Explain when you know you need to rename a mixed number to subtract

We have already learned about renaming fractions when we have two different denominators. To rename a fraction means that we are going to take the fractions and write an equivalent fraction that has a common denominator.

13=39

This is an example of renaming one-third to be three-ninths. The fractions are equivalent or equal, but the second fraction has a denominator of 9.

Sometimes when we subtract mixed numbers, we must rename the mixed numbers in a different way.

What does this mean? It means that when we are subtracting a mixed number from a whole number, we must rename to subtract correctly.

Let’s look at an example.

Example

6−456––––––––

In this example, we are trying to take a fraction from a whole number. We have to RENAME this whole number to do this.

How can we rename 6 to have a whole number part and a fraction part?

Think back. Remember when we learned that any fraction where the numerator and the denominator are the same that the fraction is equal to one?

1=44 or 33 or 55

Do you remember this? Well, if we can take one and rename it as a fraction, then we can use that to help us in our subtraction.

In the example above, we need to take 6 and make it a mixed number so that we can subtract. To do this, we borrow a one from the six and make it five. Then we take that one and make it into a fraction that has sixths as a denominator since that is the denominator of the fraction we are subtracting.

6=566

Next, we rewrite the problem.

Example

566−456–––––––– 116

This is our final answer..

Sometimes, we also have to rename a mixed number if the fraction we are subtracting is larger than the first fraction.

Example

619−349––––––