# 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

• ### Word Problems on H.C.F. and L.C.M. | Highest Common Factor | Lowest Co

We have already learnt H.C.F, L.C.M and the relationship between the two and now we will learn on how to do word problems on H.C.F. and L.C.M. Note: In word problems on H.C.F. and L.C.M we have to remember two points: • When we are asked to find out maximum, highest

• ### Worksheet on H.C.F. and L.C.M. | HCF × LCM = 1st Number × 2nd Number

This topic will provide worksheet to students on H.C.F and L.C.M which will help to judge themselves their level of understanding of the topic and the areas where they need more careful study and analysis. This worksheet will serve as a yardstick for measuring the level of

• ### Relationship between H.C.F. and L.C.M. |HCF× LCM=1st Number×2nd Number

This topic discusses about the relationship between H.C.F and L.C.M in case of two numbers. The relationship between H.C.F and L.C. M of two number states that: H.C.F × L.C.M = First number × Second number Hence from this relationship we can find the following: H.C.F

• ### Examples to Find Least Common Multiple of Three Numbers by using Divis

This topic would provide examples on how to find least common multiple of three numbers. Various examples on finding L.C.M would help the learners in understanding the topic better. Here are few examples illustrated on finding the least common multiple of three numbers using

• ### To Find Lowest Common Multiple by using Division Method | Examples

This topic discusses about finding the lowest common multiple using division method. Steps to find the loqest common multiple using the division method: Step 1: Write the numbers in a row separating by commas Step 2: Then divide the given numbers (if possible both the

• ### Examples to Find Least Common Multiple of Two Numbers |Division Method

This topic would provide examples to find least common factor by using division method. This topic will help learners to clear their doubts and improve their understanding and knowledge on how to find out least common multiple (L.C.M) by division method.

• ### Examples to find Least Common Multiple by using Prime Factorization

This topic would provide various examples on finding the least common multiple using the method of prime factorization. Here are few examples illustrated on finding the least common multiple using the prime factorization method. 1. Find the least common multiple (L.C.M) of

• ### To Find Least Common Multiple by using Prime Factorization Method

This topic would discuss about how to find the least common multiple by using prime factorization method. Steps to find out the least common multiple by using prime factorization method: •First find all the prime factors of the given number .Then write all the prime factors

• ### Least Common Multiple (L.C.M.) | Lowest Common Multiple | Examples

In the last topic we have discussed about common multiples that is same multiples of two or more numbers. Now here we will discuss about the least common multiple that is the smallest common multiple of two or more numbers. Here are few examples illustrated on least common

• ### Common Multiples | What is Common Multiples? | Three Common Multiples

This topic would deal with common multiples. If some of the multiples of two or more number are same then those same multiples are termed as common multiples. Here are few examples illustrating common multiples: List the two common multiples of 5 and 6

• ### Multiples | Important Facts about Multiple | Even and Odd Multiples

This topic would deal with multiples. Multiples of a number are actually the tables of a certain number. If we are talking about multiple of 2 then it is actually the tables of 2. When we have learnt table we have learnt the tables till 10 or 12 that is till 2 multiplied

• ### Highest Common Factor of Three Numbers by using Division Method

This topic would discuss about finding highest common factor using the division method. We have already learnt finding the highest common factor by prime factorization method but it is not suitable when we are dealing with large numbers. Division method is quite convenient

• ### Find Highest Common Factor of Two Numbers by using Division Method

We have already learnt the method of finding highest common factor using division method. Here are few more examples given to clear your understanding, concepts and improve your knowledge on how to find H.C.F. this topic would provide a wide range of examples will help the

• ### To Find Highest Common Factor by using Division Method | Examples

This topic would discuss about finding the highest common factor of three numbers using the division method. We have learnt in our last topic about finding the highest common factor of two numbers. While doing with three numbers first we will find the highest common factor

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