Equalities & Inequalities — Practice Worksheet — Equalities & Inequalities: Balancing the Four Operations

Part A — Balancing equalities & inequalities

The equals sign does not mean "the answer comes next" — it means both sides have the same value. We can complete, check and build true number sentences using the four operations, brackets and the order of operations.

A balance scale with 7 plus 5 on the left pan and 15 minus 3 on the right pan, sitting level. — A true equality balances: both sides equal 12.

Complete the statement (make both sides equal)

Q1. 8 + 6 = 20 − Q2. 5 × 4 = + 8

Q3. 36 ÷ 4 = × 3 Q4. 15 − 7 = + 3

True or false? (Is it balanced?)

Q5. 9 + 3 = 4 × 3

Q6. 18 − 5 = 2 × 7

Q7. (6 + 4) × 2 = 6 + 4 × 2

Q8. 24 ÷ (2 + 2) = 24 ÷ 2 + 2

Brackets & order of operations

Q9. Work out: (a) 3 + 4 × 5 (b) (3 + 4) × 5 (c) 20 − (6 + 2) (d) 20 − 6 + 2

Q10. Place brackets to make this true: 4 + 2 × 3 = 18.

Answer:

Construct your own

Q11. Write an equality where one side uses subtraction and the other uses multiplication, both equal to 12.

Q12. Write an inequality comparing 7 × 3 and 5 × 4. Which is larger?