1. 3-4 Warm Up Problem of the Day Lesson Presentation
Dividing Rational Numbers
Pre-Algebra
Warm Up
Problem of the Day
Lesson Presentation

2. 3-4 Warm Up Multiply. –2 1. –3 2. –15 – 10 3. 0.05(2.8) 0.14
Pre-Algebra
3-4
Dividing Rational Numbers
Warm Up
Multiply.
5 6
1 2 –2 1. –3 2. 23
–15 – 10
(2.8)
0.14
4. –0.9(16.1)
–14.49

3. Problem of the Day
Katie made a bookshelf that is 5 feet long. The first 6 books she put on it took up 8 inches of shelf space. About how many books should fit on the shelf?
45 books

4. Learn to divide fractions and decimals.

5. Vocabulary
reciprocal

6. A number and its reciprocal have a product of 1
A number and its reciprocal have a product of 1. To find the reciprocal of a fraction, exchange the numerator and the denominator. Remember that an integer can be written as a fraction with a denominator of 1.

7. Multiplication and division are inverse operations
Multiplication and division are inverse operations. They undo each other.
1 3
2 5
2 15 =
2 5 = ÷
2 15
1 3
Notice that multiplying by the reciprocal gives the same result as dividing.
5 2
2 15
2 • 5 15 • 2
1 3 = =

8. Additional Example 1A: Dividing Fractions
Divide. Write the answer in simplest form.
5 11
1 2 A. ÷
5 11 ÷
1 2
5 11 •
2 1 =
Multiply by the reciprocal.
5 11 •
2 1 =
No common factors.
10 11 =
Simplest form

9. Additional Example 1B: Dividing Fractions
Divide. Write the answer in simplest form.
3 8 B. 2 ÷ 2
3 8 ÷ 2 =
19 8
2 1 ÷
Write as an improper fraction. =
19 8
1 2
Multiply by the reciprocal.
19 • 1
8 • 2 =
No common factors
19 16 =
3 16 = 1
19 ÷ 16 = 1 R 3

10. A. ÷ 28 45 Divide. Write the answer in simplest form. 7 15 3 4 7 15 ÷
Try This: Example1A
Divide. Write the answer in simplest form.
7 15
3 4 A. ÷
7 15 ÷
3 4
7 15 •
4 3 =
Multiply by the reciprocal.
7 • 4
15 • 3 =
No common factors.
28 45 =
Simplest form

11. B. 4 ÷ 3 ÷ ÷ 3 4 1 Divide. Write the answer in simplest form.
Try This: Example1B
Divide. Write the answer in simplest form.
2 5 B. 4 ÷ 3 =
22 5
3 1 ÷
Write as an improper fraction.
2 5
÷ 3 4 =
22 5
1 3
Multiply by the reciprocal.
22 • 1
5 • 3 =
No common factors.
7 15
= or 1
22 15
22 ÷ 15 = 1 R 7

12. When dividing a decimal by a decimal, multiply both numbers by a power of 10 so you can divide by a whole number. To decide which power of 10 to multiply by, look at the denominator. The number of decimal places is the number of zeros to write after 1.
1.32
0.4
1.32
0.4 10
13.2 4 = =
1 decimal place
1 zero

13. Additional Example 2: Dividing Decimals
Divide.
0.384 ÷ 0.24
0.384
0.24
0.384 ÷ 0.24 =
100
38.4 24 =
38.4 24 =
Divide. =
1.6

14. Try This: Example 2
Divide.
0.585 ÷ 0.25
0.585
0.25
0.585 ÷ 0.25 =
100
58.5 25 =
58.5 25 =
Divide. =
2.34

15. A. 100 35 5.25 for n = 0.15 n 0.15 has 2 decimal places, so use . 5.25
Additional Example 3A: Evaluating Expressions with Fractions and Decimals
Evaluate the expression for the given value of the variable.
5.25 A.
for n = 0.15 n
0.15 has 2 decimal places, so use
5.25
0.15 =
100
525 15 =
Divide. = 35

16. Additional Example 3B: Evaluating Expressions with Fractions and Decimals
Evaluate the expression for the given value of the variable.
4 5 B.
k ÷ for k = 5
5 4 =
5 1 •
4 5
5 ÷
5 • 5
1 • 4 =
254
1 4 6

17. A. for b = 0.75 = = = 3.4 0.75 has 2 decimal places, so use . Divide.
Try This: Example 3A
Evaluate the expression for the given value of the variable.
2.55 A.
for b = 0.75 b
0.75 has 2 decimal places, so use
2.55
0.75 =
100100
25575 =
Divide. =
3.4

18. u ÷ , for u = 9 B. = 9 ÷ = = 15 No common factors. 63 ÷ 4 = 15 R 3
Try This: Example 3B
Evaluate the expression for the given value of the variable.
4 7
u ÷ , for u = 9 B. =
9 1 9 ÷
4 7
7 4
Write as in improper fraction and multiply by the reciprocal.
9 • 7
1 • 4 =
No common factors. =
3 4 15
63 ÷ 4 = 15 R 3

19. Understand the Problem
Additional Example 4: Problem Solving Application
A cookie recipe calls for cup of oats. You have cup of oats. How many batches of cookies can you bake using all of the oats you have? 34
1 2 1
Understand the Problem
The number of batches of cookies you can bake is the number of batches using the oats that you have. List the important information:
The amount of oats is cup.
One batch of cookies calls for cup of oats. 12 34

20. Additional Example 4 Continued2
Make a Plan
Set up an equation.

21. Additional Example 4 Continued
Solve 3
Let n = number of batches. 12 34
= n ÷ 34 21
= n • 64
, or 1 batches of the cookies. 12

22. Additional Example 4 Continued
Look Back 4
One cup of oats would make two batches so 1 is a reasonable answer. 12

23. Try This: Example 4
A ship will use of its total fuel load for a typical round trip. If there is of a total fuel load on board now, how many complete trips can be made?
1 6
5 8

24. Understand the Problem
Try This: Example 4 Continued 1
Understand the Problem
The number of complete trips the ship can make is the number of trips that the ship can make with the fuel on board. List the important information:
It takes of the total fuel load for a complete trip. You have of a total fuel load on board right now. 58
1 6

25. ÷ = Try This: Example 4 Continued 2 Make a Plan Set up an equation.
Amount of fuel on board
Amount of fuel for one trip
Number of trips
÷ =

26. Try This: Example 4 Continued
Solve 3
Let t = number of trips. 58 16
= t ÷ 61
= t • 58
, or 3 round trips, or 3 complete round trips.
308 34

27. Try This: Example 4 Continued
Look Back 4
A full tank will make the round trip 6 times, and is a little more than , so half of 6, or 3, is a reasonable answer. 58 12

28. Lesson Quiz: Part 1
Divide.
5 6
1 2 –1 89 1. 2 ÷ –1
2. –14 ÷ 1.25
–11.2
÷ 0.65 6
112 x
4. Evaluate for x = 6.3.
17.7

29. Lesson Quiz: Part 2 5.
A penny weighs 2.5 grams. How many pennies would it take to equal one pound (453.6 grams)?
181