Subtracting Mixed Numbers

1
Subtracting Mixed Numbers

• Lesson 4-5

2
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.

3
Borrowing not required
7
7
3
6
4
8
5
5
5
5
8
8
2
1
8
This answer is in simplest form.
4
A Picture of Renaming
3
1
3
1
5
6

• 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 can cross out five of the sixths.

• We have subtracted the fractions. Now subtract
  the wholes.
• Take away one whole.

• Now we have two sixths, but we need to take away
  five sixths. We dont have enough sixths.
• Rename one whole to six sixths.

• We are left with one whole and three sixths.

5
Rename Mathematically
2
3
3

1
1
8
2
6
x 2
3
6
6
1
1
5
5
x 1
6
6
1
3
We already had two sixths, and now we have
borrowed one whole, which is six more sixths.
The LCM of 3 and 6 is 6.
6
We have equivalent fractions, but we dont have
enough sixths to subtract.
Two and six are eight. We now have eight sixths.

1
1
2
Borrow from the whole number. Rename the whole
as six sixths.
Subtract the fractions, then the whole numbers.
Simplify.
6
Another Example
8
1

14
14
9
9
21
1
7
x 7
14
2
4
4
10
5
x 2
14
7
4
11
The LCM of 2 and 7 is 14.
14
We do not have enough fourteenths, so we must
borrow from the 9.
This answer is in simplest form.
7
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.

8
Example
7
8
1

8
8
8
8
3
5
8
We choose eight eighths because the denominator
of the fraction is 8.
4
3
8
9
Homework Time