How to Subtract Fractions from Whole Numbers

Instructor: Julie Zundel

Julie has taught high school Zoology, Biology, Physical Science and Chem Tech. She has a Bachelor of Science in Biology and a Master of Education.

At first glance, subtracting fractions from whole numbers might look scary, but it is relatively simple. This lesson will go through the steps required to subtract both fractions and mixed numbers from whole numbers.

Whole Numbers, Fractions and Mixed Numbers

You've been jogging for about three months and you are up to 3 miles a day. Wow! Good job. You've just learned that your route is changing and you'll be going 1/16th of a mile less. You need to figure out how far you're going each day now. But how? Well, in order to accomplish this math problem you need to know how to subtract fractions from whole numbers.

Before we delve into that problem, let's get some vocabulary under our belt. Whole numbers are numbers that don't have fractions or decimals and aren't negative. For example: 10, 13, 14 are all whole numbers. Makes sense, right?

Fractions, on the other hand, are numbers that are parts of a whole number and are made up of a numerator, or top number, and a denominator, or bottom number. The denominator tells you how many parts your whole is broken up into and the numerator tells you how many of those parts you have. So, if you have 1/4 of a pie, you have 1 out of 4 pieces of pie.

One-fourth of a piece of pie
one fourth

Finally, mixed numbers are a combination of whole numbers and fractions. Here you have a whole number and a fraction. 2 and 1/2 is a mixed number. The 2 is your whole number and the 1/2 is the fraction. If you had 2 and 1/2 pies, you would have two whole pies and a half of another pie. Yum!

Okay, we are almost ready to see how far you're running each day.

Whole Numbers Minus Fractions

You need to do the following problem: 3 - 1/16 = ?. Although it may look scary, check out the steps below.

  • Step 1: You need to turn the whole number into a fraction. Good news, it's not that hard. Any whole number can be made into a fraction by putting the whole number as the numerator and the number 1 as the denominator. In our example, three is our whole number and is the same as 3/1 so, there you go! Now you have:

3/1 - 1/16 = ?

  • Step 2: You need to get a common denominator. In other words, the bottom number of the two fractions needs to be the same. But how in the world do you do that? Well, change the denominator in 3/1 to 16. You do this by multiplying the denominator by 16. But, if you do that, you have to multiply the numerator by 16 as well. In this step, it is very important to always remember that what you do to the denominator must also be done to the numerator. So, 3 x 16 = 48. Now you have: 48/16 - 1/16 = ? Take a look at the image for step 2 if you're confused.

Step 2
step 2

Now, before we go on, it's important you realize that 48/16 is just another way to write the number 3. Don't believe me? Go ahead and divide 48 by 16 and you will get 3.

  • Step 3: Subtract the numerators (but not the denominators).

48/16 - 1/16= 47/16. Now that's not a very rewarding answer. If you told me you were jogging 47/16 miles everyday I wouldn't be all that impressed, but 47/16 is actually pretty close to 2.9 (divide 47 by 16 to see that this is true). So, although it's not 3 miles, you're still doing pretty well.

Before we go on, why don't you try to do some practice on your own.

  1. 4 - 5/8 = ?
  2. 10 - 3/4 = ?

Let's see how you did. Remember we need to change the whole number into a fraction that has the same denominator as the fraction. For the first problem, change 4 into a fraction by making 4 the numerator and 1 the denominator: 4/1. Now you can change 4/1 into a fraction with 8 as the denominator by multiplying both the denominator and the numerator by 8. Remember, 32/8 is the same as 4. Now you can do the problem by subtracting the numerators only. In this problem, 32/8 - 5/8 = 27/8.

Now let's do the second problem. Again, you need to change 10 into a fraction with the same denominator as your fraction. First, make your whole number 10 become the fraction 10/1. Then make the denominator 4 (don't forget to multiply the numerator also). You now have 40/4. Now you can subtract: 40/4 - 3/4 = 37/4.

Whole Numbers Minus Mixed Numbers

Now that you know how to subtract fractions from whole numbers, you're ready to subtract mixed numbers from whole numbers. Let's get started. Let's say you;ve changed your running route and have now subtracted 1 and 5/6 from your 3 mile run. How far are you running now? Let's do the following problem: 3 - 1 and 5/6 = ?

  • Step 1: Change the whole number so it is a mixed number. How? Well, you can write 3 as 2 and 6/6ths. Remember, 6/6 is the same as 1, so 2 and 6/6 is the same as 3. We chose 6/6 because, just like before, you want the same denominator as the fraction.

Step 1: Change whole number into a mixed number
step 1

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