11+ Balance Equations Practice
(GL Assessment)

Balance equation questions bring a flash of arithmetic into the GL Assessment 11+ Verbal Reasoning paper. Your child is given a sum with a missing number inside brackets, and they have to work out the value that makes both sides equal. A question such as "9 + 6 = 5 times the gap" is solved by finding the left side, which is 15, then asking what times 5 makes 15, which is 3.

This is part of the numerical reasoning strand that GL threads through Verbal Reasoning. GL does not label this exact type by name, so we group it, in our research, with the number-based VR questions, and our estimate from analysing practice papers is that numerical reasoning of this kind accounts for somewhere around 8 to 12 per cent of a paper. As with everything else in the paper, answers are multiple choice with five options (A to E) on a separate answer sheet. The mental skill being tested is solid: read both sides, calculate the fixed side, then reverse the remaining operation to find the gap.

On this page your child practises the genuine format, with the equation laid out clearly and five number options to choose from. Each explanation follows the same dependable three steps: work out the side you can, restate the equation, then solve the small piece that remains. Where the harder questions need the order of operations, the explanation makes the BODMAS step explicit.

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What the GL 11+ Tests on Balance Equations

These questions stay within familiar arithmetic, but the demands grow. GL does not publish a breakdown, so the points below are our research estimate of what raises the difficulty:

  • Single-operation balances (one calculation on each side, such as "12 minus 4 equals 2 times the gap")
  • The four operations (addition, subtraction, multiplication and division all appear on either side)
  • Missing number on the right (the bracket sits after the operator, as in "equals 5 times the gap")
  • Missing number on the left (the bracket comes first, as in "the gap plus 2 equals 7")
  • Order of operations (BODMAS), where one side has two steps and the multiply or divide must be done first
  • Larger numbers and tighter answer options that punish a careless calculation

Difficulty rises from a single operation on each side with small numbers, up to two-step sides that require BODMAS, where doing the operations in the wrong order produces a tempting but wrong answer.

Sample Balance Equations Questions

Five questions drawn from PrepStep’s balance equations bank, spanning Foundation to Challenging. Tap “Show worked explanation” to see the full method after you’ve had a go. The correct answer is highlighted on each question so you can check immediately.

Question 1 Foundation

Solve the equation:

3 + 7 = 20 ÷ ( )

  1. 2✓
  2. 3
  3. 1
  4. 10
  5. 20
Show worked explanation

Step 1: Work out the left side: 3 + 7 = 10. Step 2: The equation now reads 10 = 20 ÷ ( ). Step 3: Ask 'what divides 20 to give 10?' — that's 2. So ( ) = 2. ✓

Question 2 Foundation

Solve the equation:

14 − 8 = 18 ÷ ( )

  1. 2
  2. 4
  3. 6
  4. 9
  5. 3✓
Show worked explanation

Step 1: Work out the left side: 14 − 8 = 6. Step 2: The equation now reads 6 = 18 ÷ ( ). Step 3: Ask 'what divides 18 to give 6?' — that's 3. So ( ) = 3. ✓

Question 3 Intermediate

Solve the equation:

30 ÷ 5 + 12 = 2 × ( )

  1. 9✓
  2. 8
  3. 21
  4. 18
  5. 10
Show worked explanation

Step 1: BODMAS — divide first: 30 ÷ 5 = 6, then 6 + 12 = 18. Step 2: The equation now reads 18 = 2 × ( ). Step 3: Ask 'what times 2 makes 18?' — that's 9. So ( ) = 9. ✓

Question 4 Intermediate

Solve the equation:

5 × 4 + 8 = 4 × ( )

  1. 6
  2. 8
  3. 5
  4. 7✓
  5. 28
Show worked explanation

Step 1: BODMAS — multiply first: 5 × 4 = 20, then 20 + 8 = 28. Step 2: The equation now reads 28 = 4 × ( ). Step 3: Ask 'what times 4 makes 28?' — that's 7. So ( ) = 7. ✓

Question 5 Challenging

Solve the equation:

12 ÷ 4 × 6 = 2 × ( )

  1. 9✓
  2. 8
  3. 18
  4. 12
  5. 10
Show worked explanation

Step 1: BODMAS — divide and multiply left to right: 12 ÷ 4 = 3, then 3 × 6 = 18. Step 2: The equation now reads 18 = 2 × ( ). Step 3: Ask 'what times 2 makes 18?' — that's 9. So ( ) = 9. ✓

Common Mistakes to Avoid

Common mistake 1 of 4

Ignoring the order of operations.

Tip: When one side has two steps, such as "30 divided by 5 plus 12", the multiply or divide must come before the add or subtract. Teach your child to underline the multiply or divide and do it first, because working left to right gives the wrong total.

Common mistake 2 of 4

Solving the wrong side first.

Tip: The smart move is to fully calculate the side that has no missing number, then balance against it. A child who tries to work with the bracketed side first often gets tangled. Find the fixed value, then reverse the operation to fill the gap.

Common mistake 3 of 4

Choosing the value of the fixed side instead of the gap.

Tip: If the left side comes to 15, a child may pick 15 from the options rather than the number that goes in the bracket. The fixed total is usually planted among the choices as a trap, so your child must answer the actual question, which is the missing number.

Common mistake 4 of 4

Rushing the final reverse step.

Tip: Once the equation reads, for example, "15 equals 5 times the gap", the answer is found by dividing, not multiplying. Encourage your child to say the reverse step in words ("what times 5 makes 15?") so the right operation is obvious.

Frequently Asked Questions

What are balance equation questions in the GL 11+ Verbal Reasoning exam?

They are arithmetic questions with a missing number inside brackets, where your child finds the value that makes both sides of the equation equal. For example, "9 + 6 = 5 times the gap" is solved by working out 15, then finding what times 5 makes 15, which is 3. They test mental calculation and the order of operations within the numerical part of Verbal Reasoning.

How are balance equations tested in the GL 11+ exam?

Through multiple choice with five number options (A to E) on a separate answer sheet. The equation is printed clearly with the gap shown in brackets, and the missing number can sit on either side. Harder questions place two operations on one side, so the order of operations matters.

Do these questions need BODMAS?

The harder ones do. When one side has two steps, such as "20 minus 2 times 7", the multiplication is done before the subtraction, giving 6 rather than 126. Getting the order right is the single most common dividing line between a correct and an incorrect answer on the tougher balance equations.

Why does my child pick the wrong option when their working is right?

Most often they answer with the value of the fixed side instead of the missing number in the bracket, because that total is usually planted among the choices. The remedy is to reread the question after calculating and confirm they are giving the number that fills the gap, not the side they worked out on the way.

How can my child improve at balance equations for the 11+?

A steady three-step routine, calculate the fixed side, restate the equation, then reverse the last operation, makes these reliable marks, and it is built through regular short practice rather than occasional bursts. Free PrepStep practice gives one equation at a time with five options and an explanation that walks through each step, including the BODMAS move where it is needed.

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PrepStep has 30 balance equations questions in GL Assessment format: five options, instant feedback, and step-by-step explanations. Free to start.

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