Math Help: How to Work Out a Fraction of a Number

Mark, a math enthusiast, loves writing tutorials for stumped students and those who need to brush up on their math skills.

Whether you're a student doing homework, a chef working on a recipe, a wedding planner trying to lay out a budget, or just an average person strolling through life, chances are you'll eventually need to figure out how to work out fractions. In this article, we'll define a few simple terms, learn how to find any fraction of any number, and explore some example problems for practice. Ready? Let's do it!

Important Terms

• Fraction: A fraction is a portion of a whole. Think of it in terms of pizza—if there are 10 slices total in a pizza pie, and you've had three pieces, that means you've eaten 3/10 (three tenths) of the pie. The fraction 3/10 represents the portion of the whole pizza you've eaten.
• Numerator: In a fraction, the numerator is the number on top of (or before) the line. In the example above, 3 is the numerator of the fraction 3/10.
• Denominator: In a fraction, the denominator is the number below (or after) the line. In the example above, 10 is the denominator of the fraction 3/10.

How to Find a Fraction of a Number

To work out a fraction of a number, all you need to do is divide that number by the denominator of the fraction, then multiply your result by the numerator of the fraction.

For instance, if we wanted to find out what 3/8 of 24 is, we would divide 24 by 8 (the denominator of the fraction).

24 ÷ 8 = 3

We would now multiply this result by 1 (the numerator of the fraction).

3 x 3 = 9

So, 3/8 of 24 is 9.

Video Demonstration

Example Problems

Remember—to work out a fraction of a number, all you need to do is divide that number by the denominator of the fraction and then multiply the result by the numerator of the fraction. Let's do some example problems for practice.

Example 1: Work out 3/8 of 48

First, divide 48 by the denominator:

48 ÷ 8 = 6 (this is 1/8 of 48)

Now, multiply this result by the numerator:

6 × 3 = 18 (this is 3/8 of 48)

So, 3/8 of 48 is 18.

Example 2: Work out 2/9 of 36

First, divide 36 by the denominator:

36 ÷ 9 = 4 (this is 1/9 of 36)

Now, multiply this result by the numerator:

4 × 2 = 8 (this is 2/9 of 36)

So, 2/9 of 36 is 8.

Example 3: Work out 4/5 of 60

First, divide 60 by the denominator:

60 ÷ 5 = 12 (this is 1/5 of 60)

Now, multiply this result by the numerator:

12 × 4 = 48 (this is 4/5 of 60)

So, 4/5 of 60 is 48.

Example 4: Work out 5/11 of 77

First, divide 77 by the denominator:

77 ÷ 11 = 7 (this is 1/11 of 77)

Now, multiply this result by the numerator:

7 × 5 = 35 (this gives 5/11 of 77)

So, 5/11 of 77 is 35.

Example 5: Word Problem

A fuel tank holds 14 gallons of fuel when full. If the tank has 3/7 of fuel left in the tank, work out how many gallons of fuel are left.

Here, you need to calculate 3/7 of 14 gallons

First, divide 14 by the denominator:

14 ÷ 7 = 2 (this is 1/7 of 14)

Now, multiply this result by the numerator:

2 × 3 = 6 (this is 3/7 of 14)

So, there are 6 gallons of fuel left in the tank.

This content is accurate and true to the best of the author’s knowledge and is not meant to substitute for formal and individualized advice from a qualified professional.

Questions & Answers

Question: 12 is 3/4 of what number?

Answer: You need to divide by the top and multiply by the bottom.

12 divided by 3 is 4, and 4 times 4 is 16.

Question: What part of 5 3/5 is 7/10?

Answer: You will need to divide 7/10 by 5 3/5.

Convert 5 3/5 into an improper fraction which is 28/5

Now work out 7/10 divide by 28/5 which is the same as 7/10 times.

The answer is 1/8.

Question: What is 1/7 of 3.50?

Answer: Just divide 3.50 by 7 as 1/7 means divide by 7. This will give an anwer of 0.5.

