Fractions · Grade 3

In Grade 3 you learn: thirds; unit fractions and non-unit fractions; fractions of amounts.

A fraction is a part of a whole that has been split into equal parts. The bottom number (the denominator) says how many equal parts there are; the top number (the numerator) says how many of those parts we mean. Fractions are everywhere: half-time, a quarter of an hour, a tank three-quarters full.

Key facts

  • The parts must be equal in size.
  • Denominator (bottom): how many equal parts. Numerator (top): how many parts we have.
  • To find a unit fraction of an amount, divide by the denominator: 1/4 of 20 = 20 ÷ 4 = 5.
  • To find any fraction of an amount, divide by the bottom, then multiply by the top: 3/4 of 20 = 15.
  • With the same top number, the bigger the bottom number, the smaller the fraction: 1/8 is less than 1/3.
  • Work backwards when you know a part: if 1/5 of a number is 7, the number is 7 × 5 = 35.

Worked examples

Example 1

What fraction of the bar is shaded?

Answer: 3/8

Example 2

Find 3/5 of 40.

Answer: 24

Example 3

2/5 of the seats on a bus are empty. 18 seats are empty. How many seats does the bus have?

Answer: 45

Other years