Mixed fractions, also known as mixed numbers, consist of a whole number and a fraction. When you subtract two mixed numbers, you may have to regroup to work the problem. This study guide will help you work these types of problems.
What are Mixed Fractions?
Before you are subtracting mixed fractions with regrouping, you need to understand what mixed fractions, also known as mixed numbers, are. Here are some examples of mixed fractions:
1 2/3, 4 3/5, 6 2/5
Notice that each of these mixed fractions has a whole number and a proper fraction. Remember, a proper fraction is a fraction where the denominator is larger in value than the numerator.
Subtracting Mixed Fractions
In order to work on subtracting mixed fractions with regrouping, you need to review how to subtract mixed fractions without regrouping first. Follow the steps below:
4 7/8 - 2 1/4 =
1. Line up the two mixed numbers, so the one with the largest value is first. The one with the smallest value should be second.
2. Subtract the fractions first. Remember, they have to have the same denominator in order to subtract them. In the above example, you would need to change 1/4 to 2/8 by multiplying both the numerator and the denominator by 2. Now, you can work 7/8 - 2/8. The denominators stay the same which is 8. Then you subtract the numerators (7-2), which is 5. So, the answer to subtracting the fractions is 5/8.
3. Next, subtract the whole numbers. In the above example, it is 4-2, which equals 2.
4. The answer to subtracting mixed fractions in the above example is 2 5/8.
Subtracting Mixed Fractions with Regrouping
When you work on subtracting mixed fractions with regrouping, it is a similar process to subtracting whole numbers with regrouping. You know when you subtract whole numbers (two digits or more), you start with the ones place. Sometimes, you have to regroup or borrow from the tens place in order to work the problem. For example, 25-18=7, you would have to regroup to work the problem.
The same is true when subtracting mixed fractions if the fraction with the greatest whole number does not have the greatest fraction in value. For example, look at this problem:
6 1/2 - 3 5/8 =
The fraction with the greatest whole number is 1/2, which is smaller in value than 5/8. However, you still have to work the problem 1/2 - 5/8, just like you would if you started with the ones place in the above example problem of 25-18 (5-8). In order to work this problem correctly, you have to regroup or borrow.
When subtracting mixed numbers with regrouping, how do you borrow to subtract the fractions? You have to borrow from the whole number. Here's what you do:
1. Start with the fractions: 1/2 - 5/8.
2. Make sure both denominators are the same. If they are not the same, then you need to multiply the numerator and denominator to create an equivalent fraction. In this example, you would multiply 1/2 by 4 and get 4/8. Now, both the denominators are the same.
3. The new problem to subtract is 4/8 - 5/8. You still need to regroup in order to work this subtraction problem.
4. You have to borrow from the whole number. Remember that 1 = 8/8. So, in this example, you are going to borrow 1 or 8/8 from the 6. Now you have 5 8/8 4/8. Combine the 8/8 and 4/8, and you get 12/8.
5. Now you can work the fraction subtraction problem 12/8 - 5/8 = 7/8.
6. Next you subtract the whole numbers. Remember, you borrowed 1 from the largest whole number, so your problem is now 5 - 3 = 2.
7. Your answer is 2 7/8.
Those are the steps for subtracting mixed fractions with regrouping.