Question: What is 1/8 of an hour?

Answer: 60 divided by 8 is 7.5, so 7.5 minutes.

Question: What is 3/8 of 24?

Answer: Follow the rule divide by the bottom and times by the top.

24 divided by 8 is 3, and 3 times 3 is 9.

Question: What is 6/11 divided by 3?

Answer: First work out 3 divide by 11 to give 0.27..., and 0.27... multiplied by 6 gives 1.64 to 2 decimal places.

Question: What is 7/11 - 3/11?

Answer: The answer will be 4/11 (subtract the numerators and keep the denominator the same).

Question: What is 6 as a fraction of 15?

Answer: Put 6 on the numerator, and 15 on the denominator to give 6/15, which sipmplifies to 2/5.

Question: What is 4/7 more than 63?

Answer: You need to use the rule "divide by the bottom and times by the top". 63 divided by 7 = 9, and 9 multiplied by 4 is 36. Finally add the 36 on to the 63 to give 99.

Question: Find the nth term of this sequence: 6, 9, 14, 21, 30, 41?

Answer: These numbers are 5 more than the square number sequence n^2 so the nth term is n^2 + 5.

Question: What is 1/4 of £15.10?

Answer: To work out 1/4 of any number divide the number by 4.

£15.10 divided by 4 is £3.775, or £3.78 to the neared penny.

Question: What is 2/9 of 42?

Answer: Divide 42 by 2 give 21, and then multiply 21 by 9 to give 189.

Question: 2/3 of a number is 24. What is 5/9 of the number?

Answer: First divide 24 by to to give 12, and multiply 12 by 3 to give 36.

Now find 5/9 of 36, by dividing 36 by 9 to give 4, and multiplying 4 by 5 to give 20.

Question: What is 1/4 of 35?

Answer: Just divide 35 by 4 to give 8.75.

Question: What about 1/3 of 8?

Answer: To work out 1/3 divide the number by 3, so 8/3 = 2.6 recurring.

Question: What is 1/8 of 6?

Answer: To find 1/8 divide the number by 8.

6 divided by 8 gives 0.75.

Question: If 1/7 of a number is 140, what is the number?

Answer: Just multiply 140 by 7 to give 980.

Question: What is 1/11 of 1/6?

Answer: "Of" can mean "multiply", so work out 1/11 multiplied by 1/6 to give 1/66.

Question: What is 1/9 of 96?

Answer: To work out one ninth of a number divide the number by 9.

So 96 divided by 9 gives 10.7 (rounded to 1 decimal place).

Question: What is 4/7 of 14?

Answer: Follow the rule, "divide by the bottom and times by the top".

So 14 divided by 7 = 2, and 2 multiplied by 4 = 8.

Question: What is 5/7 of 100?

Answer: Divide 100 by 7 to get 14.28. 14.28 multiplied by 5 is 71.4, rounded to 1 decimal place.

Question: How do you figure out what is 5/8 of 4/5?

Answer: You can still use the rule divide by the bottom and times by the top even if your amount is a fraction.

Divide 4/5 by 8 to give 1/10, now multiply 1/10 by 5 to give 1/2.

Question: What is 1/5 of 7?

Answer: 1/5 of a number can be found by dividing the number of 5.

Therefore, 7 divided by 5 gives 1.4

Question: What is 1/8 of 14?

Answer: 1/8 of a number can be found by dividing the number by 8.

So 14 divided by 8 gives 1.75.

Question: 8% of 60 is 1/5 of what number?

Answer: First work out 8% of 60 which is 4.8.

So one fifth of something is 4.8.

Since 1/5 means divide by 5, multiply 4.8 by 5 to find the missing number.

The asnwer will be 24.

Question: What is 3/6 of 248?

Answer: Its probably easier to cancel 3/6 down to 1/2, so you need to work out one half of 248.

So 248 divided by 2 gives 124.

Question: What is 1/9 of 12?

Answer: To find 1/9 of a number divide the number by 9.

