Verbal Reasoning Complete the Sum

A Complete the Sum question gives you two sums joined by an equals sign. You find the number that fills the gap so both sides come out the same.

The equals sign here does not mean "the answer goes next". It means "the same as". Is 7 + 5 = 3 × 4 true or false? True, because both sides make 12. Nothing is being worked out from left to right.

Think of the equals sign as the middle of a pair of scales. Both sides have to weigh the same. Your job is to find the weight that balances them.

The method

Five beats: finish the free side, ring the target and say the balance, do what you can, undo backwards, weigh both sides.

1. Finish the free side. That is the side with no gap in it. In every one of our questions that is the left-hand side. Look before you assume.
2. Ring the target, label it, and say the balance out loud. Write a T beside it, then say what it means: "this side has to weigh 6 as well." Six words, and they prevent most of the mistakes on this type. The target is not your answer. It sits in the option list of nearly every question, waiting for anyone who forgets that.
3. Do what you can on the gapped side. Work out every part that has no gap in it. In 5 × 4 − [?], that is 5 × 4 = 20.
4. Undo backwards, last sign first. Say the step as a sentence before you work anything out: "twenty take away something makes six." Then swap each sign for its opposite. Start with the one furthest from the gap.
5. Weigh both sides again. Put your number in and work out both sides properly. It costs five seconds, and it is the step that catches a slip.

About 30 seconds each.

Rules to watch

• The gap is often not the last thing. In 22 of our 47 questions it sits somewhere else. Ten put it first and twelve put it in the middle. The easiest questions all put it last. A whole tier of practice builds the habit before anything breaks it.
• Undo backwards, one sign at a time. Going back feels like doing the signs again, so [?] × 2 − 4 gets solved as divide-then-add. Take the sign furthest from the gap first. Write both steps down.
  1. Gap first. [?] × 2 − 4 has to make 10. Undo the − 4: 10 + 4 = 14. Then undo the × 2: 14 ÷ 2 = 7.
  2. Gap in a times sum. 2 × [?] ÷ 3 has to make 12. Undo the ÷ 3: 12 × 3 = 36. Then undo the × 2: 36 ÷ 2 = 18.
  3. Gap you divide by. 60 ÷ [?] + 10 has to make 20. Undo the + 10: 20 − 10 = 10. So 60 ÷ [?] = 10, and [?] = 6.
• Do × and ÷ before + and −. On every one of our questions both readings give the same answer, so you are safe either way. A real paper makes no such promise.
• Trying the options is allowed. It is not cheating, and it is often not slower. When you divide by the gap, no single take-away finds the answer, so five quick tests can be the fastest route. Stuck at thirty seconds? Try them. Never leave a blank.

Watch for these traps

We looked at all 188 wrong options in our bank. More than half of them are numbers you can already see or have already written down.

• A number you worked out on the way. 71 of the 188. Most often it is the target itself — 46 of them, in nearly every question. The other 25 are a part of a side, like the 20 in 5 × 4 − [?]. Finishing a sum feels like finishing the question. The number is right there in the list. This is why the target gets a ring and a label.
• A sum gone wrong. 47 of the 188 sit within two of the right answer. Three numbers, two signs and a clock. Most wrong answers on this type are sums that went wrong, not methods that went wrong. That is exactly why beat 5 exists.
• Undoing wrongly. 32 of the 188. Two shapes: undoing only the outer step and stopping, or using the sign instead of its opposite. In [?] × 2 − 4 making 10, stopping after 10 + 4 gives 14. That is offered.
• A number printed in the question. 26 of the 188 are simply copied off the page. Nothing has been worked out at all. If your answer is a number you can point at in the question, look again.

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 15 arcade 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.