Subtracting Mixed Numbers

Lesson 4-5

Process:

• Use the least common multiple to write equivalent fractions if the denominators are not the same.

• Subtract numerators. If you cannot subtract numerators, then rename the first mixed number.

• Subtract whole numbers.

• Simplify.

Borrowing not required:

7 34

5 58

7 68

5 58

8

1

2This answer is in simplest form.

A Picture of Renaming:

3 13

1 56

•This is a picture of three and one third.

•We want to take away one whole and five sixths.

•To do this, we need to rename to sixths.

•Now we have two sixths, but we need to take away five sixths. We don’t have enough sixths.

•Rename one whole to six sixths.

•Now we can cross out five of the sixths.

•We have subtracted the fractions. Now subtract the wholes.

•Take away one whole.

•We are left with one whole and three sixths.

Rename Mathematically:

3 13

1 56

31

The LCM of 3 and 6 is 6.

6

6

x 2 2

x 1 5

We have equivalent fractions, but we don’t have enough sixths to subtract.

Borrow from the whole number. Rename the whole as six sixths.

21= 6

6

We already had two sixths, and now we have borrowed one whole, which is six more sixths.

Two and six are eight. We now have eight sixths.

8

Subtract the fractions, then the whole numbers.

6

3

1

Simplify.

= 11

2

Another Example:

9 12

4 57

94

The LCM of 2 and 7 is 14.

14

14

x 7 7

x 2 10

We do not have enough fourteenths, so we must borrow from the 9.

8 1= 14

1421

14

114

This answer is in simplest form.

Subtracting from a whole number:• If you are subtracting a mixed number

from a whole number, then rename the whole number.

• Borrow one whole and use the denominator from the fraction.

Example:

83 5

8

7 1=8

8

We choose eight eighths because the denominator of the fraction is 8.

8

8

8

3

4

Homework Time