Mental arithmetic can be faster (not to mention more impressive) than using your phone – all it takes is a few tricks.

"Calculate left-to-right in your head, not right-to-left as you might on paper," says "mathemagician" Arthur Benjamin, co-author of *Secrets Of Mental Math* (Three Rivers Press). "After that, it just takes practice."

**Cut the problem into small bits**

Even the most daunting of mental-arithmetic problems can normally be separated into easy ones – all it takes is a little addition or subtraction. "For a very simple but practical example: it's easy to calculate a ten percent tip. How do you calculate a 15 per cent tip?

Well, take the ten per cent tip, cut it in half and add it to the original. So if the bill is £40, ten per cent of that is £4, half again is an additional £2. So 15 per cent of £40 = £6." The same principle would apply to 17.5 per cent.

**Pay attention to complements**

A complement is the distance between a number and the nearest convenient round number – normally ending in zeroes. "So the complement of 78 is 22 – it's the number you add to reach 100," says Benjamin. "On paper, 1234 minus 678 is messy. But you start by over-subtracting: 1234 minus 700 equals 534. I've subtracted too much, so I have to add back the complement. How much was 700 above 678? 22. You've turned a hard subtraction problem into an easy addition problem: 534 plus 22 equals 556.

**Conquer and divide**

"If you have a seven-digit number divided by a three-digit number, the answer is going to be a four-digit number or possibly one more," says Benjamin. (The same trick can be used when multiplying – just add instead.) "Therefore, if you were going to calculate 4,000,000 divided by 600, your answer is going to have four digits. Then simplify it: four-sixths is like two-thirds, which is about 0.667. You know the length, therefore you know your answer is going to be in the vicinity of 7,000." (It's 6,666.667.)