Part 3: Multiplication

# 3.6: Multiplying a decimal and a fraction

Notes

To multiply a decimal number and a fraction together, 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 x 3/4
- = (48 / 100) x (3 / 4)
*[whole number numerator, product of 10s denominator]* - = (48 x 3) / (100 x 4)
*[use 3.3: Multiplying fractions to multiply numerators and denominators]* - = 144 / 400
*[use 3.1: Multiplying integers to calculate 48 x 3]* - = 36 / 100
*[use 1.3: Simplifying fractions to have a product of 10s in the denominator]* - = 0.36

Here’s another example:

- 0.084 x 1/3
- = (84 / 1000) x (1 / 3)
- = (84 x 1) / (1000 x 3)
- = 84 / 3000
- = 28 / 1000
- = 0.028

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 x 1.25
- = (2 / 5) x (5 / 4)
- = (2 x 5) / (5 x 4)
- = 10 / 20
- = 5 / 10
- = 0.5

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

- 5/6 x 0.4
- = (5 / 6) x (2 / 5)
- = (5 x 2) / (6 x 5)
- = 10 / 30
- = 1 / 3

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

Video Tips

Practice Exercises

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