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How to Multiply Fractions With Whole Numbers

Posted by Christine Sarikas | Mar 31, 2021 6:00:00 PM

General Education

 

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Need to learn how to multiply fractions with whole numbers? Or how to divide fractions by whole numbers? The process is probably easier than you think! We break down the 4 simple steps to follow for multiplying fractions by whole numbers, as well as the one extra step to divide fractions and whole numbers. Learn this important math skill, then test your knowledge by taking our quiz at the end of this guide.

 

How to Multiply Fractions With Whole Numbers: 4 Steps

Multiplying fractions by whole numbers can seem intimidating, but the process is actually quite simple: just four steps to follow. We walk you through each of the steps with our first sample question, then provide two additional examples so you'll have a solid grasp on how to multiply fractions with whole numbers.

 

Sample Question 1: ⅜  x 6

 

Step 1: Turn the Whole Number Into a Fraction

Your first step is turning the whole number into its own fraction. This is easy: you just give it a denominator of 1. So, from our example, 6 becomes 6/1. This is true because 6 divided into 1 group still equals 6. This is true for any whole number: 3 = 3/1, 17 =17/1, etc.

Now we have ⅜ x 6/1

 

Step 2: Multiply the Numerators

Next, we multiply the two numerators (the top number in a fraction).

3 x 6 = 18, so now we have the numerator for our answer: 18/__

 

Step 3: Multiply the Denominators

Now multiply the two denominators (the bottom number in a fraction). When you're multiplying a fraction with a whole number, this will be easy because you're just multiplying by 1.

8 x 1 = 8. 

Add it to our answer to get: 18/8. There we go!

 

Step 4: Simplify

But we're not done yet. It might be possible to simplify the fraction. The simplest form of the fraction is when the top and bottom of the fraction are the smallest whole numbers they can be. For example, the fraction 18/8 isn’t in its simplest form because it can still be reduced down to 9/4 by dividing both the top and bottom of the fraction by 2.

9/4 is the fraction in its simplest form, but you may prefer to change it into a mixed number since 9/4 is greater than 1.

4 goes into 9 twice, with a remainder of 1, so the answer can also be written as 2 ¼.

You might also want to give the answer as a decimal. We have an entire guide on converting fractions to decimals (as well as the other way around), but here's how to do this one simply. The 2 remains the same, since it's a whole number. You probably already know that ¼ is equal to 0.25, so that becomes the value on the right side of the decimal, for a final answer of 2.25.

 

Sample Question 2: 4 x ⅖ 

Step 1: 4/1 x

Step 2: 4 x 2 = 8

Step 3: 5 x 1 = 5

Step 4: Our answer, 8/5, can't be simplified any further as an improper fraction (where the numerator is larger than the denominator), but it can be converted into a mixed number. 5 goes into 8 once, with 3 remaining, so the mixed number answer is 1 ⅗. 

To convert ⅗ into a decimal, first we want to get the denominator to a value of 10. To do this, just multiply both parts of the fraction by 2, getting 6/10. Now we want to get the denominator to equal 1 to get rid of the fraction so we divide each part of the fraction by 10. That gives us .6/1, which is also equal to just .6. Combine that with the whole number (1) from the answer, and your final answer in decimal form is 1.6.

 

Sample Question 3: 5 x 2 3/7   

Step 1: The fraction is in the form of a mixed number, so first we need to convert it to an improper fraction. Remember, when adding or subtracting fractions, the denominators must be the same. To get the whole number 2 to have the same denominator, make it into a fraction, 2/1, then multiply the top and bottom by 7. You'll get 14/7 which, when added to 3/7, is 17/7. Make the 5 a fraction, too. Now we have: 5/1 x17/7

Step 2: 5 x 17 = 85

Step 3: 7 x 1 = 7

Step 4: Now we have 85/7. It can't be simplified, but it can be made into a mixed number. 7 goes into 85 twelve times, with a remainder of 1. Our final answer is 12 1/7, or 12.14 in decimal form.

 

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5 Steps to Dividing Fractions by Whole Numbers (and Vice Versa)

Dividing two fractions is the same as multiplying by the second fraction's reciprocal. This means that, once you've mastered multiplying fractions by whole numbers, you pretty much know how to divide fractions by whole numbers!

Below we walk you through the steps and explain two examples, one where you divide a fraction by a whole number (using the same values as example #1 above), and another where you divide a whole number by a fraction. 

