Division of a Whole Number by a Fraction

We will discuss here about division of a whole number by a fraction.

Look at the collection of circles. It has 8 circles.

Collection of Circles

How many two’s are there in 8?

How many two’s are there in 8? So we find there are 4 two in 8.

Now what does the following statement mean?

How many halves are there in 8? To find this, let us divide each of the 8 circles into halves.

Circles into Halves

We find there are 16 halves in 8

So, the answer is 8 ÷ ½ = 16

i.e. = 8 ÷ ½ = 8 × 2/1 = 8 × 2/1 = 16

Therefore, the rules for the division of a whole number by a fractional number is

Whole Number ÷ Fraction = Whole Number × Reciprocal of Fraction.

Hence, we conclude that to divide whole number by a fractional number, we multiply the whole number by multiplicative inverse of the fractional number.

Note: Wherever mixed numbers are used first change them into improper fractions.

For Example:

1. 4 ÷ 1/3

[We know, Whole Number × Reciprocal of Fraction]

Reciprocal of Fraction of ‘1/3’ is ‘3’

= 4 × 3

= 12



2. 16 ÷ 2/5

Reciprocal of Fraction of ‘2/5’ is ‘5/2’

= 16 × 5/2

= (16 × 5)/2

Division of a Whole Number by a Fraction




= 8 × 5

= 40



3. 24 ÷ 1 3/5

= 24 ÷ (1 × 5 + 3)/5

= 24 ÷ 8/5

Reciprocal of Fraction of ‘8/5’ is ‘5/8’

= 24 × 5/8




= 3 × 5

= 15



4. 49 ÷ 7/3

Reciprocal of Fraction of ‘7/3’ is ‘3/7’

= 49 × 3/7




= 7 × 3

= 21



5. 11 9/9 ÷ 12/7

= (11 × 9 + 9)/9 ÷ 12/7

= 108/9 ÷ 12/7

Reciprocal of Fraction of ‘12/7’ is ‘7/12’

= 108/9 × 7/12





= 7



6. 91 ÷ 91/34

Reciprocal of Fraction of ‘91/34’ is ‘34/91’

= 91 × 34/91




= 34

Multiplication is Repeated Addition.

Multiplication of Fractional Number by a Whole Number.

Multiplication of a Fraction by Fraction.

Properties of Multiplication of Fractional Numbers.

Multiplicative Inverse.

Worksheet on Multiplication on Fraction.

Division of a Fraction by a Whole Number.

Division of a Fractional Number.

Division of a Whole Number by a Fraction.

Properties of Fractional Division.

Worksheet on Division of Fractions.

Simplification of Fractions.

Worksheet on Simplification of Fractions.

Word Problems on Fraction.

Worksheet on Word Problems on Fractions.




5th Grade Numbers Page

5th Grade Math Problems

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


New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.



Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



Share this page: What’s this?

Recent Articles

  1. Fraction as a Part of Collection | Pictures of Fraction | Fractional

    Feb 24, 24 04:33 PM

    Pictures of Fraction
    How to find fraction as a part of collection? Let there be 14 rectangles forming a box or rectangle. Thus, it can be said that there is a collection of 14 rectangles, 2 rectangles in each row. If it i…

    Read More

  2. Fraction of a Whole Numbers | Fractional Number |Examples with Picture

    Feb 24, 24 04:11 PM

    A Collection of Apples
    Fraction of a whole numbers are explained here with 4 following examples. There are three shapes: (a) circle-shape (b) rectangle-shape and (c) square-shape. Each one is divided into 4 equal parts. One…

    Read More

  3. Identification of the Parts of a Fraction | Fractional Numbers | Parts

    Feb 24, 24 04:10 PM

    Fractional Parts
    We will discuss here about the identification of the parts of a fraction. We know fraction means part of something. Fraction tells us, into how many parts a whole has been

    Read More

  4. Numerator and Denominator of a Fraction | Numerator of the Fraction

    Feb 24, 24 04:09 PM

    What are the numerator and denominator of a fraction? We have already learnt that a fraction is written with two numbers arranged one over the other and separated by a line.

    Read More

  5. Roman Numerals | System of Numbers | Symbol of Roman Numerals |Numbers

    Feb 24, 24 10:59 AM

    List of Roman Numerals Chart
    How to read and write roman numerals? Hundreds of year ago, the Romans had a system of numbers which had only seven symbols. Each symbol had a different value and there was no symbol for 0. The symbol…

    Read More