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5-4 Regrouping to Subtract Mixed Numbers
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Lesson QuizzesLesson Quizzes
5-4 Regrouping to Subtract Mixed Numbers
Warm UpAdd or subtract.
1. 2.
3. 4.
5 8
6 5
911__
1120__ 2
9__
5-4 Regrouping to Subtract Mixed Numbers
Problem of the Day
Complete the magic square so that every row, column, and diagonal has the same sum.
2
1 1
11
21 78__
58__
58__ 1
2__
12__1
78__
34__1 1
8__1
14__
38__
38__ 1
8__ 3
4__
14__
2
5-4 Regrouping to Subtract Mixed Numbers
Learn to regroup mixed numbers to subtract.
5-4 Regrouping to Subtract Mixed Numbers
Jimmy and his mother planted a tree when it was 1 ft
tall. Now the tree is 2 ft tall. How much has the tree
grown since it was planted?
34__
14__
14__ 3
4__
The difference in the heights can be represented by
2 – 1 .
14__
14__3
4__
You will need to regroup 2 because the fraction
in 1 is greater than .
14__Divide one whole of 2 into fourths.
5-4 Regrouping to Subtract Mixed Numbers
21
4__ 1
5
4__
–1
1
4__
– 1______ ______
= 2
4__ 1
2__
3
4__
Regroup 2 as 1 .3
4__
5
4__
The tree has grown ft since it was planted.12__
141
14
14
14
14
1
14
14
14
14
1
1
1414
5-4 Regrouping to Subtract Mixed Numbers
2
3__
6 53
3__
–32
3__ –3
2
3__
______ ______
2
Subtract the fractions and then the whole numbers.
Write 6 as a mixed number with a denominator of 3. Rename 6 as 5 + .3
3__
1
3__
6 – 3
6 – 4 = 2 Estimate the difference.
2 is close to the estimate of 2. The answer is reasonable. 1
3__
Additional Example 1A: Regrouping Mixed Numbers Subtract. Write each answer in simplest form.
5-4 Regrouping to Subtract Mixed Numbers
Additional Example 1B: Regrouping Mixed Numbers
Subtract. Write each answer in simplest form.
1
3__ 3
4__
54
12__ 4
16
12__
–29
12__ –2
9
12__
______ ______
2 7
12__ Subtract the fractions and then the
whole numbers.
Rename 5 as 4 + 1 = 4 + + . 4
12 __ 4
12__ 12
12__ 4
12__
The LCM of 4 and 3 is 12.
5 – 2
5 – 3 = 2 Estimate the difference.
2 is close to the estimate of 2. The answer is reasonable. 7
12__
5-4 Regrouping to Subtract Mixed Numbers
Check It Out: Example 1A
Subtract. Write each answer in simplest form.
1
6__ 5
6__
71
6__ 6
7
6__ Rename 7 as 6 + 1 = 6 + + .
–25
6__ –2
5
6__
______ ______
4 2
6__
Subtract the fractions and then the whole numbers.
16__ 1
6__ 6
6__ 1
6__
Write the answer in simplest form.
= 41
3__
7 – 2
7 – 3 = 4 Estimate the difference.
4 is close to the estimate of 4. The answer is reasonable. 1
3__
5-4 Regrouping to Subtract Mixed Numbers
2
5__ 7
10__
84
10__ 7
14
10__
Rename 8 as 7 + 1 = 7 + + . –6 7
10__ –6
7
10__
______ ______
1 7
10__ Subtract the fractions and then the
whole numbers.
410__ 4
10__ 10
10__ 4
10__
10 is a multiple of 5, so 10 is a common denominator.
8 – 6
8 – 7 = 1 Estimate the difference.
1 is close to the estimate of 1. The answer is reasonable. 7
10__
Check It Out: Example 1B
Subtract. Write each answer in simplest form.
5-4 Regrouping to Subtract Mixed Numbers
Additional Example 2A: Measurement Application
Li is making a quilt. She needs 15 yards of fabric.
Li has 2 yards of fabric. How many more yards does
she need?
3
4__
15 144
4__ Write 15 as a mixed number with a
denominator of 4. Rename 15 as 14 + .
–23
4__ –2 3
4__
______ ______
12
Subtract the fractions and then the whole numbers.
44__
1
4__
Li needs another 12 yards of fabric.1
4__
5-4 Regrouping to Subtract Mixed Numbers
Additional Example 2B: Measurement Application
If Li uses 11 yards of fabric, how much of the 15
yards will she have left?
1
6__
15 146
6__ Write 15 as a mixed number with a
denominator of 6. Rename 15 as 14 + .
–111
6__ –11
1
6__
______ ______
3
Subtract the fractions and then the whole numbers.
66__
5
6__
Li will have 3 yards of fabric.5
6__
5-4 Regrouping to Subtract Mixed Numbers
Check It Out: Example 2A
Peggy is making curtains. She needs 13 yards of fabric.
Peggy has 4 yards of fabric. How many more yards does she need?
5
6__
13 126
6__ Write 13 as a mixed number with a
denominator of 6. Rename 13 as 12 + .
–45
6__ –4 5
6__
______ ______
8
Subtract the fractions and then the whole numbers.
66__
1
6__
Peggy needs another 8 yards of fabric.1
6__
5-4 Regrouping to Subtract Mixed Numbers
Check It Out: Example 2B
If Peggy uses 9 yards of fabric, how much of the 13
yards will she have left?
1
4__
13 124
4__ Write 13 as a mixed number with a
denominator of 4. Rename 13 as 12 + .
–91
4__ –9 1
4__
______ ______
3
Subtract the fractions and then the whole numbers.
44__
3
4__
Peggy will have 3 yards of fabric left.3
4__
5-4 Regrouping to Subtract Mixed Numbers
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
5-4 Regrouping to Subtract Mixed Numbers
Lesson Quiz
Subtract. Write each answer in simplest form.
1. 2.
3. 4.
5. Irena put 10 cups of food in the bird feeder. The birds ate
3 cups. How many cups are left?
3
8__
35
7__ 4
9
10__
17
9__ 5
13
16__
6 cups5
8__
5-4 Regrouping to Subtract Mixed Numbers
1. Subtract and identify the answer in simplest form.
A. C.
B. D.
Lesson Quiz for Student Response Systems
5-4 Regrouping to Subtract Mixed Numbers
2. Subtract and identify the answer in simplest form.
A. C.
B. D.
Lesson Quiz for Student Response Systems
5-4 Regrouping to Subtract Mixed Numbers
3. Subtract and identify the answer in simplest form.
A. C.
B. D.
Lesson Quiz for Student Response Systems
5-4 Regrouping to Subtract Mixed Numbers
4. A Dachshund weighs pounds. A Dandi
Dinmont Terrier weighs 18 pounds. What is
the difference, in pounds, in their weights?
A. C.
B. D.
Lesson Quiz for Student Response Systems
