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.

Balance Equations vs Number Series, Letter Pair Series and Letter Sums: How to Tell Them Apart

These four are the number-handling side of verbal reasoning. Number series and letter pair series both continue a pattern, one with numbers and one with letters. Letter sums and balance equations are pure arithmetic: one adds up letter values, the other finds a missing number that keeps an equation balanced.

Comparing Balance Equations, Number Series, Letter Pair Series and Letter Sums
Question type What it tests What it looks like The classic mix-up
Balance EquationsThis page Whether your child can find the missing number that makes both sides of an equation equal. A number sentence with a gap; your child works out the value that balances both sides. For example, "3 + 7 = 20 ÷ ?" gives 2. Treating it like letter sums and swapping in alphabet values, when balance equations use ordinary numbers only.
Number Series Whether your child can spot the rule linking a run of numbers and give the next one. A line of numbers with the last one missing; your child finds the step or pattern and continues it. For example, "4, 9, 14, 19, ?" gives 24. Confusing it with letter pair series and expecting letters, when this pattern runs on numbers alone.
Letter Pair Series Whether your child can continue a sequence of letter pairs by tracking each letter's move through the alphabet. Pairs of letters that step through the alphabet; your child finds the next pair. For example, "AB, CD, EF, ?" gives "GH". Treating it like letter sums and adding the letters, when they form a moving sequence to continue, not a total.
Letter Sums Whether your child can turn letters into their alphabet positions and add, subtract or compare the totals. Letters stand for their place in the alphabet, A is 1 up to Z is 26, and your child does the sum. For example, "C + E = 8". Confusing it with balance equations and hunting for a missing number, when here the letters give the numbers to add.

If you are continuing a run of numbers it is number series, and a run of letter pairs it is letter pair series; if you are adding letter values it is letter sums, and filling a missing number in a sum it is balance equations.

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.

About these questions

Every PrepStep 11+ question is original, written to mirror the style and difficulty of the GL Assessment 11+ and grounded in a library of real past-paper patterns, with a worked explanation for each one. PrepStep is built by Ben Jackson, its founder and a parent who has taken one child through the 11+ with another preparing now. Last reviewed: August 2026.

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.

What is the difference between number series, letter pair series and letter sums in the 11+?

They look similar because letters and numbers appear together, but the task differs. Number series asks your child to continue a run of numbers by finding the rule. Letter pair series asks them to continue a run of letter pairs, tracking how each letter moves through the alphabet. Letter sums asks them to swap each letter for its alphabet position, A is 1 up to Z is 26, then adds the totals. One continues a pattern; the other totals letters.

Explore the other GL Assessment verbal reasoning topics, each with free sample questions and worked explanations.

All verbal reasoning topics Synonyms Antonyms Verbal Analogies Odd Two Out Compound Words Hidden Words Move a Letter Missing Letters Letter Codes Letter Pair Series Number Series Letter Sums Word Code Analogies Number Word Codes Logic and Language Shared Letter Free 11+ practice papers & tests All GL question types explained

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