Mental Maths for the DAA: no-calculator tips and shortcuts

The Numerical Reasoning section of the Defence Aptitude Assessment (DAA) is fast, and it gives you no calculator. You get only a few minutes to work through roughly a dozen questions, so the maths itself is never advanced — it is your speed and accuracy under pressure that are really being tested. The good news is that mental maths is a skill you can train. Learn a handful of reliable shortcuts, practise them until they are automatic, and the section stops feeling like a race. This guide walks through the techniques that matter most, with the working shown at every step.

Percentages: find 10% first, then scale

The single most useful habit is to find 10% and build from there. To get 10% of any number, just move the decimal point one place to the left. From 10% you can reach almost any percentage by scaling.

Say you need 15% of 240:

1. 10% of 240 = 24.
2. 5% is half of 10%, so 5% = 12.
3. Add them: 15% = 24 + 12 = 36.

The same building blocks handle other percentages: 20% is 10% doubled, 30% is 10% tripled, and 1% is 10% divided by ten. For a percentage change, work out the difference, divide it by the original amount, then multiply by 100. If a figure rises from 40 to 50, the increase is 10; 10 ÷ 40 = 0.25, which is a 25% increase.

Fractions of amounts

To take a fraction of a quantity, divide by the bottom number then multiply by the top. For 3/4 of 160:

1. Divide by 4: 160 ÷ 4 = 40.
2. Multiply by 3: 40 × 3 = 120.

Keep the common fractions instant. Half is a straight halving, a quarter is halving twice, and a tenth is the decimal-point trick from above. Once those feel automatic, most fraction questions become one or two quick steps.

Ratios and sharing

To split an amount in a ratio, add the parts to find how many shares there are, work out the value of one share, then multiply. To share £40 in the ratio 3:1:

1. Add the parts: 3 + 1 = 4 shares in total.
2. One share = £40 ÷ 4 = £10.
3. The larger portion is 3 shares: 3 × £10 = £30; the smaller is 1 share = £10.

Always check the parts add back to the total: £30 + £10 = £40. That quick sense-check catches most slips.

Times tables, doubling and halving, and multiplying by 10 or 100

Solid times tables up to 12 are the foundation for everything else, so drill any that are shaky. Beyond that, two tricks do a lot of heavy lifting. Doubling and halving lets you rebalance an awkward multiplication: to work out 16 × 5, halve the 16 and double the 5, giving 8 × 10 = 80. And multiplying by 10 or 100 is simply moving the decimal point — one place for 10, two places for 100 — so 34 × 100 = 3,400. Combine them and larger sums come apart easily: 25 × 12 is 25 × 10 = 250, plus 25 × 2 = 50, giving 300.

Speed, distance and time

These questions all rest on one triangle: put distance on top, with speed and time underneath. Cover the quantity you want and the triangle shows the sum — speed = distance ÷ time, distance = speed × time, and time = distance ÷ speed.

Take 90 km covered in 1 hour 30 minutes, asking for the average speed:

1. Convert the time to hours: 1 hour 30 minutes = 1.5 hours.
2. Speed = distance ÷ time = 90 ÷ 1.5 = 60 km/h.

The trick with these is getting the units right first — turn minutes into hours before you divide, and the rest falls into place.

Conversions, rounding and checking your answer

A few conversions come up often enough to be worth memorising. For distance, kilometres ≈ miles × 1.6, and going the other way, miles ≈ kilometres ÷ 1.6. So 60 km is roughly 60 ÷ 1.6 ≈ 37.5 miles. It is also handy to know that 1 kg is about 2.2 lb and 1 hour is 60 minutes.

Finally, use estimation and rounding to check yourself and to eliminate options. Round the numbers to something friendly, get a rough answer, and any option that is nowhere near can be crossed off straight away. If a sum looks like 19 × 21, round to 20 × 20 = 400 and you know the real answer sits near there — so an option of 40 or 4,000 is clearly wrong. On a multiple-choice test, ruling out the impossible answers is often quicker and safer than a full calculation.

Practise little and often

Mental maths rewards short, frequent sessions far more than the odd long one. A few minutes a day drilling percentages, fractions and times tables will do more than a single marathon before test day. Work through our numerical reasoning practice under realistic time pressure, review anything you get wrong, and build a steady rhythm. For more detail on the section itself, see the numerical reasoning guide, and for the bigger picture read how to prepare for the DAA. This is independent practice and is not affiliated with, endorsed by or connected to the RAF, the Royal Navy or the Ministry of Defence.