5-9 Renaming to Subtract Mixed Numbers
Learn to rename mixed numbers to
subtract.
Course 1
5-9 Renaming to Subtract Mixed Numbers
3
Jimmy and his family planted a tree when it was 1__ ft
4
1
tall. Now the tree is 2 __ ft tall. How much has the tree
4
grown since it was planted?
3
1 – 1__
The difference in the heights is 2 __
.
4
4
1
You will need to rename 2 __ because the fraction
4
1
__
3
in 1 4 is greater than __ .
4
1
Divide one whole of 2__ into fourths.
4
Course 1
5-9 Renaming to Subtract Mixed Numbers
1
1
1
1
1
5
1
__
4 Rename 2
as 1 __.
4
4
1 1 1 1 1
4 4 4 4 4
1 1 1
4 4 4
1 1
4 4
1
__
2
4
3
–1 __
4
______
5
1 __
4
3
– 1__
4
______
1
2
__
= __
2
4
1
__
The tree has grown
ft since it was planted.
2
Course 1
5-9 Renaming to Subtract Mixed Numbers
Additional Example 1A: Renaming Mixed Numbers
Subtract. Write each answer in simplest form.
1
5
__
A. 7
– 2 __
6
6
1
7 __
6
7
6 __
6
5
–2 __
6
______
5
–2 __
6
______
1
1
6
1
Rename 7 __ as 6 + 1 __ = 6 + __ + __.
6
6
6
6
Subtract the fractions and then the
whole numbers.
2
1
4 __ = 4 __ Write the answer in simplest form.
6
3
Course 1
5-9 Renaming to Subtract Mixed Numbers
Additional Example 1B: Renaming Mixed Numbers
Subtract. Write each answer in simplest form.
2
7
__
__
B. 8
–6
5
10
4
8 __
10
14
7 __
10
7
–6 __
10
______
7
–6 __
10
______
7
1 __
10
Course 1
10 is a multiple of 5, so 10 is a
common denominator.
4
4
10
4
Rename 8 __ as 7 + 1 __ = 7 + __ + __ .
10
10
10
10
Subtract the fractions and then the
whole numbers.
5-9 Renaming to Subtract Mixed Numbers
Additional Example 1C: Renaming Mixed Numbers
Subtract. Write each answer in simplest form.
2
3
C. 6 – 3 __
6
2
–3 __
3
______
Course 1
3
5 __
3
2
–3 __
3
______
1
2 __
3
Write 6 as a mixed number with a
3 .
denominator of 3. Rename 6 as 5 + __
3
Subtract the fractions and then the
whole numbers.
5-9 Renaming to Subtract Mixed Numbers
Additional Example 1D: Renaming Mixed Numbers
Subtract. Write each answer in simplest form.
3
1
__
__
D. 5
–2
4
3
4
5 __
12
16
4 __
12
9
–2 __
12
______
9
–2 __
12
______
7
2 __
12
Course 1
The LCM of 4 and 3 is 12.
4
4
12
4
Rename 5 __ as 4 + 1 __ = 4 + __ + __ .
12
12
12
12
Subtract the fractions and then the
whole numbers.
5-9 Renaming to Subtract Mixed Numbers
Try This: Example 1A
Subtract. Write each answer in simplest form.
1
5
__
__
A. 5
–2
8
8
1
5 __
8
5
–2 __
8
______
9
4 __
8
5
–2 __
8
______
4
1
2 __ = 2 __
8
2
Course 1
1
1
4
1
Rename 5 __ as 4 + 1 __ = 4 + __ + __ .
8
8
4
8
Subtract the fractions and then the
whole numbers.
Write the answer in simplest form.
5-9 Renaming to Subtract Mixed Numbers
Try This: Example 1B
Subtract. Write each answer in simplest form.
1
7
__
__
B. 7
–3
6
12
2
7 __
12
14
6 __
12
7
–3 __
12
______
7
–3 __
12
______
7
3 __
12
Course 1
12 is a multiple of 6, so 12 is a
common denominator.