12 divided by 9 is 4/3 or 1.3 recurring.

Question: What is 5/8 of 40 ?

Answer: 40 divided by 8 is 5, and 5 multiplied by 5 is 25.

Question: If 1/9 is 49 what is the number?

Answer: Just multiply 49 by 9 to give 441.

Question: What is 1/5 of 8?

Answer: To work out 1/5 divide the number by 5.

8 divided by 5 is 1.6.

Question: What is 4/11 of 66?

Answer: Use the method divide by the bottom and times by the top.

66 divided by 11 is 6, and 6 times 4 is 24.

Question: What is 4/5 of 12?

Answer: Follow the rule divide by the bottom and multiply by the top.

12 divided by 5 is 2.4, and 2.4 times 4 is 9.6.

Question: Can you work out 3/12 of 48?

Answer: Follow the rule divide by the denominator and multiply by the numerator.

48 divided by 12 gives 4, and 4 multiplied 3 gives 12.

Question: Orla spent one-quarter of her money on a t-shirt, and 3 eighths on a jumper. What fraction of her money had she left?

Answer: She spent 5/8 on clothes if you add the two fractions together, so 3/8 are left over.

Question: What is 9/13 of 182?

Answer: Divide 182 by 13 to give 14, then multiply 14 by 9 to give 126.

Question: What is 6/8 of 40?

Answer: 40 divided by 8 is 5, and 5 multiplied by 6 is 30.

Question: What is 1/7 0f 15000?

Answer: To work out 1/7 of a number divide the number by 7.

So 15000 divided by 7 gives 2142.86 rounded to decimal places.

Question: How do you calculate 1/7 x 4?

Answer: 4 can be written as a fraction as 4/1.

Now, multiply the two fractions together 1/7 times 4/1 = 4/7.

Question: What is 4/5 of 30?

Answer: First work out 1/5 of the number by dividing by 5, so 30 divided by 5 is 6.

Now work out 4/5 by mutiplying the answer by 4, so 6 multiplied by 4 gives 24.

Question: What is 1\5 x 4\5?

Answer: Just multiply the numerators and denominators together of both fractions to give 4/25.

Question: What is 1/4 of 1640?

Answer: To find one quarter of a number divide the number by 4.

So 1640 divided by 4 is 410.

Question: What is 5/6 of 66?

Answer: Follow the rule divide by the bottom and times by the top.

66 divided by 6 is 11, and 11 multiplied by 5 is 55.

Question: What is 2/3 of 11?

Answer: Apply the rule divide by the bottom and times by the top.

11 divided by 3 gives 11/3.

11/3 multiplied by 2 gives 22/3 which as a mixed number is 7 1/3.

Question: What is two tenths of twenty?

Answer: One tenth of twenty is 2, and 2 times 2 is 4.

Question: What is 5/9 out of 27?

Answer: This is working out a fraction of an amount, so apply the rule "divide by the bottom and times by the top".

So 27 divided by 9 is 3, and 3 multiplied by 5 is 15.

Question: 1/6 of what number is 11?

Answer: To find one sixth of something you divide by 6.

But since you have the answer already to the question, then multiply the 11 by 6 instead to give 66.

Question: Can you work out 5/6 of 84?

Answer: Fisrt work out 84 divided by 6 to give 14. Now multiply 14 by 5 to give 70.

Question: 60 is 3/8 of what number?

Answer: Use the rule in the article in reverse.

Divide 60 by 3 to give 20, and now multiply 20 by 8 to give 160.

Question: What is 3/7 of 84?

Answer: 84 divided by 7 is 12, and 12 multiplied by 3 is 36.

Question: What is 1/3 of 5.28 million?

Answer: To work out 1/3 you just need to divide your number by 3. So 5,280,000 divided by 3 is 1,760,000.

© 2011 Mark

Comments

Offenderman on April 22, 2018:

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bum face on February 21, 2013:

Thanks this helped!!! Xxxxxx