4.7: Dividing a decimal and a fraction

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.