# One Number as a Percentage of Another Number (Mathematics Lesson)

# One Number as a Percentage of Another Number

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%.#### An Example Question

What is 45 out of 60 as a percentage?Step 1

45 ÷ 60 = 0.75

Step 2

0.75 × 100% = 75%

**Don't forget:**a percentage has a

**%**("percent") sign after it.

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

#### An Example Question

What is 12 out of 60 as a percentage?Step 1

Start with the formula:^{n1}/

_{n2}× 100%

**Don't forget:**/ means ÷

Step 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%

# A Real Example of How to Express One Number as a Percentage of Another Number

The slider below gives another example of expressing one number as a percentage of another number.##### Interactive Test

**show**

Here's a second test on finding one number as a percentage of another.

Here's a third test on finding one number as a percentage of another.

##### Note

# 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".

# 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