1. 3-12 Solving Equations Containing Fractions Warm Up Problem of the Day
Course 2
Warm Up
Problem of the Day
Lesson Presentation

2. Dividing Fractions and Mixed Numbers
Course 2
3-11
Dividing Fractions and Mixed Numbers
Warm Up
Multiply or divide 7 9 3 6 7 18 1. 9 8 5 6 27 20 7
or 1 2. ÷ 2 77 5
or 15 1 5 3. 2 7 1 2 1 4 4. 2
÷ 1 2

3. Solving Equations Containing Fractions
Course 2
3-12
Solving Equations Containing Fractions
Warm Up – one step equations
Solve.
1. x – 16 = 8
2. 7a = 35 3.
4. y + 21 = 31
x = 24
a = 5 x 12
x = 132
= 11
y = 10

4. Dividing Fractions and Mixed Numbers
Course 2
3-11
Dividing Fractions and Mixed Numbers
Find the reciprocal 7 9 5 6 3 6 9 8 1 4 7 1 2 1 5 2 3

5. Course 2
3-12
Solving Equations Containing Fractions
Learning Objective: to solve one-step equations that contain fractions.

6. Additional Example 2A: Solving Equations by Multiplying
Course 2
3-12
Solving Equations Containing Fractions
Additional Example 2A: Solving Equations by Multiplying
Solve. Write the answer in simplest terms. 3 8 1 4 x = 3 8 = 1 4 x 3 8
Multiply by the reciprocal of . 2 3 8 . 8 3 1 4 . 8 3 x =
Then simplify. 1 2 3 x =
Caution!
To undo multiplying by 3 8 3 8
, you can divide by 8 3
or multiply
by its reciprocal, .

7. Additional Example 2B: Solving Equations by Multiplying
Course 2
3-12
Solving Equations Containing Fractions
Additional Example 2B: Solving Equations by Multiplying
Solve. Write the answer in simplest terms. 8 9
4x = 8 9
4x =
Multiply by the reciprocal of 4. 2 . 1 4 8 9 . 1 4 4 x =
Then simplify. 1 2 9
x =

8. Solving Equations Containing Fractions
Course 2
3-12
Solving Equations Containing Fractions
Check It Out: Example 2A
Solve. Write the answer in simplest terms. 3 4 1 2 x = 3 4 = 1 2 x 3 4
Multiply by the reciprocal of . 2 3 4 . 4 3 1 2 . 4 3 x =
Then simplify. 1 2 3 x =

9. Solving Equations Containing Fractions
Course 2
3-12
Solving Equations Containing Fractions
Check It Out: Example 2B
Solve. Write the answer in simplest terms. 6 7
3x = 6 7
3x =
Multiply by the reciprocal of 3. 2 . 1 3 6 7 . 1 3 3 x =
Then simplify. 1 2 7
x =

10. Additional Example 3: Physical Science Application
Course 2
3-12
Solving Equations Containing Fractions
Additional Example 3: Physical Science Application
The amount of copper in brass is of the total weight. If a sample contains 4 ounces of copper, what is the total weight of the sample? 3 4 1 5
Let w represent the total weight of the sample. 3 4
w = 4 1 5
Write an equation. 3 4
w · 4 3 1 5 4 3
= 4
Multiply by the reciprocal of 3 4 7 1 5
Write 4
as an improper
w = 21 5 4 3
fraction. 1 28 5
w =
or 5 3 5
Then simplify. 3 5
The sample weighs 5
ounces.

11. Solving Equations Containing Fractions
Course 2
3-12
Solving Equations Containing Fractions
Check It Out: Example 3
The amount of copper in zinc is of the total weight. If a sample contains 5 ounces of copper, what is the total weight of the sample? 1 4 1 3
Let w represent the total weight of the sample. 1 4
w = 5 3
Write an equation. 1 4
w · 4 1 1 3 4 1
= 5
Multiply by the reciprocal of 1 4 1 3
Write 5
as an improper
w = 16 3 4 1
fraction. 64 3
w =
or 21 1 3
Then simplify. 1 3
The sample weighs 21
ounces.

12. Insert Lesson Title Here
Course 2
3-12
Solving Equations Containing Fractions
Insert Lesson Title Here
Lesson Quiz
Solve. Write each answer in simplest form. 1. 2. 3. 4. 3 8 5 8
x – = 1 7 16 19 32 5 32
y + = x 4 3 7 12 7 5
or 1 = 3 4 1 3 16 9 7
or 1 x = 1
5. Over the course of a week, Marissa ate some apples from a basket on the table. She left 20 apples in the basket. This was five-eights the number of apples her mother had picked earlier in the week. How many apples did her mother pick? 32