD, BDEF, ABGF, AGCH, CDHE, EFGH.
• Eight corners or vertices are A, B, C, D, E, F, G, H.
• Twelve edges and opposite sides of the rectangle are AB = CD = EH = GF, AC = BD = EF = GH, DE = BF = CH = AG.

Cuboid Formulas

The cuboid formulas are provided-below. Get the total surface area, diagonal, perimeter, and volume of the cuboid. Let us consider l, b, h are the length, breadth, and height of the cuboid respectively.

Cuboid Surface Area

The surface area is nothing but the total region covered by all the faces. Generally, the cuboid surface area is classified into two types they are lateral surface area and total surface area. It is also defined as the sum of areas of six faces of the cuboid.

Lateral Surface Area

The lateral surface area is the sum of the areas of all faces except the top and bottom faces.

Cuboid Lateral Surface Area = (Area of ABCD + Area of BDEF + Area of EFGH + Area of AGCH)
= (b × h) + (b × h) + (l × h) + (l × h)

= 2h(l + b)

Total Surface Area

Cuboid Total Surface Area is the sum of the faces.

Total Surface Area of the Cuboid = (Area of ABCD + Area of BDEF + Area of EFGH + Area of AGCH + Area of ABGF + Area of CDHE)

= (l × b) + (l × b) + (b × h) + (b × h) + (l × h) + (l × h)

= 2lb + 2bh + 2hl

= 2(lb + bh + lh)

Cuboid Diagonal

The length of the diagonal of a cuboid is along the lines.

Diagonal = √(l² + b² + h²)

Cuboid Perimeter

The perimeter is the sum of the edges of all edges.

The perimeter of the Cuboid = AB + BF + FE + BD + DE + CD + CH + AC + GH + AG + GF + HE

= l + l + l + l + b + b + b + b + h + h + h + h

= 4(l + b + h)

Cuboid Volume

Cuboid volume is the product of the base area and height.

Volume = length x breadth x height

= lbh

Read More Related Articles:

• Volume of Cubes and Cuboids
• Worked-out Problems on Volume of a Cuboid

Properties of Cuboid

Here is the list of Properties of Cuboids such as faces, edges, vertices, angles, etc. They are as follows

• A cuboid has 6 faces, twelve edges, and 8 vertices.
• It has rectangular-shaped faces.
• The angles are plane and at a right angle.
• Opposite edges are parallel to each other.

Solved Examples on Cuboid

Example 1:

Calculate the volume, diagonal, surface area, and perimeter of the cuboid, if the cuboid length is 8 cm, width is 5 cm, and height is 10 cm.

Solution:

Given that,

Cuboid length l = 8 cm

breadth b = 5 cm

height h = 10 cm

Cuboid volume v = lbh

= 8 x 5 x 10

= 400 cm³

Diagonal of the cuboid = √(l² + b² + h²)

= √(8² + 5² + 10²)

= √(64 + 25 + 100)

= √(189)

= 3√(21) cm

Perimeter = 4(l + b +h)

= 4(8 + 5 + 10)

= 4(23)

= 92 cm

Total Surface Area = 2(lb + bh + lh)

= 2(8 x 5 + 5 x 10 + 8 x 10)

= 2(40 + 50 +80)

= 2(170)

= 340 cm²

∴ Perimeter, diagonal, total surface area, and volume of the cuboid are 92 cm, 3√(21) cm, 340 cm² & 400 cm³.

Example 2:

The lunchbox measures 20 cm long, 10 cm wide, and 5 cm high. what is the total surface area, the lateral surface area of the box?

Solution:

Given that,

Lunchbox length l = 20 cm

Width b = 10 cm

Height h = 5 cm

Total Surface Area of the lunchbox = 2(lb + bh + lh)

= 2(20 x 10 + 10 x 5 + 20 x 5)

= 2(200 + 50 + 100)

= 2(350)

= 700 cm²

Lateral Surface Area of the lunchbox = 2h(l + b)

= 2 x 5(20 + 10)

= 10(30)

= 300 cm²

∴ The total surface area of the lunchbox is 700 cm², lateral surface area is 300 cm².

Example 3:

If the cuboid volume is ∛(126) m³, breadth is 2 m and height is 3 m. Find its length?

Solution:

Given that,

The volume of the cuboid = ∛(126) m³

lbh = ∛(126) m³

l x 2 x 3 = ∛(126)

l x 6 = ∛(126)

l = ∛(126) / 6

l = 21 m

∴ The cuboid length is 21 m.

Example 4:

If the volume of a room is 792 m³ and the area of the floor is 132 m², find the height of the room.

Solution:

Given that,

The volume of a room = 792 m³

Area of the floor = 132 m²

Height of the room = Volume of a room / Area of the floor

= 792/132

= 6 m

Therefore, the height of the room is 6 m.

The most important part of elementary education is learning multiplication tables. Check the 20 Times Table Multiplication Chart here and master the table at an early age to build a foundation in mathematics. With the help of the multiplication table of 20, you can get perfect in various topics like algebra, fractions, divisions, etc. Know the tips to memorize 20 Tables and become perfect with all the multiplication tables.

