Part 4: Division

# 4.7: Dividing a decimal and a fraction

Notes

To divide a decimal number and a fraction, write the decimal as a fraction with a whole number as the numerator and a product of 10s as the denominator. For example:

- 0.48 ÷ 3/4
- = (48 / 100) ÷ (3 / 4)
*[whole number numerator, product of 10s denominator]* - = (48 / 100) x (4 / 3)
*[use 4.4: Dividing fractions]* - = 192 ÷ 300
*[use 3.3: Multiplying fractions]* - = 64 / 100
*[use 1.3: Simplifying fractions to have a product of 10s in the denominator]* - = 0.64

Here’s another example:

- 0.084 ÷ 1/3
- = (84 / 1000) ÷ (1 / 3)
- = (84 / 1000) x (3 / 1)
- = 252 / 1000
- = 0.252

Sometimes, it is easier to write the decimal as a fraction in simplest terms rather than with a whole number as the numerator and a product of 10s as the denominator. For example:

- 2/5 ÷ 1.25
- = (2 / 5) ÷ (5 / 4)
- = (2 / 5) x (4 / 5)
- = 8 / 25
- = 32 / 100
- = 0.32

Sometimes, it is more accurate to leave the answer as a fraction rather than a decimal. For example:

- 5/6 ÷ 2.5
- = (5 / 6) ÷ (5 / 2)
- = (5 / 6) x (2 / 5)
- = 10 / 30
- = 1 / 3

The video below works through some examples of dividing a decimal and a fraction.

Video Tips

Practice Exercises

Do the following exercises to practice dividing a decimal and a fraction.