Expressing One Number As a Percentage of Another Number
(KS3, Year 7)

The Lesson

One number can be expressed as a percentage of another number. For example, 3 out of 5 can be written as 60%.

How to Express One Number As a Percentage of Another Number

Expressing one number as a percentage of another is easy. Divide one number by the other number, then multiply by 100%.

Question

What is 45 out of 60 as a percentage?

Step-by-Step:

1

Divide 45 by 60.
45 ÷ 60 = 0.75

2

Multiply the answer (0.75) by 100%.
0.75 × 100% = 75%
Don't forget: a percentage has a % ("percent") sign after it.

Answer:

45 out of 60 expressed as a percentage is 75%.

A Formula to Express One Number As a Percentage of Another Number

Expressing one number as a percentage of another involves writing one number as a fraction of the other and multiplying by 100%. For example, to express 3 out of 5 as a percentage, we would write 3 out of 5 as a fraction and multiply by 100%:

More generally, to express a number n1 out of of a number n2 as a percentage, use the formula below:

A Real Example of Using a Formula to Express One Number As a Percentage of Another Number

Question

What is 12 out of 60 as a percentage?

Step-by-Step:

1

Start with the formula:
n1n2 × 100%
Don't forget: / means ÷.

2

Substitute the numbers into the formula. The formula is for n1 out of n2.In our example, we are finding 12 out of 60, so n1 = 12 and n2 = 60.
1260 × 100% = 12 ÷ 60 × 100% 1260 × 100% = 0.2 × 100% 1260 × 100% = 20%

Answer:

12 out of 60 expressed as a percentage is 20%.

Lesson Slides

The slider below gives another example of expressing one number as a percentage of another number. Open the slider in a new tab

What Is a Percentage?

A percentage expresses a part of a whole number as parts out of 100. "Per cent" means "per 100" or "out of 100". A percentage is shown by the symbol %.

The Fraction in the Formula

The formula for expressing the percentage of one number (which we'll call n1) out of another number (which we'll call n2) is:

Notice that we have created a fraction with the numbers n1 and n2. n1 is the top number if the fraction (called the numerator) and n2 is the bottom number of the fraction (called the denominator).

By writing this fraction, we have expressed n1 out of n2 as a fraction. Read more about how to express one number as a fraction of another number This fraction is then multiplying a number (100%). Read more about how to find a fraction of a number
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See Also

What is a percentage? Finding the percentage of a number Expressing one number as a fraction of another number Finding a fraction of a number