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# 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

**n**out of of a number

_{1}**n**as a percentage, use the formula below:

_{2}## 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:

^{n1}⁄

_{n2}× 100%

**Don't forget:**/ means ÷.# 2

Substitute the numbers into the formula. The formula is for n

_{1}out of n_{2}.In our example, we are finding 12 out of 60, so n_{1}= 12 and n_{2}= 60.^{12}⁄

_{60}× 100% = 12 ÷ 60 × 100%

^{12}⁄

_{60}× 100% = 0.2 × 100%

^{12}⁄

_{60}× 100% = 20%

## Answer:

12 out of 60 expressed as a percentage is 20%.## 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 n_{1}) out of another number (which we'll call n

_{2}) is:

Notice that we have created a fraction with the numbers n

_{1}and n

_{2}. n

_{1}is the top number if the fraction (called the numerator) and n

_{2}is the bottom number of the fraction (called the denominator).

By writing this fraction, we have expressed n

_{1}out of n

_{2}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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