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4-8 Dividing Fractions and Mixed Numbers
Warm Up
Problem of the Day
Lesson Presentation
Course 2
4-8 Dividing Fractions and Mixed Numbers
Warm Up
Multiply.
1. 7 ·
9
9 ·
2.
8
3. 2 1
5
7
18
7
27
or 1
20
20
77 or 15 2
·7
5
5
3
6
6
5
1 ·1
2
4.
2 4
Course 2
5
8
4-8 Dividing Fractions and Mixed Numbers
Problem of the Day
The Jeffers family is putting in a new
fence around their yard. The yard is in
the shape of a square. If they put nine
fence posts on each side of the square,
how many posts will be used?
32
Course 2
4-8 Dividing Fractions and Mixed Numbers
Learn to divide fractions and mixed
numbers.
Course 2
Fractions
and Here
Mixed Numbers
4-8 Dividing
Insert Lesson
Title
Vocabulary
reciprocal
Course 2
4-8 Dividing Fractions and Mixed Numbers
When you divide 8 by 4 you find how many
4’s there are in 8. Similarly, when you divide
1
1
2 by 3 , you find how many 3 ’s there are in 2.
There are six
Course 2
1
’s
3
in 2.
4-8 Dividing Fractions and Mixed Numbers
Reciprocals can help you divide by fractions.
Two numbers are reciprocals if their product
is 1. The reciprocal of 1 is 3 because
3
1 · 3 = 1 · 3 = 3 = 1.
3 1
3
3
To divide by a fraction, find its reciprocal and then
multiply.
2 ÷1 = 2 · 3 = 6
3
Course 2
4-8 Dividing Fractions and Mixed Numbers
Additional Example 1A & 1B: Dividing Fractions
Divide. Write each answer in simplest form.
2
3
A. 7 ÷ 5
3 ÷ 2 = 3 5
·
7
5
7 2
·
= 3 5
7 · 2
15 or 1 1
=
14
14
3
B.
÷ 12
8
3 ÷ 12 = 3 · 1
8
12
8
13
1
·
=
12 4
8
1
=
32
Course 2
Multiply by the reciprocal of
2
.
5
Multiply by the reciprocal of 12.
Simplify.
4-8 Dividing Fractions and Mixed Numbers
Try This: Example 1A & 1B
Divide. Write each answer in simplest form.
1
3
A. 5 ÷ 2
3 ÷ 1 = 3 2
·
5
2
5 1
·
= 3 2
5 · 1
6 or 1 1
=
5
5
3
B.
÷ 3
4
3 ÷ 3 =3 · 1
4
3
4
13
1
·
=
3 1
4
1
=
4
Course 2
Multiply by the reciprocal of
1
.
2
Multiply by the reciprocal of 3.
Simplify.
DividingLesson
Fractions
andHere
Mixed Numbers
4-8 Insert
Title
Additional Example 2A & 2B: Dividing Mixed Numbers
Divide. Write each answer in simplest form.
÷11
A. 5 2
3
4
5 2 ÷ 1 1 = 17 ÷ 5
3
4
4
3
B.
3 ÷ 1
22
4
= 17 · 4
3
5
= 68 or 4 8
15
15
3 ÷2 1 = 3 ÷
4
2
4
= 3 ·
4
3 ·
=
24 ·
= 3
10
Course 2
5
2
2
5
1
2
5
Write mixed numbers as improper
fractions.
5
Multiply by the reciprocal of .
4
1
as an improper fraction.
2
Write 2
Multiply by the reciprocal of 5 .
2
Simplify.
4-8 Dividing Fractions and Mixed Numbers
Additional Example 2C: Dividing Mixed Numbers
Divide. Write the answer in simplest form.
C. 8 2 ÷ 13
3
27
26 ÷ 13 Write 8 2 as an improper fraction.
8 2 ÷ 13 =
3
27
27
3
3
26
27 Multiply by the reciprocal of 13 .
=
·
27
3
13
226 · 27 9
=
3 · 13 1
1
= 18 or 18
1
Course 2
DividingLesson
Fractions
andHere
Mixed Numbers
4-8 Insert
Title
Try This: Example 2A & 2B
Divide. Write each answer in simplest form.
÷11
A. 3 2
3
2
3 2 ÷ 1 1 = 11 ÷ 3
3
2
2
3
B.
3 ÷ 2
15
5
= 11 · 2
3
3
= 22 or 2 4
9
9
3 ÷1 2 = 3
5
5
5
= 3
5
3
=
15
= 3
7
Course 2
7
5
· 5
7
1
· 5
· 7
÷
Write mixed numbers as improper
fractions.
3
Multiply by the reciprocal of .
2
2
as an improper fraction.
5
Write 1
Multiply by the reciprocal of 7 .
5
Simplify.
4-8 Dividing Fractions and Mixed Numbers
Try This: Example 2C
Divide. Write the answer in simplest form.
C. 7 1 ÷ 18
5
5
36 ÷ 18 Write 7 1 as an improper fraction.
7 1 ÷ 18 =
5
5
5
5
5
36
5_ Multiply by the reciprocal of 18 .
=
·
5
5
18
2 36 · 5 1
=
5 · 181
1
= 2 or 2
1
Course 2
4-8 Dividing Fractions and Mixed Numbers
Additional Example 3: Social Studies Application
The life span of a golden dollar coin is 30 years, while
paper currency lasts an average of 1 1 years. How many
2
times longer will the golden dollar stay in circulation?
30 ÷ 1 1 = 30 ÷ 3
Write the number as an improper fraction.
2
1
2
30 · 2
3
Multiply by the reciprocal of .
=
1
3
2
10 30 · 2
=
Simplify.
1 · 31
= 20 or 20
1
The golden dollar will stay in circulation about
20 times longer than paper currency.
Course 2
4-8 Dividing Fractions and Mixed Numbers
Try This: Example 3
The average life of a queen ant is approximately 3 years.
The life span of a worker ant is 3 year. How many
7
times longer will the queen ant live?
3 ÷ 3 = 3 ÷3
Write the number as an improper fraction.
7
1 7
3· 7
3
Multiply by the reciprocal of .
=
1 3
7
1 3 · 7
=
Simplify.
1 · 31
= 7 or 7
1
The queen ant will live 7 times longer than the
worker ant.
Course 2
Fractions
and Here
Mixed Numbers
4-8 Dividing
Insert Lesson
Title
Lesson Quiz
Divide. Write each answer in simplest form.
4
1. 8 ÷
5
2. 5 ÷ 1
9
8
3
÷6
3.
5
1
1
4. 2 ÷ 3
7
2
10
40 or 4
4
9
9
1
10
35
44
5. There are 5 1 yards of silk in a roll. If it takes 3
4
4
of a yard to make one designer scarf, how many
scarves can be made from the roll?
7
Course 2