Unit 4 – Number Patterns and Fractions
Lesson 8 – Dividing Fractions
Green – Divide Fractions and Mixed Numbers
HELPFUL STRATEGY: It is often very difficult to figure out what numbers to multiply or
divide when problems contain fractions. If you substitute “easy” whole numbers into the
problem and solve, it makes the steps to solving the problem much easier to see.
1. Emily needs to read 85 pages from her history book. If she can read 1 1 page per
minute, how long will it take her to finish her assignment?
2. Janie wants to make raisin cookies. She needs 8
15-ounces box of raisins contains 2
her cookies?
16
1
cups of raisins for the cookies. A
2
3
cups. How many boxes must Janie buy to make
4
3. Eight friends buy 3 family size pizzas together and split them evenly. What fraction
of a pizza does each get?
4. 3
5
of a pie is to be divided among 4 people. What fraction of the pie does each
person get?
5.
A man had 5 bags of flour, each weighing
Find the weight of each bag of flour.
2
The division problem 2
fit into 2 pies?
9
kg. He repacked them into 3 equal bags.
10
÷¼
÷ ¼ can be said another way: How many times will ¼ of a pie
Look at the following fraction division problems and see if you can solve them mentally.
The first three are done for you.
6. 4 ÷
7. 2
1
1
⇒ will fit into four 8 times.
2
2
1 1
1
÷ ⇒ will fit into two and a half 10 times
2 4
4
1
Unit 4 – Number Patterns and Fractions
Lesson 8 – Dividing Fractions
8. 3
1 1
1
÷ ⇒ will fit into three and a quarter 26 times.
4 8
8
9.
1 1
÷
2 8
10. 2
11.
3 1
÷
4 8
12. 5 ÷
13. 20
1 1
÷
2 4
14.
1 1
÷
4 4
1
5
1 1
÷
2 16
3
pies were to be split evenly among
7
the people at the picnic, how much pie would each person get?
15. There were 48 people attending a picnic. If 3
16. Grace drove 159 miles and used 5
gallon of gas?
3
gallons of gas. How far could she go with one
10
17. Claire had to cut a board that was 9
each piece be?
18. Heather worked for 15
Heather's hourly wage?
1
feet long into 6 equal pieces. How long would
5
3
3
hours. She was paid a total of 102 dollars. What is
4
8
19. Christine has two boxes of crackers that she will share evenly with six friends (so
seven people all together) during a 7-day canoe trip. What fraction of a box will each
person eat per day?
2
Unit 4 – Number Patterns and Fractions
Lesson 8 – Dividing Fractions
Solutions
1. 80 minutes
85 17
85 16
is the same as
÷
×
= 80
1 17
1
16
3. 3
8
2. 3 boxes
4.
3
20
5. 2.7 kg
6. 8
7. 10
8. 26
9. 4
10. 9
11. 6
12. 25
13. 82
14. 8
15. 1/14 pie
16. 30 miles
17. 1
8
feet
15
18. $6.50 per hour
19. 2/49 of a box
2 boxes ÷ 7 people = 2/7 of a box for each person for the whole trip. Because the
trip is a 7 day trip, the 2/7 of a box must be divided by 7 to find the amount for
each day.
2 7
÷
7 1
2 1
2
× =
7 7 49
3
Unit 4 – Number Patterns and Fractions
Lesson 8 – Dividing Fractions
Bibliography Information
Teachers attempted to cite the sources for the problems included in this problem set. In some cases,
sources may not have been known.
Problems
Bibliography Information
1, 6-19
Zaccaro, Edward. Challenge Math (Second
Edition): Hickory Grove Press, 2005.
3
Geldof, W. Homework Book 3 /4, 2nd edition.
NZ Mathematics Curriculum, Sigma
Publications, 1999.
4