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Subtracting Fractions with Regrouping

Instructor: Stephanie Matalone

Stephanie taught high school science and math and has a Master's Degree in Secondary Education.

In this lesson, we will go over the basics of subtracting fractions with mixed numbers. We will specifically focus on scenarios when the the whole number needs to be regrouped into the fraction so the numbers can be properly subtracted.

Introduction

So you've probably talked about regrouping before when subtracting two multiple digit numbers. Let's say you had 53 dollars and you spent 25 of it. In order to see how much you have left, you would subtract 25 from 53. To do this by hand, you simply write 53 on top with 25 on the bottom.

You always start by subtracting the ones place which is 3 minus 5...uh oh! Because 3 is smaller than 5, you have to borrow from the tens column. This process of borrowing is also known as regrouping. We have a 5 in the tens place, which means 5 sets of ten. We will borrow one of those set of tens by bringing it over to the ones place. A one in the tens place equals a 10 in the ones place! This turns the 3 in the ones place into 13 (10 + 3 = 13) and the in the tens place into 4. Now, we can properly subtract the ones place (13 - 5 = 8). We put that 8 under the line in the ones place and now we can subtract the tens place (4 - 2 = 2). Thus, our final answer is 28!


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Mixed Fractions

When subtracting fractions, we need to regroup if we are dealing with mixed numbers. Mixed numbers are simply whole numbers and fractions put together. Mixed numbers are the 'proper' way to represent and improper fraction that is greater than one.

For example, the improper fraction of 7/4 can be represented as the mixed number of 1 and 3/4.This is because 4/4 is equal to one. You can pull that fraction out of 7/4, leaving the 3/4 behind and turning to 4/4 into its whole number equivalent of 1!


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Subtracting Fractions

Let's start with an easier one first. Let's say you need to subtract 1 and 1/4 from 3 and 3/4. First, start by subtracting the fractions, ensuring they have the same denominator before you do so. Since both have a denominator of 4, we can go ahead and subtract the numerators (3 - 1 = 2). This leaves us with 2/4. But, don't forget that 2/4 can be simplified to 1/2. Next we can subtract the whole numbers (3 - 1 = 2). Thus, our final answer is 2 and 1/2.


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Regrouping Fractions

Now it's time to put it all together! Let's look at some examples where we actually have to regroup our fractions. We will do this by borrowing from the whole number this time (instead of the tens place like in the first example). We will use what we borrow from the whole number to make our fraction bigger so we can actually subtract the fractions. Not to worry, it will all make more sense in a minute!

Example 1


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First start by subtracting the fractions as we did earlier. When we try to do this, we see the denominators are the same, so we look to subtract the numerators. We have 1 - 3 which is a problem because 3 is bigger than 1. So, we need to borrow from the whole number of 6! To do so, we turn 6 into 5 by borrowing a 1.

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