Fractions — multi-step expressions (grade 7)

Fractions — multi-step expressions (grade 7)

Multi-step expressions with fractions

In grade 6 you learned each of the four fraction operations separately. In grade 7 we combine them in a single expression — and suddenly the order matters.

The order of operations holds for fractions too

1. Parentheses — solve what is inside the parentheses first.

2. × and ÷ — left to right.

3. + and − — left to right.

Exactly the same rule as for whole numbers. The only difference: the operands are fractions.

Worked examples

Example 1 — × and + without parentheses

1/2 + 1/3 × 3/4

Multiplication first: `1/3 × 3/4 = 3/12 = 1/4`. Then addition: `1/2 + 1/4 = 2/4 + 1/4 = 3/4`.

Example 2 — parentheses change the order

(1/2 + 1/3) × 3/4

Parentheses first: `1/2 + 1/3 = 3/6 + 2/6 = 5/6`. Then multiplication: `5/6 × 3/4 = 15/24 = 5/8`.

Notice — the parentheses changed the result from 3/4 to 5/8.

Example 3 — dividing a fraction by a fraction

2/3 ÷ (1/2 − 1/6)

Parentheses first: `1/2 − 1/6 = 3/6 − 1/6 = 2/6 = 1/3`. Then division: `2/3 ÷ 1/3 = 2/3 × 3/1 = 6/3 = 2`.

Tips

  • Addition/subtraction: rewrite to a common denominator first, then + or −.
  • Multiplication: multiply numerators, multiply denominators, simplify.
  • Division: multiply by the reciprocal of the second fraction, then proceed as in multiplication.
  • Always simplify the final result to lowest terms.

Try it yourself