Maths: Written Calculation

In a written calculation question, you get one sum to work out, like a long multiplication, and five answers to choose from.

There's no calculator, and only one of the five answers is right.

In GL's papers the sum is sometimes set in a one-line story, but the working underneath is the same. The video above and the worked example below work through the same question, with the options in the same order. Then both work a second question, where two answers are still standing after the checks.

The method

Four steps: estimate first, cross off by size, check how it ends, work it if two are left.

Worked example

What is 397 × 56?

A. 22,629 B. 22,232 C. 21,835 D. 4,367 E. 2,382

1. Estimate first. 397 is nearly 400, and 56 is nearly 60. Four 6s are 24. Add the three zeros, and 400 × 60 = 24,000. So the answer should be about 24,000.
2. Cross off by size. D is only about 4,000. That's far too small, so D is out. E is about 2,000, smaller still, so E is out too. A, B and C are all close, so they stay.
3. Check how it ends. 7 × 6 = 42, so the answer must end in a 2. A ends in a 9, so A is out. C ends in a 5, so C is out too.
4. Work it if two are left. Here only B is left, so there's nothing to work out. It's close to 24,000, and it ends in a 2. So the answer is B.

Answer: B — 22,232 (397 × 56 ≈ 400 × 60 = 24,000, and 7 × 6 = 42, so it ends in 2)

A second worked example

Sometimes the checks leave two answers.

What is 43 × 54?

A. 2,422 B. 2,365 C. 387 D. 2,322 E. 172

1. Estimate first. 43 × 54 is about 40 × 50, which is 2,000.
2. Cross off by size. C is only a few hundred, so C is out. E is even smaller, so E is out too.
3. Check how it ends. 3 × 4 = 12, so it ends in a 2. B ends in a 5, so B is out. But A and D both end in a 2.
4. Work it if two are left. Two are, so use the column method. 43 × 4 = 172. For 43 × 50, hold the ones place with a zero, then work out 43 × 5. That row is 2,150. Now add the two rows, 172 and 2,150, and carry with care. 7 and 5 make 12, so carry the 1. 1, 1 and the carried 1 make 3. That's 2,322. A is a hundred too many: the carried 1 was counted twice, so A is out. Check it against the estimate: 2,322 is close to 2,000. So the answer is D.

Answer: D — 2,322 (172 + 2,150 = 2,322)

Things to watch out for

1. Shift the tens row. A zero holds the ones place. In 397 × 56, the second row is × 50, not × 5. Forget to shift it, and the rows add up to 4,367. That's option D, far too small. With a zero in the ones, the row becomes 19,850, and the total is 22,232.
2. Line up the points. Fill the gap with a zero. What is 3.4 + 2.91? Line them up by their last figures, and you get 3.25. That's option A. Line up the decimal points instead, and fill the gap with a zero: the answer is 6.31. The estimate agrees: about 3 + 3 = 6.
3. Check the power of ten. × 10 moves each figure one place. What is 2.8 × 10? × 10 makes it bigger, so 0.28 is out. Each figure moves one place to the left: 28. 20.8 moved the 2, but left the 8 behind. 280 would be × 100, and 2,800 would be × 1,000.
4. A dropped carry. Only careful working catches it. What is 327 × 23? Option D, 7,421, is the right size, and it ends in a 1, as it should. So only careful working catches it. 8 and 4 make 12: carry the 1. 9, 5 and the carried 1 make 15. So it's 7,521: option E.

Related

• The complete 11+ question-type guide
• Maths: Place Value and Ordering — the column a figure sits in gives its value
• Maths: Word Problems — picture the story, then plan and finish every step
• Maths: Algebra — work backwards from the end number

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.