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

Your opinion means everything

If you feel this course helped (or is helping) you prepare for the GMAT, we’d love to hear from you!

Free “Question of the Day” emails!