How to Divide Fractions by Whole Numbers
Dividing fractions by whole numbers is straightforward once you understand the relationship between division and multiplication.
Step-by-Step Guide
-
Write the whole number as a fraction
Any whole number can be written as a fraction by putting it over 1.
For example, 4 becomes 41\frac{4}{1}14. -
Rewrite the division problem as multiplication
Dividing by a number is the same as multiplying by its reciprocal.
The reciprocal of a fraction is obtained by swapping its numerator and denominator.
For example, the reciprocal of 41\frac{4}{1}14 is 14\frac{1}{4}41. -
Multiply the fraction by the reciprocal of the whole number
If you have ab÷4\frac{a}{b}\div 4ba÷4, rewrite it as:
ab×14\frac{a}{b}\times \frac{1}{4}ba×41
- Multiply the numerators and denominators
Multiply the top numbers together and the bottom numbers together:
a×1b×4=a4b\frac{a\times 1}{b\times 4}=\frac{a}{4b}b×4a×1=4ba
- Simplify the fraction if possible
Example
Divide 35\frac{3}{5}53 by 2.
- Write 2 as 21\frac{2}{1}12.
- Find the reciprocal of 21\frac{2}{1}12, which is 12\frac{1}{2}21.
- Multiply:
35×12=3×15×2=310\frac{3}{5}\times \frac{1}{2}=\frac{3\times 1}{5\times 2}=\frac{3}{10}53×21=5×23×1=103
So, 35÷2=310\frac{3}{5}\div 2=\frac{3}{10}53÷2=103.
Summary
Step| Action| Example
---|---|---
1| Write whole number as fraction| 2=212=\frac{2}{1}2=12
2| Find reciprocal of whole number| 12\frac{1}{2}21
3| Multiply fraction by reciprocal| 35×12\frac{3}{5}\times \frac{1}{2}53×21
4| Multiply numerators and denominators| 310\frac{3}{10}103
5| Simplify if needed| Already simplified
If you want, I can provide more examples or practice problems!
