Verbal Reasoning Complete the Sum
The SCALE method in four minutes — one real question, solved step by step.
A Complete the Sum question gives you two sums joined by an equals sign, with one number missing. You find the number that will complete the sum correctly, so both sides come out the same.
The equals sign does not mean "the answer comes next". It means "the same as". Think of it as the middle of a pair of scales. The two sides are the two pans, and they have to weigh the same.
The video above and the worked example below take apart the same question. One thing is different: the video shows the five options in another order, so the answer, 14, is lettered D in the video and may carry a different letter here. Same number, different place in the line-up.
The method
Five steps: solve the free side, call it the target, answer the part without the gap, level the scales, end by weighing both sides — and their first letters spell SCALE, because every sum like this is a pair of scales.
- Step 1 of 5
Solve the free side
That is the side with no gap in it. Work it out in full: that number is what the free side weighs. - Step 2 of 5
Call it the target
The other side must make it too. The target is what the side with the gap must weigh, not the missing number. - Step 3 of 5
Answer the part without the gap
On the side with the gap, work out the rest first. That number is only part of the side. - Step 4 of 5
Level the scales
Ask what the gap must take off, or add, so that side weighs the target. The sign before the gap tells you which. After a take away, the gap is the part take away the target. After an add, it is the target take away the part. - Step 5 of 5
End by weighing both sides
Put your number in the gap and work out each side again. Both sides must match. A near miss tips the scales.
About 30 seconds each.
Rules to watch
- The free side is on the left, and the gap comes last. In all seven of GL's practice questions, the left side has no gap, and the missing number is the last one in the sum, after a + or a −. So the gap only ever takes weight off or adds it on. Every one of our practice questions is built the same way.
Watch for these traps
We looked at all seven Complete the Sum questions in GL's practice papers, and at all 28 wrong answers.
- A sum gone wrong. The most common wrong answers are near misses, close to the right one. 13 of GL's 28 sit within two of it, and every question has some. One small slip, and a wrong number is waiting in the list. In the worked example, 12 and 16 sit either side of 14. Weighing both sides catches them, because a near miss tips the scales: 20 − 12 leaves 8, and 20 − 16 leaves 4, not 6.
- A number you worked out on the way. Sometimes the target, or part of a side, is offered too. In 7 × 8 − 6 = 9 × 5 + [?], the free side makes 50, and 9 × 5 makes 45. Both are offered, but the gap only has to add 5.
- A number you can see in the question. Sometimes a number is copied straight from the sum. In 6 × 7 = 50 − [?], 50 and 7 are printed in the sum, and both are offered. The answer is 8. If your answer is a number you can see, weigh both sides before you choose it.
Stuck? Put each option in the gap in turn and weigh both sides. Only one makes them level. Never leave a blank.
Try these yourself
Now have a go yourself — tap the number that makes both sides equal.
Related
- The complete 11+ question-type guide
- VR: Letters for Numbers — letters standing in for numbers
- VR: Number Series — spot the pattern and continue it
All example questions come from the Brainblox question bank — practise this question type inside 25+ learning games, timed mock exams and focused practice. Brainblox is an independent app: not affiliated with, endorsed by or licensed by any exam board, school or assessment publisher, and it contains no past papers.