 

Sample Question 4: ⅜ / 6

 

Step 1: Turn the Whole Number Into a Fraction

Just as we did when we went over multiplying fractions by whole numbers, turn 6 into a fraction by adding a 1 to the denominator: 6/1

 

Step 2: Flip the Second Number

This is the extra step that's needed for dividing fractions. Right now we have ⅜ / 6/1. Flip the second number, and change the division sign to a  multiplication sign: ⅜ x ⅙ 

Once you do that, you work through the problem just as you did with the examples above.

 

Step 3: Multiply Numerators

3 x 1 = 3

 

Step 4: Multiply Denominators

8 x 6 = 48

That gives us 3/48

 

Step 5: Simplify

Don't forget to simplify! We can divide both the numerator and denominator by 3, which gives us a final answer of 1/16 or 0.0625.



Sample Question 5: 4 / ⅖ 

 

Step 1: 4/1 / ⅖ 

Step 2: 4/1 x 5/2 

Step 3: 4 x 5 = 20

Step 4: 1 x 2 = 2

Step 5: 20/2 simplifies to 10!

 

3 Tips for Avoiding Mistakes 

Now you know the basic steps for how to multiply fractions with whole numbers as well as how to divide fractions with whole numbers, but it's still possible to make careless errors when working through these problems, even if you understand the concepts well. Reduce your chances of making a mistake by following these three tips.

 

#1: Know Whether to Expect a Big or Small Number

One of the best ways to check for and avoid silly mistakes is to quickly know if your answer is way off from what you expected. When you divide or multiply fractions and whole numbers, there are certain patterns you can expect.

Answer will likely be > 1

  • Fraction multiplied by a whole number
  • Whole number multiplied by a fraction
  • Whole number divided by a fraction

Answer will likely be < 1

  • Fraction divided by a whole number

Now, obviously, knowing this trick won't just give you the right answer, but if you're working through a problem like ⅖ / 4 and you get a number greater than 1, you can be pretty sure you should go back and recheck your work.

 

#2: Keep Numerators and Denominators Organized

It can be easy to get numerators and denominators confused, especially when division is involved and you're flipping fractions. Most mistakes are made when people multiply the wrong numbers or put a numerator answer in the denominator spot (or vice versa).

Avoid this by keeping your work neat and always making it clear what are numerators and what are denominators. For example, after you multiply the numerators, add a dash under your answer (like 4/___)so you remember what you just solved for and that the next value you solve for will be the denominator.

 

#3: Always Make Sure to Simplify

As soon as you finish the multiplication and write your answer down, you might be tempted to move right on to the next question. Spend an extra few seconds seeing if your answer can be simplified though. Some teachers will take points off for correct, but non-simplified answers, and you definitely don't want to get deductions after you've done all the work right! Simplify as far as you can and, if your fraction's value is greater than 1, convert it to a mixed number if that's what your teacher prefers (some have different preferences, so ask to make sure you're doing all the steps you need to).

 

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Quiz: Dividing and Multiplying Fractions by Whole Numbers

Ready to test your knowledge of how to multiply fractions with whole numbers? In this section are ten questions. For each, you'll be multiplying fractions by whole numbers or dividing fractions by whole numbers. Give them a try, then check your answers with the key below.

#1: 5 x 4/3

#2: 2/9 x 11

#3: 12 x ⅕ 

#4: ½ / 3

#5: 4/9 x 7

#6: ⅞ x 2

#7: 8 / ⅔ 

#8: 5/12 x 5

#9: 5 / 4/7

#10: 4/15 x 9

 

Answer Key

#1: 6 ⅔
#2: 2 4/9
#3:  2 ⅖
#4:
#5: 3 1/9
#6: 1 ¾
#7: 12
#8: 2 1/12
#9: 8 ¾ 
#10: 2 6/15

 

What's Next?

Want to learn more about decimals, fractions, and percentages? Check out The 3 Steps to Convert Decimals to Fractions (and Back)

f you're unsure what high school math classes you should be taking, this guide will help you figure out your schedule to be sure you're ready for college!

Now that you're an expert in multiplying and dividing fractions, challenge yourself by learning how to convert Celsius to Fahrenheit!

 

Have friends who also need help with test prep? Share this article!
Christine Sarikas
About the Author

Christine graduated from Michigan State University with degrees in Environmental Biology and Geography and received her Master's from Duke University. In high school she scored in the 99th percentile on the SAT and was named a National Merit Finalist. She has taught English and biology in several countries.



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