Dividing Fractions and Mixed Number

Contributed by:

NEO Wed, Feb 02, 2022 12:30 PM UTC

This pdf includes the division of mixed numbers (mixed numerals) and how to divide them with examples for better understanding.

1. 5-9
5-9 Dividing
DividingFractions
Fractionsand
andMixed
MixedNumbers
Numbers
Warm Up
Problem of the Day
Lesson Presentation
L-12
6.NS.1
Course1 1

2. 5-9 Dividing Fractions and Mixed Numbers
Warm Up
Multiply. Write each answer in simplest
form.
1
1. 2 __ • 2 5
2
1
2. 1 __
2
• 3 __
1 __ or 5 1
21 _
2 4 4
1
3. 3 __
3
•3 10
4. 1
__
25 • 1
__
14 11 3
__ or 2 __
4 4
Course 1

3. 5-9 Dividing Fractions and Mixed Numbers
Problem of the Day
Rachel is building a doghouse. She
needs to cut a 12-foot-long board into
lengths of 65 in. How many lengths can
she cut, and will there be any wood left?
If so, how much?
2 cuts; yes, 14 in.
Course 1

4. 5-9 Dividing Fractions and Mixed Numbers
Learn to divide fractions and mixed
numbers.
Course 1

5. 5-9 Dividing Fractions and Mixed Numbers
Vocabulary
reciprocal
Course 1

6. 5-9 Dividing Fractions and Mixed Numbers
Reciprocals can help you divide
by fractions. Two numbers are
reciprocals if their product is 1.
Copy to Notebook!
Course 1

7. 5-9 Dividing Fractions and Mixed Numbers
Additional Example 1A: Finding Reciprocals
Find the reciprocal.
1
__
9
1
__ 1
__
• = 1 Think: 9 of what number is 1?
9
1
__ 1
__ 9
__
• 9 =1 of is 1.
9 9 1
1
__
The reciprocal of 9 is 9.
Course 1

8. 5-9 Dividing Fractions and Mixed Numbers
Additional Example 1B: Finding Reciprocals
Find the reciprocal.
2
__
3
2
__ 2
__
• =1 Think: 3 of what number is 1?
3
2 __3 6 2
__ 3
__ • = __ =1 of __ is 1.
3 2 6 3 2
2
__ 3
__
The reciprocal of 3 is 2 .
Course 1

9. 5-9 Dividing Fractions and Mixed Numbers
Additional Example 1C: Finding Reciprocals
Find the reciprocal.
1
3 __
5
1 16
16
__ • =1 Write 3 __ as __.
5 5 5
16 5
__ • __ 80 16 5
__ of __
= __ = 1 is 1.
5 16 80 5 16
16 5
The reciprocal of __ is __ .
5 16
Course 1

10. 5-9 Dividing Fractions and Mixed Numbers
Check It Out: Example 1A
Find the reciprocal.
1
__
4
1
__ 1
__
• =1 Think: 4 of what number is 1?
4
1 1
__ 4
__ • 4 =1 of __is 1.
4 4 1
1
__
The reciprocal of 4 is 4.
Course 1

11. 5-9 Dividing Fractions and Mixed Numbers
Check It Out: Example 1B
Find the reciprocal.
4
__
5
4
__ 4
__
• =1 Think: 5 of what number is 1?
5
4 __5 20 4
__ 5
__ • = __ = 1 of __ is 1.
5 4 20 5 4
4
__ 5
__
The reciprocal of 5 is 4 .
Course 1

12. 5-9 Dividing Fractions and Mixed Numbers
Check It Out: Example 1C
Find the reciprocal.
1
4 __
8
33 1 33.
Write 4 __ as __
__ • =1
8 8 8
33 8
__ • __ 264 33 8
__ of __
= ___ = 1 is 1.
8 33 264 8 33
33
__ 8
__
The reciprocal of 8 is 33 .
Course 1

