Mental Math: How to Subtract Numbers Faster

In the previous post, we have learned a faster way to add numbers near multiples of 10. In this post, we are going to learn to subtract numbers faster, but first let’s review some basic terms.

In the subtraction

8 – 6 = 2

8 is the minuend, 6 is the subtrahend and 2 is the difference.

In subtracting numbers, numbers may be added to the minuend and subtrahend in order to simplify calculations. The strategy is to change the subtrahend to multiples of ten, hundred, thousands, etc. Doing this will speed up calculation and with enough practice, may be done mentally. Here are some examples.

Example 1

1.) What is 55 – 18?

In this case, 18 is near 20, so we can add 2. If we add 2 to 20, we should also add 2 to 55. So, the expression becomes

(55 + 2) – (18 + 2).

Simplifying, we have 57 – 20 = 37. And really, 55 – 18 = 37. 

Notice that 57 – 20 is a lot easier to subtract mentally than 55 – 18.

Example 2

What is 77 – 62?

In this example, we can subtract 2 from 62 in order to make it 60. If we do this, we should also subtract 2 from 77 making the new expression

(77 – 2) – (62 – 2)

which is the same as

75 – 60 = 15.

Example 3

Subtract: 254 – 196

This subtraction really looks difficult to calculate mentally. Notice that if we add 4 to 196, it will become 200. If we add 4 to 196, we should also 4 to 254 making the new expression

(254 + 4) – (196 + 4)

become

258 – 200 = 58.

See? It’s a lot easier.

Example 4

Subtract: 1281 – 993

Notice that 993 is near 1000, so we add 7 to it make it 1000. We also add 7 to 1285. The new expression is

(1281 + 7) –  (993 + 7)

which is the same as

1288 – 1000 = 288.

Why The Math Trick Works

This method can be easily proven with simple algebra. If you have to numbers m and n where you want to subtract (m > n), then the expression for it is

m – n.

Notice that if we add a to both the minuend and subtrahend,

(m + a) – (n + a)

we can simplify this to

m + ana = mn.

Still we are back to the original expression. This means that in subtraction, we can add/subtract the same number from its minuend and subtrahend and the difference will still the same.

Practice Calculating Mentally!

  1. 56 – 39
  2. 322 – 197
  3. 2756 – 1998

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