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Speed Arithmetic - How to Multiply and Divide by 5 Without a Calculator

Updated on March 31, 2020
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I am a former maths teacher and owner of Doingmaths. I love writing about maths, its applications and fun mathematical facts.

Multiplying by the Number 5

How to Use Quick Mental Arithmetic to Multiply and Divide by 5

There are many instances in life when it's useful to be able to multiply or divide by 5, e.g. when splitting a bill between a group of 5, when calculating the price of 5 identical items etc. Of course, nowadays most of us can pull out our phone, bring up a calculator app and solve this, but if you know the correct method, it can often be substantially quicker to solve it mentally.

In this article I will show you how to multiply and divide by 5 quickly in your head, without the need for a calculator or even a piece of paper.

How to Multiply by 5

Let's look at solving 23 × 5. There are many ways to approach this using mental methods, but we're going to look at one particular method here which is super quick and easy to use on any example.

To start with, consider that 5 = 10 ÷ 2. By swapping the 5 in our original problem for this 10 ÷ 2, we get

23 × 5 = 23 × 10 ÷ 2

As multiplying by 10 and dividing by 2 are both much easier to do mentally than multiplying by 5, we can now split our sum up into these two easier steps. It doesn't matter which order you do them in, but I tend to divide by 2 first as it is generally slightly easier to halve the smaller number. So we get:

  • 23 ÷ 2 = 11.5
  • 11.5 × 10 = 115

So we get a final answer of 23 × 5 = 115.


Multiplying by 5: A Trickier Example

This method works with any example, so let's try a trickier example with a decimal number.

72.8 × 5

Again, we use our two steps of dividing by 2 and multiplying by 10:

  • 72.8 ÷ 2 = 36.4
  • 36.4 × 10 = 364

to give us a final answer of 72.8 × 5 = 364.

How to Divide by 5

In order to divide by 5 we use almost the same technique as before but reverse the operations. Let's try 145 ÷ 5.

As with multiplying, we are going to use the fact that 5 = 10 ÷ 2, but this time as we are dividing by 5, we will switch the operations around so get:

145 ÷ 5 = 145 ÷ (10 ÷ 2)

= 145 ÷ 10 × 2

Breaking this down into separate steps give us:

  • 145 ÷ 10 = 14.5
  • 14.5 × 2 =29

So 145 ÷ 5 = 29.

Dividing by 5 - Trickier Examples

As with the multiplying method, this method also works with trickier examples.

Let's try 2410 ÷ 5.

  • 2410 ÷ 10 = 241
  • 241 × 2 = 482

Or even with a decimal number, 365.6 ÷ 5.

  • 365.6 ÷ 10 = 36.56
  • 36.56 × 2 = 73.12

For Further Examples Watch This Video From the DoingMaths YouTube Channel

© 2020 David

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