Understanding Division of Fractions - Weebly
Name
Reteaching
9-1
Divide a fraction by a whole number.
Find _18 4 4.
Use a model to show _18 .
Divide each eighth into 4 equal parts.
1
1.
5 __
Each section shows _____
32
(8 3 4)
1 4 4 5 __
1.
_
8
32
1 1 1 1 1 1 1 1
8 8 8 8 8 8 8 8
1
32
Divide a fraction by a fraction.
Find _34 4 _14.
Use a number line.
Count the number of _14s in _34.
0
1
4
2
4
3
4
Use repeated subtraction.
Subtract _14 from _34 until the difference
is 0.
3 2_
1 5_
2
_
4
4
4
2 2_
1 5_
1
_
1
4
4
4
1 2_
1 50
_
4
4
Count the number of times you
subtracted to find the quotient.
3 4 _
1 53
_
4
4
There are three _14s.
3 4_
1 53
_
4
4
Solve each division sentence. Use a model if you wish.
1. 3 4 _13 5
9
2. _15 4 4 5
__
1
20
Find each quotient. Simplify if possible.
3. 3 4 _12 5
3 4 __
1 5
6. __
16
16
9. 8 4 _14 5
6
3
32
9
5 4 _13 5 15
7 4 __
1 5
__
7
12
12
9 4 __
1 5
4. __
10
10
5. _15 4 3 5
7.
8. _12 4 6 5
10.
11. _67 4 _17 5
__
1
15
__
1
12
6
12. Draw a Picture The square dancing club meets for 3 hours. Every _34 hour, the
dancers change partners. How many different partners will each dancer have in one
meeting? Draw a picture to show your solution.
3 4 _34 5 4; 4 partners. Check students¡¯ drawings.
13. Writing to Explain Explain why the quotient of two fractions less
than 1 is always greater than either fraction.
The quotient is always greater than the fractions because
you are dividing by a number less than one.
26
Topic 9
? Pearson Education, Inc. 6
Reteaching 9-1
Understanding Division of
Fractions
Name
Practice
9-1
Understanding Division of
Fractions
Solve each division sentence using the models provided.
9
1. 3 ? _13 =
1
2
1
4
3
4. 8 ? _14 ?
7. _78 ? _18 ?
10. 6 ? _23 ?
1
6
0
Find each quotient. Simplify if possible.
32
7
__
1
5. _17 ? 4 ?
11 ? __
1 ?
8. __
12
12
9
11. 7 ? _13 ?
5
3. _56 ? _16 ?
24
2
6
3
6
4
6
28
6. 5 ? _12 ?
10
11
1 ?3?
9. __
12
36
21
15 ? __
1 ?
12. __
16
16
Practice 9-1
0
__
1
2. _14 ? 6 ?
5
6
__
1
15
13. Draw a Picture Olivia has a piece of ribbon _12 yard long. If she cuts it
into 6 equal pieces, what will be the length of each piece, in yards?
1 yard
Check students pictures: __
12
14. Geometry A regular polygon has a perimeter of 12 units. If each
side measures _34 unit, how many sides does the polygon have?
16
15. Which division expression is
shown by this model?
1
2
3
4
5
6
7
8
9
10
0
9 ? __
1
A __
10
10
9
1
B 1? __
10
9
D 10 ? __
10
9 ?1
C __
10
? Pearson Education, Inc. 6
16. Writing to Explain When you divide a whole number by a fraction
less than 1, will the quotient be greater than or less than the whole
number? Explain, and give an example.
The quotient will be greater because you are
dividing by a number less than 1. 4 ¡Â _13 = 12:
There are more fraction parts than wholes.
1
2
3
4
5
6
1
7
2
1
Each section 3
8
9
10
11
12
3
Topic 9
27
Name
Reteaching
9-2
Dividing a Whole Number by
a Fraction
Number
Reciprocal
Product
3
1
_
1
1
_
1
1
8
2
_
3
3
8
_
1
3
_
2
Find 14 _47.
Step 1
Step 2
Step 3
Rewrite the division as
multiplication using the
reciprocal of the divisor.
Divide out common factors
if possible. Then multiply.
If your answer is an
improper fraction, change it
to a mixed number.
The reciprocal of _47 is _74 .
