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:

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.

Practice Exercises

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