ACT Number Fluency guide: number distance and fast mental maths
Updated 9 September 2026 · 6 min read
Number Fluency is the ACT section that worries applicants who did not enjoy maths at school. It should not. There is nothing here beyond arithmetic you already know, and the section is far more about method than ability.
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What comes up
Two things. Number-distance questions, formerly the BARB section of that name, show you three numbers and ask which two are furthest apart or closest together. And rapid arithmetic: single-step sums, no calculator, no working out on paper.
There is no algebra, no data interpretation, no multi-step word problems. If you can add, subtract, multiply and take a simple percentage, you already have everything the section requires.
Number distance: the shortcut
Given three numbers there are three possible pairs, so the obvious approach is to work out all three gaps and compare them. That works, but it is slower than it needs to be.
Faster: find the largest and smallest number first. For "which two are furthest apart", that pair is your answer, and you never calculate a gap at all. It works every time, because the widest gap is always between the extremes.
For "which two are closest together" you do have to compare, but only two gaps matter — the ones between neighbouring values once you have them in order. The gap between the extremes can never be the smallest, so you can discard it immediately.
Arithmetic worth having automatic
Every second spent working something out is a second not spent answering. These are worth knowing on sight rather than calculating:
- Times tables to twelve. If any of these are slow, that is the highest-value hour of preparation available to you.
- Ten per cent is a decimal point moved one place. Everything else follows: five per cent is half of that, twenty per cent is double it.
- Fifty per cent, twenty-five per cent. Half, and half again.
- Adding by rounding. For 58 plus 67, do 60 plus 67 and take off 2. Almost always faster than column addition in your head.
- Subtracting by counting up. For 91 minus 34, count from 34 to 91 rather than borrowing.
What to practise
Not maths. Speed. If you can already do the arithmetic, drilling more sums slowly will not raise your score — practising the same sums against a clock will. Our number fluency practice mixes both question styles and is timed by default.
For how this section fits with the other four, read the Army Cognitive Test explained.
Frequently asked questions
What is Number Fluency on the Army Cognitive Test?
It combines number-distance questions, where you decide which two of three numbers are furthest apart or closest together, with single-step mental arithmetic. No calculator is allowed.
Can you use a calculator on the ACT?
No. Number Fluency is mental arithmetic, which is part of why speed matters so much in the section.
What is the quickest way to answer number-distance questions?
For the furthest-apart version, simply identify the largest and smallest of the three numbers — that is always the answer, and you never need to calculate a gap. For closest-together you only need to compare neighbouring values, since the extremes can never be closest.
How hard is the maths on the Army Cognitive Test?
It is straightforward school arithmetic — addition, subtraction, multiplication, division and simple percentages. The difficulty comes from the pace, not the content.
Is forcesready.co.uk affiliated with the British Army?
No. forcesready.co.uk provides independent practice materials and is not affiliated with, endorsed by, or associated with the British Army or the Ministry of Defence.
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