Mentally calculating x percent of y

Can you quickly calculate 15% of 42 in your head? In this lesson, we’ll examine a fast way to perform this calculation and others.

 

The technique I’ll demonstrate is based on the fact that it's incredibly easy to find 10% of any value, and 1% of any value.

 

Finding 10% of a value

You probably already know that the “trick” is to move the decimal point one space to the left. Some examples:

10% of 5.2 = 0.52

10% of 4,321 = 432.1

10% of 837,160 = 83,716

 

Finding 1% of a value

To find 1% of a value, just move the decimal point two spaces to the left. Some examples:

1% of 5.2 = 0.052

1% of 4,321 = 43.21

1% of 837,160 = 8,371.6

 

Once we know how to find 10% and 1%, we can apply some number sense to quickly find other percents.

 

Finding 5% of a value

If we can find 10% of y, then 5% of y will equal half of 10% of y.

For example, since 10% of 240 = 24, we know that 5% of 240 is half of 24. In other words, 5% of 240 = 12

Likewise, since 10% of 3.6 = 0.36, we know that 5% of 3.6 = 0.18 (i.e., half of 0.36)

 

Finding 15% of a value

Now that we’re experts at finding 10% and 5% in our heads, we can combine percents. For example, let's find 15% of 260

To mentally perform this calculation, we need to recognize that 15% = 10% + 5%.

10% of 260 = 26

And 5% of 260 = 13

So, 15% of 260 = 26 + 13 = 39

 

Here’s another one: 15% of 42

10% of 42 = 4.2

5% of 42 = 2.1

So, 15% of 42 = 4.2 + 2.1 = 6.3

 

Combining percents

Now that we’ve found 15% by combining 10% and 5%, we can use the same approach to find other percents. We need only take the required percent and break it into sums of 10% and/or 1%.

 

Let’s begin by finding 2% of 0.31

To perform this calculation, we’ll use the fact 2% = 1% + 1%

1% of 0.31 = 0.0031

1% of 0.31 = 0.0031

So, 2% of 0.31 = 0.0031 + 0.0031 = 0.0062

 

Aside: This technique can prevent test-takers from making careless errors. When students find 2% of 0.31 by calculating (0.02)(0.31), there’s a chance that they’ll misplace the decimal point in the final answer. When we find 1% by moving the decimal point 2 spaces to the left, such mistakes are less likely.

 

Okay, now try 21% of 210

Here, we’ll use the fact 21% = 10% + 10% + 1%

10% of 210 = 21

10% of 210 = 21

1% of 210 = 2.1

So, 21% of 210 = 21 + 21 + 2.1 = 44.1

 

Last one: 55% of 70

One approach is the recognize that 55% = 10% + 10% + 10% + 10% + 10% + 5%, however a faster approach is to recognize that 55% = 50% + 5%.

50% of 70 = 35

5% of 70 = 3.5

So, 55% of 70 = 35 + 3.5 = 38.5

 

This technique takes only a few minutes to master, and it can save you valuable time on test day.

 

Now try the following calculations in your head (scroll down the page to find the answers):

a) 15% of 90

b) 11% of 170

c) 3% of 11,000

d) 115% of 82

 

 

 

 

 

Answer key

a) 13.5

b) 18.7

c) 330

d) 94.3

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