To divide fractions by whole numbers or whole numbers by fractions: 1) Write the division as a fraction divided by a whole number or vice versa. 2) Change the division sign to a multiplication sign and multiply by the reciprocal of the divisor. 3) Simplify the resulting fraction by multiplying the numerators and denominators. For example, to divide 11/8 by 2: 11/8 ÷ 2 becomes 11/8 × 1/2 = 11/16.

1. Multiplication And
Division Of Fractions
And Whole Numbers

2. Opening Prayer

3. What is multiplying a
fraction and a whole
number?
When a whole number is divided by a fraction,
the number of groups of the fraction that fit
inside the whole is determined. Multiplying the
given whole number by the reciprocal fraction is
the most popular way to divide whole numbers
by fractions.

4. Dividing Fractions
with Whole
Numbers
In the general form, it can be understood as,
x/y ÷ a = x/ya, where x/y is the fraction and 'a' is
any whole number.

5. Steps of Dividing
Fractions with Whole
Numbers
• Dividing fractions with whole numbers
results in a value less than the given fraction.
• Example: 2/3 into 4 equal parts.
• So, 2/3 ÷ 4 = 2/3 × 1/4 = 2/12 = 1/6.
• Here, you can observe that 1/6 < 2/3.

7. Fractions by Whole
Numbers?
• To divide fractions by
whole numbers, one
should be aware of the
concept of reciprocal.

8. How to Divide
Fractions by Whole
Numbers?
• Step 1: Write the division fact as dividend ÷ divisor, where
the given fraction will be the dividend and the given whole
number will be the divisor.
• Step 2: Change the division sign into multiplication and
write the reciprocal of the divisor (whole number).
• Step 3: Find the product by multiplying numerator with
numerator and denominator with denominator. That will
be the required answer.

9. EXAMPLE
let us divide 11/8 by 2.
• Step 1: 11/8 ÷ 2
• Step 2: 11/8 × 1/2 (as the reciprocal of 2 is 1/2)
• Step 3: 11/8 × 1/2 = 11/16.
• Therefore, 11/8 ÷ 2 = 11/16.

11. Division of Whole Number by
Fraction
Step 1: Find the reciprocal of the given fraction.
Step 2: Multiply the reciprocal with the given
whole number. The product will be required
answer.
For example, to divide 3 by 2/5, we just need to
multiply 3 by 5/2 (reciprocal of 2/5). This implies,
3 × 5/2 = 15/2.

12. Dividing Fractions with
Whole Numbers
Examples
Example 1: Divide 1/9 by 7.
Solution: To divide 1/9 by 7, we will use the steps for
dividing fractions with whole numbers. First, we will
write it as a division fact 1/9 ÷ 7. Now change the
division sign with the multiplication sign and replace 7
by its reciprocal. The reciprocal of 7 is 1/7. So we get
1/9 × 1/7 = 1/63. Therefore, 1/9 ÷ 7 = 1/63.

13. Dividing Fractions with
Whole Numbers
Examples
Example 2: Sergio wants to cut the 5/3rd portion of a strip into
8 equal parts. What will be the fraction of each piece after this
division?
Solution: If Sergio will cut 5/3 portion into 8, it means we need to divide
5/3 by 8. The concept of dividing fractions with whole numbers needs to
be applied.
⇒ 5/3 ÷ 8
⇒ 5/3 ×1/8
= 5/24
Therefore, the fraction of each piece will be 5/24.

14. Dividing Fractions with
Whole Numbers
Examples
Example 3: What will be the value
obtained when 20 is divided by 1/20?
Solution: For the division of a whole number by
a fraction, we need to multiply the reciprocal of
the fraction by the whole number. The
reciprocal of 1/20 is 20. This implies, 20 × 20 =
400. Therefore, 20 ÷ 1/20 = 400.

15. LET’S PRACTICE!

16. Q.1. Mark the correct
answer.
Divide 10/17 by 10.
a. 17
b. 170
c. 100/17
d. 1/17
Correct Answer: D

17. Q.2. What will be
the value obtained
if we divide 1/100
by 100?
a. 1
b. 1/10000
c. 10000
d. 1/100
Correct Answer: B

18. What is the Rule for Dividing
Fractions with Whole Numbers?
The rule for dividing fractions by
whole numbers is that we need to
multiply the reciprocal of the whole
number to the given fraction. By
this simple rule, we can solve any
problem based on this concept.

19. How do you Divide a Whole
Number by a Fraction 5th Grade?
For dividing whole numbers with
fractions, we need to multiply the
reciprocal of the fraction with the
whole number. In mathematics, this
concept is generally learnt in grade 5
when learners get to know about the
division of fractions.

21. THANK YOU!