14
__
7
1
_74
49
__
2
49 24_
1
__
2
2
2
14 ¡Â _47 = 14 ¡Á _74
Find the reciprocal of each fraction or whole number.
_7
5
1. _57
2. 11
__
1
11
3. _92
_2
9
Find each quotient. Simplify if possible.
4. 12 _45
7. 24 _34
10. 36 _89
15
32
40_12
5. 2 ¡Â _14
8. 18 _89
11. 42 _78
8
20_14
48
8
6. 16 ¡Â __
10
10
9. 25 ¡Â __
11
12. 40 ¡Â _45
20
27_12
50
13. Karolyn makes rolls for a friend¡¯s dinner party. She uses 3 lb of
butter. Each stick of butter weighs _14 lb. How many sticks of butter
does Karolyn need to make her rolls?
12 sticks
32
Topic 9
? Pearson Education, Inc. 6
Reteaching 9-2
To divide a whole number by a fraction, you can multiply the whole
number by the reciprocal of the fraction. The reciprocal of a number
has the numerator and the denominator reversed. The product of a
number and its reciprocal is 1.
Name
Practice
9-2
Dividing a Whole Number by
a Fraction
Find the reciprocal of each fraction or whole number.
_9
1. _59
5
2. 8
_1
3. _73
8
Find each quotient. Simplify if possible.
24
42 4 _79 5 54
_
22 4 _56 5 26 2
5
15 4 _13 5 45
48
10 4 _56 5 12
_
7 4 _23 5 10 1
2
6 4 _15 5 30
4. 8 4 _25 5
5. 4 4 _16 5
6. 18 4 _38 5
7.
8.
9.
10.
13.
11.
14.
12.
15.
7
Practice 9-2
20
12 4 _12 5 24
_
20 4 _34 5 26 2
3
9 4 _18 5 72
_3
16. Writing to Explain Will the quotient of 5 4 _78 be greater than or less
than 5? Explain.
The quotient will be greater than 5 because you are
dividing by a number that is less than 1.
17. Reasoning How many times will you need to fill a _12 cup
measuring cup to measure 4 cups of flour?
8
18. Geometry The distance around a circular flower bed is 36 feet.
Jasper wants to put stakes every 8 inches ( _23 of a foot) around the
bed. How many stakes does he need?
54 stakes
19. Algebra Which expression is equal to 9 3 _32 ?
A 2 4 _39
B 3 4 _92
C 9 4 _23
? Pearson Education, Inc. 6
D 9 4 _32
Topic 9
33
Name
Reteaching
9-3
Dividing Fractions
To divide by a fraction, you can multiply by its reciprocal. The reciprocal
of a number has the numerator and the denominator reversed.
Step 1
Step 2
Step 3
Rewrite the division as
multiplication using the
reciprocal of the divisor.
Divide out common factors
if possible. Then multiply.
If your answer is an
improper fraction, change it
to a mixed number.
3 is __
10 .
The reciprocal of __
10
3
4
_
2
5
1
3 _
10
4 __
4 ¡Á __
_
5
5
10
3
10
___
3
3
Find each quotient. Simplify if possible.
4
1. _12 _14 _12
2
8 =
2. _47 __
21
Reciprocal of _14
3. _13 _12
6. _37 3
9. _59 _12
9 _
4
12. __
5
10
_2
3
4. _25 ¡Â _23
7
7. _13 _89
_1
1_19
1_18
10. _35 _34
13. _13 _38
8 2_
2
_
3
3
8
_
_3
_4
7
__
21
8
1_12
8
Reciprocal of __
21
5
7
5. _58 ¡Â __
10
8
_4
5
_8
9
8. _56 ¡Â _18
_3
11. _34 ¡Â _56
14. _47 ¡Â _34
__
25
28
6_23
__
9
10
__
16
21
3 -gallon servings
15. Aaron has _78 gallon of bottled water. How many __
16
can he pour?
4_23 servings
16. Draw a Picture Show how Rebecca can divide _34 of a cake into
9 pieces. What fraction of the whole cake will each piece be?
1
Sample answer: Each piece is __
12 of
the cake.
? Pearson Education, Inc. 6
Reteaching 9-3
3.
Find _45 ¡Â __
10
38
Topic 9
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