2
2
12
2
Rename 7 __ as 6 + 1 __ = 6 + __ + __ .
12
12
12
12
Subtract the fractions and then the
whole numbers.
5-9 Renaming to Subtract Mixed Numbers
Try This: Example 1C
Subtract. Write each answer in simplest form.
3
4
C. 5 – 2 __
5
3
–2 __
4
______
4
4 __
4
3
–2 __
4
______
1
2 __
4
Course 1
Write 5 as a mixed number with a
4
denominator of 4. Rename 5 as 4 + __ .
4
Subtract the fractions and then the
whole numbers.
5-9 Renaming to Subtract Mixed Numbers
Try This: Example 1D
Subtract. Write each answer in simplest form.
1
2
__
D. 8
– 4 __
2
3
3
8 __
6
9
7 __
6
4
–4 __
6
______
4
–4 __
6
______
5
3 __
6
Course 1
The LCM of 2 and 3 is 6.
3
3
6
3
Rename 8 __ as 7 + 1 __ = 7 + __ + __.
6
6
6
6
Subtract the fractions and then the
whole numbers.
5-9 Renaming to Subtract Mixed Numbers
Additional Example 2A: Measurement Application
Li is making a quilt. She needs 15 yards of fabric.
3
A. Li has 2 __ yards of fabric. How many more yards does
4
she need?
4
14 __
4
15
3
–2 __
4
______
3
–2 __
4
______
Write 15 as a mixed number with a
4
denominator of 4. Rename 15 as 14 + __ .
4
Subtract the fractions and then the
whole numbers.
1
__
12
4
Li needs another 12
Course 1
1
__
yards of fabric.
4
5-9 Renaming to Subtract Mixed Numbers
Additional Example 2B: Measurement Application
1
6
B. If Li uses 11 __ yards of fabric, how much of the 15
yards will she have left?
15
1
__
–11
6
______
Li will have 3
Course 1
6
14 __
6
1
__
–11
6
______
5
__
3
6
Write 15 as a mixed number with a
6
denominator of 6. Rename 15 as 14 + __ .
6
Subtract the fractions and then the
whole numbers.
5
__
yards of fabric.
6
5-9 Renaming to Subtract Mixed Numbers
Try This: Example 2A
Peggy is making curtains. She needs 13 feet of fabric.
5
__
A. Peggy has 4
yards of fabric. How many more yards
6
does she need?
13
5
–4 __
6
______
6
12 __
6
5
–4 __
6
______
Write 13 as a mixed number with a
6
denominator of 6. Rename 13 as 12 + __ .
6
Subtract the fractions and then the
whole numbers.
1
__
8
6
Peggy needs another 8
Course 1
1
__
yards of fabric.
6
5-9 Renaming to Subtract Mixed Numbers
Try This: Example 2B
1
__
B. If Peggy uses 9
yards of fabric, how much of the 13
4
yards will she have left?
13
1
__
–9
4
______
4
12 __
4
1
–9 __
4
______
Write 13 as a mixed number with a
4
denominator of 4. Rename 13 as 12 + __ .
4
Subtract the fractions and then the
whole numbers.
3
__
3
4
Peggy will have 3
Course 1
3
__
yards of fabric left.
4
to Subtract
5-9 Renaming
Insert Lesson
Title Mixed
Here Numbers
Lesson Quiz
Subtract. Write each answer in simplest form.
4 – 3 __
6
1. 7 __
7
7
2
3. 7 – 5 __
9
1
5
__
3
7
7
__
9
7
4
__
__
2. 8
–3
10
5
4
9
__
10
9
3 – 4 __
13
4. 10 __
5 __
8
16
16
5. Irena put 10 cups of food in the bird feeder. The birds ate
5
3 cups. How many cups are left?
3 __
6__ cups
8
Course 1
8