3.6: Multiplying a decimal and a fraction

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.