PROBLEM SOLVING

Forming Expressions

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

1 · WHAT YOU NEED TO KNOW

The idea

Algebra uses letters to represent numbers and relationships.

Picture itFollow what happens to the unknown
2 · THE METHOD

Follow these steps

  1. Translate the rule or wording into an expression.
  2. Substitute known values carefully, using brackets for negative values.
  3. Simplify in the correct order and check the result against the original relationship.
3 · WORKED EXAMPLES

See the method in action

Example 1

There are 2 sets of counters, each holding x items, and 9 loose items. Which expression gives the total?

  1. One set contains 2x + 9 items.
  2. The variable items and loose items are added, giving 2x + 9.
Answer: 2x + 9
Example 2

Each set contains 7 sets of counters, each holding x items, plus 20 loose items. Which expression gives the number of items in 3 sets?

  1. One set contains 7x + 20 items.
  2. Multiply both terms by 3: 3(7x + 20) = 21x + 60.
Answer: 21x + 60
4 · ELEVENSPRINT TIP

A useful shortcut

Simplify in the correct order and check the result against the original relationship.

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.