Number Speed and Accuracy: Fast, Correct Arithmetic

The number section of an aptitude test like the GIA is generally described as basic arithmetic under a time limit: adding, subtracting, multiplying and comparing numbers. It is not testing how much maths you remember from school. It is testing how fluently you handle small calculations when the clock is running. Many capable people do worse than they expect simply because they have not done mental arithmetic in years, and that rust is fixable.

Whether a calculator is permitted depends on the instructions for your session. Assume it is not allowed unless you are clearly told otherwise, and practise that way.

What the section rewards

Two things: speed on the easy items, and a low error rate. Time spent on one awkward calculation is time taken from several simple ones, so you want to recognise quickly which kind of item you are looking at. Easy items should become automatic. Awkward ones should be answered by estimation, or skipped.

Make the basics automatic

If you still stop to think about 7 times 8 or 13 plus 9, you pay a small cost on every question. Spend a few minutes a day on times tables up to 12 and on adding and subtracting across tens. The aim is not understanding, which you already have, but recall that needs no effort. Two sessions of five minutes will show a noticeable difference to most people.

Six mental shortcuts

1. Round and adjust. 49 + 38: add 50 + 38 = 88, then subtract 1 to get 87. 996 + 47 is 1000 + 47 minus 4, which is 1043.
2. Split by place value. 47 + 36: add the tens (40 + 30 = 70) and the units (7 + 6 = 13), giving 83.
3. Multiply by 5 via 10. 5 times 46 is half of 460, which is 230.
4. Multiply by 9 or 11. 9 times 34 is 10 times 34 minus 34, which is 340 minus 34, giving 306. 11 times 34 is 340 plus 34, giving 374.
5. Double and halve. 16 times 25: halve 16 to 8, double 25 to 50, then 8 times 50 is 400.
6. Subtract by counting up. 1,000 minus 638: from 638 to 640 is 2, to 1000 is 360, so the answer is 362.

You do not need all of these. Choose the three that feel natural and practise them until they are automatic. Using a shortcut you only half know is slower than plain arithmetic.

Estimate first, then compute

Estimation is a quick error check, and in comparison items it may be the whole answer. Suppose you must decide which is larger, 48 times 21 or 52 times 19. Rounding both to 50 times 20 gives 1,000 for each, which tells you the two are close and that rounding alone cannot decide. So compute exactly: 48 times 21 is 48 times 20 (960) plus 48, giving 1,008. And 52 times 19 is 52 times 20 (1,040) minus 52, giving 988. The first is larger. The estimate did useful work by warning you that precision was needed.

A useful rule: if the answer options differ greatly in size, estimate and pick. If they are close together, compute exactly. Looking at the options before deciding how much work a question needs is one of the few places where doing so is a good idea.

Error-proofing

Most wrong answers are slips, not misunderstanding. Common ones to watch for:

• Carrying errors in addition across a ten or a hundred.
• Sign errors in subtraction when the second number is larger.
• Misreading the operation. The sign changes between items, and it is easy to run on autopilot.
• Last-digit check. A cheap sanity check is to compute only the last digit in your head. The last digit of 47 times 36 must be the last digit of 7 times 6, which is 2. If your result ends in anything else, you made a slip.

Worked example set

Try these without paper, then check below. A) 68 + 57. B) 203 minus 78. C) 15 times 12. D) 1,200 divided by 8.

A) 68 + 57: 68 + 60 is 128, minus 3 is 125. B) 203 minus 78: 203 minus 80 is 123, plus 2 is 125. C) 15 times 12: 15 times 10 is 150, plus 15 times 2 which is 30, giving 180. D) 1,200 divided by 8: 1,200 divided by 4 is 300, and half of that is 150. Notice how each used a tiny adjustment rather than a long calculation. Your own versions of these will differ, which is fine as long as they are fast and correct.

A practice routine

Five to ten minutes a day is enough:

• Minutes one to three: times tables and quick adds, against a timer.
• Minutes four to seven: mixed items, written answer only, no working.
• Last minutes: review errors and name the type (carry, sign, misread).

Track the number of errors, not just speed. When errors are low and stable, push pace. If you see errors rise as you speed up, you have found your current limit, and it is a better guide than any generic target. Our seven-day plan sets aside short, daily number sessions for this.

Handling the clock

Do not stare at an item you cannot see a quick route for. Skip, move on, and return if time allows. The time-pressure guide explains why that is usually right, and the perceptual speed guide covers a similar speed-accuracy trade-off for visual checking.

Frequently asked questions

Do I need to be good at maths?

You need to be comfortable with basic arithmetic. The section does not require algebra or advanced topics. Fluency is the issue, and fluency can be built.

Is there a calculator?

Follow your session's instructions. If they do not say, ask the sender before test day.

Should I write working on paper?

Only if paper is allowed. Practise both ways. Many items are quicker to do mentally than to write out.

How much will practice help?

Most people gain from refreshing times tables and learning a few shortcuts. We cannot state how much, because it depends on where you start.