# Division of a Whole Number by a Fraction

This topic discusses about division of a whole number by a fraction. In this we have to divide the whole number that is positive integers including zero by a fractional number. When dividing a whole number by a fraction we actually multiply the whole number by the multiplicative inverse or reciprocal of the fraction. After that the steps are same as we do in multiplication. That is the numerator is multiplied by another numerator and denominator by another denominator that is Product of the numerators/ product of the denominators. Then the answer is changed into lowest terms (if possible) and the final answer is expressed in mixed fraction (if it is an improper fraction) or in proper fraction.

Here are few examples to illustrate division of whole numbers by a fraction:

1. 250 ÷ 50/8

= 250 × 8/50 [reciprocal of 50/8]

= (250 × 8)/50 [Product of numerators and denominator]

= 2000/50

= (2000 ÷ 50)/(50 ÷50) [Changing into lowest terms]

= 40

2. 343 ÷ 49/3

= 343 × 3/49 [Reciprocal of 49/3]

= (343 × 3)/49 [Product of numerators and denominator]

= 1029/49

= (1029 ÷ 49)/(49 ÷49) [Changing into lowest terms]

= 21

3. 156 ÷ 8/3

= 156 × 3/8 [Reciprocal of  8/3]

= (156 × 3)/8 [Product of numerators and denominator]

= 468/8

= (468 ÷ 4)/(8 ÷4) [Changing into lowest terms]

= 117/2

= 58 1/2

4. 16 ÷ 4/3

= 16 × 3/4 [Reciprocal of  4/3]

= (16 × 3)/4 [Product of numerators and denominator]

= 48/4

= (48 ÷4)/(4 ÷4) [Changing into lowest terms]

= 12

5. 96 ÷ 6/5

= 96 × 5/6 [Reciprocal of  6/5]

= (96 × 5)/6 [Product of numerators and denominator]

= 480/6

= (480 ÷6)/(6 ÷6) [Changing into lowest terms]

= 80

6. 108 ÷ 9/12

= 108 × 12/9 [Reciprocal of  9/12]

= (108 × 12)/9 [Product of numerators and denominator]

= 1296/9

= (1296 ÷9)/(9 ÷9) [Changing into lowest terms]

= 144

7. 324 ÷ 36/12

= 324 × 12/36 [Reciprocal of  36/12]

= (324 × 12)/36 [Product of numerators and denominator]

= 3888/36

= (3888 ÷ 36)/(36 ÷ 36) [Changing into lowest terms]

= 108

8. 256 ÷ 18/12

= 256 × 12/18 [Reciprocal of  18/12]

= (256 × 12)/18 [Product of numerators and denominator]

= 3072/18

= (3072 ÷ 6)/(18 ÷ 6) [Changing into lowest terms]

= 512/3

It is an improper fraction hence should be changed into mixed fraction

= 170 2/3

9. 1424 ÷ 15/3

= 1424 × 3/15 [Reciprocal of  15/3]

= (1424 × 3)/15 [Product of numerators and denominator]

= 4272/15

= (4272 ÷ 3)/(15 ÷ 3) [Changing into lowest terms]

= 1424/5

It is an improper fraction hence should be changed into mixed fraction

= 284 4/5

## You might like these

• ### Ribosomes and Inclusion Bodies | Definition | Stored Food | Pigments

Definition of ribosome- Ribosome is the organelles which is associated with protein synthesis. It is made up of two subunits. The larger one is spherical in shape and the smaller one is oval in shape. Ribosomes are attached with the endoplasmic reticulum and formed rough

• ### Worksheet on Divisibility Rules | Questions on Test of Divisibility

This is a worksheet which will provide few problems on the divisibility rule of 2, 3, 4, 5, 6, 7, 8, 9, and 10. 1. Check whether the following numbers are divisible by 2 or 3 or both? (i) 2562 (ii) 5693 (iii) 2201 (iv) 7480 (v) 5296 (vi) 4062 (vii) 4568 (viii) 1425 (ix) 1110

