OPERATIONS

Working Backwards

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

1 · WHAT YOU NEED TO KNOW

The idea

Working backwards starts from the final value and reverses each step.

Picture itPlan, solve, then check
2 · THE METHOD

Follow these steps

  1. List the original operations in order.
  2. Begin with the final value.
  3. Apply inverse operations in reverse order, then check forwards.
3 · WORKED EXAMPLES

See the method in action

Example 1

A number is multiplied by 3, then 5 is added. The result is 32. What was the starting number?

  1. Reverse the steps: 32 − 5 = 27; then 27 ÷ 3 = 9.
Answer: 9
Example 2

5 equal boxes contained the same number of counters. After 18 counters were removed, 477 remained. How many were originally in each box?

  1. Restore the 18: 477 + 18 = 495.
  2. Divide by 5: 495 ÷ 5 = 99.
Answer: 99
4 · ELEVENSPRINT TIP

A useful shortcut

Apply inverse operations in reverse order, then check forwards.

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.