Mental math tricks
๐ In short
Can you work out 99 + 47 in two seconds without paper? With a few clever tricks, yes! Mental math is exercise for the brain: we break numbers apart, round them and rearrange them until a hard sum becomes easy.
๐คฉ Did you know?
- To multiply a two-digit number by 11, add its two digits and put the result in the middle: 11 ร 23 = 253.
- Long ago, merchants calculated in their heads very quickly, because there were no calculators.
- Squaring a number ending in 5 is easy: 25 ร 25 = 625; work out 2 ร 3 = 6 and write 25 after it.
- Practicing mental math for 5 minutes a day makes you much faster within a month.
๐ Find out more
๐ Round, then fix
99 is very close to 100. So to work out 99 + 47 we do 100 + 47 = 147, then take away the extra one: 146. In the same way, 58 + 29 = 58 + 30 โ 1 = 87.
๐ Break the number apart
To work out 46 + 37 we break it apart: 40 + 30 = 70, and 6 + 7 = 13, so the sum is 70 + 13 = 83. To work out 8 ร 15: 8 ร 10 + 8 ร 5 = 80 + 40 = 120.
๐ก Doubling and halving
To work out 5 ร 16, take half of 16 and multiply by 10: 8 ร 10 = 80. To work out 4 ร 23, double twice: 23, then 46, then 92.
๐ฏ Rearrange to make it easy
In 7 + 8 + 3 + 2 we add the friends of ten first: (7 + 3) + (8 + 2) = 10 + 10 = 20. And in 4 ร 7 ร 25 we start with 4 ร 25 = 100, then 100 ร 7 = 700.
๐งฎ Worked examples
- 198 + 56 = 200 + 56 โ 2 = 254Round, then fix.
- 25 ร 12 = 25 ร 4 ร 3 = 300Look for 100.
- 63 โ 28 = 63 โ 30 + 2 = 35Subtract 30, then add the two back.
๐ Key words
- Mental math
- Calculating in your head with no paper or calculator
- Rounding
- Swapping a number for a nearby one that's easier to work with
- Double
- The number times 2
๐งช Try it at home
At the market with your parents, work out the total price of three things in your head before the shopkeeper does. Use rounding: 19 is nearly 20!
๐งฉ Test yourself
1 What's the easiest way to work out 99 + 25?
2 What is 5 ร 18?
3 What is 11 ร 34?