1. IWBAT divide fractions and decimals.

2. Vocabulary
reciprocal

3. WRITE: A number and its reciprocal have a product of 1
WRITE: 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.

4. Recall: Multiplication and division are inverse operations
Recall: 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 • • 2
1 3 = =

5. Ex. 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

6. Ex. 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

7. WRITE: 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 the 1.
1.32
0.4
1.32
0.4 10
13.2 4 = =
1 decimal place
1 zero

8. Ex. 2: Dividing Decimals
Find ÷ 0.24.
0.384
0.24
0.384 ÷ 0.24 =
100
38.4 24 =
38.4 24 =
Divide. =
1.6

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

10. Ex. 3B: Evaluating Expressions with Fractions and Decimals
Evaluate the expression for the given value of the variable.
4 5
k ÷ for k = 5
Multiply by the reciprocal.
5 4 =
5 1 •
4 5
5 ÷
5 • 5
1 • 4 =
25 4
1 4 6
Divide.
When k = 5, k ÷ =
4 5
1 4 6

11. Ex. 4: Problem Solving Application
1 2
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?
3 4
S – Study the problem. The number of batches of cookies you can bake is the number of batches using the oats that you have.
O - Organize the facts.
The amount of oats is cup.
One batch of cookies calls for cup of oats.
1 2
3 4

12. Ex. 4 Continued
L – Line Up a Plan
Set up an equation.

13. V – Verify the plan with action.
Ex. 4 Continued
V – Verify the plan with action.
Let n = number of batches.
1 2
3 4
= n ÷
3 4
2 1
= n •
6 4
, or 1 batches of cookies.
1 2

14. E – Evaluate your solution.
Ex. 4 Continued
E – Evaluate your solution.
One cup of oats would make two batches so 1 is a reasonable answer.
1 2