• ### Problems on Divisibility Rules | Rules to Test of Divisibility | Test

Here are few problems on the divisibility rules of 2, 3, 4, 5, 6, 7, 8, 9, and 10 which will help the learners in revising their concepts on the divisibility rules. 1. Check whether 3456 is divisible by 2? Solution: The last digit is an even number (i.e. 6) hence 3456 is

• ### Divisible by 10|Test of Divisibility by 10|Rules of Divisibility by 10

The divisibility rule of 10 states that If the last digit of a number is 0 then the given number is divisible by 10. For eg: Check whether 5400 is divisible by 10 or not? Solution: As the last digit of the number is 0 hence, 5400 is divisible by 10

• ### Divisible by 9 | Test of Divisibility by 9 |Rules of Divisibility by 9

This rule states that a number is divisible by 9 if the sum of its digits of the number is divisible by 9 For eg: Check whether 729 is divisible by 9 or not? Sum of the digits = 7 + 2 + 9 = 18 Now 18 is divisible by 9 hence, 729 is also divisible by 9 Here are few examples

• ### Divisible by 8 | Test of Divisibility by 8 |Rules of Divisibility by 8

The most common method to check whether a number is divisible by 8 is to divide and see if the quotient is a whole number or not? If the quotient is a whole number then the given number is divisible by 8. But there is an easier way to check by using the divisibility rule.

• ### Divisible by 7 | Test of Divisibility by 7 |Rules of Divisibility by 7

This rule states that if the difference between twice the digit at units place and the number formed from the remaining digits of the given number is divisible by 7 then the whole number is divisible by 7.

• ### Divisible by 6 | Test of divisibility by 6 |Rules of Divisibility by 6

This topic on divisible by 6 will discuss about the divisibility rule of 6 and few example on the same. Divisibility rule of 6: A number is divisible by 6 if the prime factor of that is 2 & 3 is divisible by 6. For Example: 216 216 is divisible by 2 as the last digit 6 is

• ### Divisible by 5 | Test of divisibility by 5 |Rules of Divisibility by 5

This topic on divisible by 5 will discuss on the divisibility rule of 5 and illustrate few example on the same. Divisibility Rule of 5: If a number ends with 0 or 5 then the number is divisible by 5. For Example: 550 Since the number ends with 0 hence the number is divisible

• ### Divisible by 4 | Rules of Divisibility by 4|Divisibility Rules & Tests

This topic i on divisibility rule of 4 and will provide examples on the same. Divisibility Rule of 4: If the last two digits of the number is divisible by 4 then the whole number is divisible by 4 For eg: 524 The last two digit of the number is 24 which is divisible by 4.

• ### Divisible by 3 | Rules of Divisibility by 3|Divisibility Rules & Tests

This topic is on the divisibility rule of 3 and few examples based on the topic. If the sum of the digits is divisible by 3 then the whole number is divisible by 3. For example 519 The sum of the digits = 5 + 1 + 9 = 15 15 is divisible by 3 hence 519 is also divisible by 3

• ### Divisible by 2 | Divisibility Rule of 2 | Test of Divisibility by 2

This topic would deal with the divisibility rule of 2 and few sums on divisibility rule of 2. Numbers that are ending with 0, 2, 4, 6, and 8 are divisible by 2. That means numbers ending with 0 or multiples of 2 are divisible by 2. We know that numbers which are multiples of

• ### Properties of Divisibility | Divisibility Property |Divisibility Rules

This topic deals with the properties of divisibility which will help us in doing our multiplication and division easy. These rules will help us to determine quickly the factors of certain number, the divisibility criteria of certain number and helps in overall strengthening

• ### Worksheet on Multiples and Factors | List the First Five Multiples

1. List the first five multiples of the following numbers: 2. Choose the numbers that are factors of 24. 3. 3. Choose the numbers that are multiples of 15. 4. Choose the numbers which are multiple of 3 as well as factor of 36

From Division of a Whole Number by a Fraction to HOME PAGE