PROBLEM SOLVING

Four Operations

Learn the reliable method for four operations, then apply it to 11+ exam-style questions.

1 · WHAT YOU NEED TO KNOW

The idea

Four-operation problems require choosing the operation from the relationship, not a keyword.

Picture itPlan, solve, then check
Bowls, fruit, scales and a measuring jug showing ratio and measurement in baking
2 · THE METHOD

Follow these steps

  1. Identify what each quantity represents.
  2. Choose addition, subtraction, multiplication or division for each relationship.
  3. Calculate in the required order and check with estimation or inverse operations.
3 · WORKED EXAMPLES

See the method in action

Example 1

There are 3 bags with 6 counters in each bag and 2 loose counters. How many counters are there altogether?

  1. The bags contain 3 × 6 = 18 counters.
  2. Add the 2 loose counters: 18 + 2 = 20.
Answer: 20
Example 2

Add 3/4 and 3/8, divide the result by 3/16, then subtract 3. What is the exact answer?

  1. First, 3/4 + 3/8 = 9/8.
  2. Dividing by 3/16 means multiplying by 16/3, giving 6.
  3. Finally, 6 − 3 = 3.
Answer: 3
4 · ELEVENSPRINT TIP

A useful shortcut

Calculate in the required order and check with estimation or inverse operations.

5 · COMMON MISTAKES

Watch out for these

6 · TRY IT YOURSELF

Three fresh questions

Ready to check the method? You will get three fresh, validated questions.