13. 5-9 Dividing Fractions and Mixed Numbers
Look at the relationship between the
3
__ 4
__
fractions 4 and 3 . If you switch the
numerator and denominator of a fraction,
you will find its reciprocal. Dividing by a
number is the same as multiplying by its
reciprocal.
1
__
24 ÷ 4 = 6 24 • 4 = 6
Copy to Notebook!
Course 1

14. 5-9 Dividing Fractions and Mixed Numbers
Additional Example 2A: Using Reciprocals to
Divide Fractions and Mixed Numbers
Divide. Write each answer in simplest form.
8
__ ÷7
7
8
__ 8 1 Rewrite as multiplication using the
÷ 7 =__ • __ 1
__
7 7 7 reciprocal of 7, .
7
8•1
= ____ Multiply by the reciprocal.
7•7
8
= __ The answer is in simplest form.
49
Course 1

15. 5-9 Dividing Fractions and Mixed Numbers
Additional Example 2B: Using Reciprocals to
Divide Fractions and Mixed Numbers
5 2
__ ÷ __
6 3
5 __
__ 2 __5 3 Rewrite as multiplication using the
÷ = •__ 2
__ 3
__
6 3 6 2 reciprocal of 3 , 2 .
1
5•3
= ____ Simplify before multiplying.
6•2
2
5
= __ Multiply.
4
1
__ You can write the answer as a
=1
4 mixed number.
Course 1

16. 5-9 Dividing Fractions and Mixed Numbers
Additional Example 2C: Using Reciprocals to
Divide Fractions and Mixed Numbers
3 1
2 __ ÷ 1 __
4 12
Write the mixed numbers as
3 1 11 13 3 11
2 __ ÷ 1 __ = __ ÷ __ improper fractions. 2 __ = __
4 12 4 12 1 13 4 4
and 1 __ = __
12 12
11 12
= __ • __ Rewrite as
4 13 multiplication.
11 • 123
______
= Simplify before multiplying.
4 • 13
1
33
= __ Multiply.
13
7
__ You can write the answer as a
=2
13 mixed number.
Course 1

17. 5-9 Dividing Fractions and Mixed Numbers
Check It Out: Example 2A
Divide. Write each answer in simplest form.
2
__ ÷3
3
2
__ 2 1 Rewrite as multiplication using the
÷ 3 =__ • __ 1
__
3 3 3 reciprocal of 3, .
3
2•1
= ____ Multiply by the reciprocal.
3•3
2
= __ The answer is in simplest form.
9
Course 1

18. 5-9 Dividing Fractions and Mixed Numbers
Check It Out: Example 2B
7 1
__ ÷ __
10 5
7
__ 1 __
__ 7 5
__ Rewrite as multiplication using the
÷ = • 1 __
__ 5
10 5 10 1 reciprocal of 5 , 1 .
1
7•5
= ____ Simplify before multiplying.
10 • 1
2
7
= __ Multiply.
2
1 You can write the answer as a
= 3 __
2 mixed number.
Course 1

19. 5-9 Dividing Fractions and Mixed Numbers
Check It Out: Example 2C
2 1
3 __ ÷ 1 __
3 9
2
__ 1
__ 11
__ 10 Write the mixed numbers as
__
3 ÷1 = ÷ 2
__ 11
__
3 9 3 9 improper fractions. 3 =
3 3
1
__ 10
__
and 1 = .
9 9
11 9
= __ • __ Rewrite as
3 10 multiplication.
11 • 9 3
______
= Simplify before multiplying.
3 • 10
1
33
= __ Multiply.
10
3
__ You can write the answer as a
=3
10 mixed number.
Course 1

20. 5-9 Dividing Fractions and Mixed Numbers
Lesson Quiz
Find the reciprocal.
1
__ 11
__ 8
__ 13
__
1. 2.
13 8
11 1
Divide. Write each answer in simplest form.
4 1
__ 13 1 __ 2
7 , or 1 __
3. __ ÷ 20 4.__ ÷__
2 5
7 35 2 2 5
3
__ 1
__
5. Rhonda put 2 4 pounds of pecans into a 4 -pound
bag. How many bags did Rhonda fill?
11 bags
Course 1

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