20 Times Table Multiplication Chart

For all the complex calculations, we use calculators. But for simple calculations, using the calculator is not the correct way. Memorizing the tables will help you to improve your problem-solving skills. It is always recommended for the students to memorize the tables from at least 2 to 20. If you memorize the multiplication tables, then you can quickly solve all the problems and it can be used as a building block in maths. Check how each integer gives the solution when multiplied by 20. Follow the tips and tricks to know the multiplication table of 20.

Tips to Memorise Multiplication Tables

1. To memorize the multiplication table, you have to know how many numbers are increased to get each resultant.
2. Add the same number to which you are finding the multiple.
3. To find the first number, you have to double it, and then again to find the second number, you have to add the multiplication number.
4. Break up the numbers into manageable chunks.
5. Practice each table until you get perfect for it.
6. Practice the number of multiplication facts.

Do Check:

• 14 Times Table
• 15 Times Table Multiplication Chart

20 Times Table Multiplication Chart

20 Times Table Multiplication Chart shows that the multiplication of 20 with various whole numbers present. Here is the table of 20.

To obtain the multiplication table of 20, we need to multiply each natural number by 20. The multiplication chart of 20 is nothing but the repetition of addition. As we know that 20 * 1 = 20, adding 20 to that number will give the next multiple numbers. Similarly, if we add 20 to the next multiples, we get the Table of 20. The multiples of 20 till 10 are

20 * 1 = 20

20 * 2 = 40

20 * 3 = 60

20 * 4 = 80

20 * 5 = 100

20 * 6 = 120

20 * 7 = 140

20 * 8 = 160

20 * 9 = 180

20 * 10 = 200

Easy ways to learn Multiplication Chart of 20

We will mention the easy ways to learn and remember the multiplication table.

Tip 1: The order does not Matter

When two numbers are multiplied, the order in which the numbers are multiplied does not matter. You can multiply the first number with the second or the second number with the first.

So, you don’t have to memorize both 4*3 and 3*4, just you have to remember that 4 and 3 make 12. Memorizing the numbers in such a way will cut the job in half.

Tip 2: Divide the table into “Chunks”

It is really hard to remember the whole table at once. So, divide the table into chunks and memorize it.

1. Start learning the multiplication tables with 5
2. Now, learn the multiplication numbers up to 9 times 5.
3. Learn the multiplications which you use them more and also learn simple tables like 2,3,4 etc.
4. Also, learn the numbers which multiply with the repeated numbers like 5 * 5, 7 * 7, 8 * 8 etc.

Some Patterns   

There are a few patterns that help you to remember some patterns.

2x is nothing but doubling the number. It is nothing but adding the number to itself.

Therefore, the pattern is 2,4,6,8,10…

5x comes with the pattern of ending with 0 or 5.

Therefore, the pattern is 5,10,15,20,25,30

9x comes with the pattern of “ones” place going down and “tens” place going up.

Therefore, the pattern is 9, 18, 27, 36, 45, 54, 63…

10x is the easiest way to remember. You just need to add zero to the number before it.

Therefore, the pattern is 10,20,30,40,50,60…

The Hard Ones

The hard ones are 6 * 7 = 42, 6 * 8 = 48, 7 * 8 = 56

Better you often say it in your mind and remember them.

Importance of Multiplication Tables

Being reliant on one’s memory is much brighter than something else. If you remember the multiplication chart, you will get the feeling of self-confidence. With the help of the multiplication table, you can keep the information at the fingertips to use it whenever required. It increases the memory power and stimulates the calculation speed. Students who master the multiplication tables from 2 to 20 can know the method of holding and observing things.

Tables from 2 to 10 are basic and fundamental, it helps in the calculation of simple arithmetic operations. Quick computation and a great deal of time are the major advantages of mastering multiplication charts.

Solved Examples involving Multiplication Table of 20

Problem 1:

There are 3 monkeys. Each monkey has 20 bananas. How many bananas are there in total?

Solution:

As given in the question,

No of monkeys = 3

No of bananas each monkey has = 20

To find the total number of bananas, we have to apply the law of multiplication.

Therefore, the total number of bananas = 3 * 20 = 60

Thus, all the monkeys have 60 bananas in total.

Hence, the final solution is 60 bananas.

Problem 2:

The first squirrel has 134 nuts. The second squirrel has 20 times as many nuts as the first squirrel. How many nuts does a second squirrel have?

Solution:

As given in the question,

No of nuts, the first squirrel has = 134

No of times the second squirrel has = 20

To find the no of nuts the second squirrel has, we have to apply the law of multiplication

Therefore, the nuts that the second squirrel has = 134 * 20

= 2680

Thus, the second squirrel has 2680 nuts

Hence, the final solution is 2680 nuts

Problem 3:

To find out the cost of the stolen diamonds, multiply the cost of one diamond with the total number of diamonds stolen.

Solution:

As given in the question,

Cost of one diamond = Rs. 16000

Total number of diamonds stolen: 20

Total worth of stolen diamonds = 20 * Rs 16000 = Rs. 3,20,000

Thus, the final solution is 3,20,000 Rupees