1. 4-12 Solving Equations Containing Fractions Warm Up Problem of the Day
Course 2
Warm Up
Problem of the Day
Lesson Presentation

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

3. Solving Equations Containing Fractions
Course 2
4-12
Solving Equations Containing Fractions
Problem of the Day
Write 15 positive integers less than 1,000 with digits that, when added together, total 4.
4, 13, 22, 31, 40, 103, 112, 121, 130, 202, 211, 220, 310, 400

4. Learn to solve one-step equations that contain fractions.
Course 2
4-12
Solving Equations Containing Fractions
Learn to solve one-step equations that contain fractions.

5. Solving Equations Containing Fractions
Course 2
4-12
Solving Equations Containing Fractions
Gold classified as 24 karat is pure gold, while gold classified as 18 karat is only pure. 3 4 1 4
The remaining of 18-karat gold is made up of one or more different metals, such as silver, copper, or zinc. The color of gold varies, depending on the type and amount of each metal added to the pure gold.

6. Solving Equations Containing Fractions
Course 2
4-12
Solving Equations Containing Fractions
Equations can help you determine the amounts of metals in different kinds of gold. The goal when solving equations that contain fractions is the same as when working with other kinds of numbers—to isolate the variable on one side of the equation.

7. Additional Example 1A: Solving Equations by Adding or Subtracting
Course 2
4-12
Solving Equations Containing Fractions
Additional Example 1A: Solving Equations by Adding or Subtracting
Solve. Write the answer in simplest form. 3 7 5 7
A. x – =
x – 3 7 = 5
x – 3 7 + = 5
Add to isolate x. x = 8 7 1
Simplify.

8. Additional Example 1B: Solving Equations by Adding or Subtracting
Course 2
4-12
Solving Equations Containing Fractions
Additional Example 1B: Solving Equations by Adding or Subtracting
Solve. Write the answer in simplest form. 3 4 1 8 B.
+ y = 3 4 1 8 + y = 3 4 y 3 4 1 8 3 4 +
Subtract to isolate y. – = – y 1 8 6 8 = –
Find a common denominator. 5 8 y = –
Subtract.
You can also isolate the variable y by adding the opposite of
Helpful Hint 3 4 3 4 , – ,
to both sides.

9. Additional Example 1C: Solving Equations by Adding or Subtracting
Course 2
4-12
Solving Equations Containing Fractions
Additional Example 1C: Solving Equations by Adding or Subtracting
Solve. Write the answer in simplest form. 5 12 3 8 C. +
t = – 5 12 + t = – 3 8 5 12 + t – = 3 8
Subtract to isolate t. = t – 9 24 10
Find a common denominator. t = – 19 24
Subtract.

10. Solving Equations Containing Fractions
Course 2
4-12
Solving Equations Containing Fractions
Try This: Example 1A
Solve. Write the answer in simplest form. 3 8 7 8
A. x – =
x – 3 8 = 7
x – 3 8 + = 7
Add to isolate x.
x = 10 8
= 1 1 4
Simplify.

11. Solving Equations Containing Fractions
Course 2
4-12
Solving Equations Containing Fractions
Try This: Example 1B
Solve. Write the answer in simplest form. 3 8 1 4 B.
+ y = 3 8 + y = 1 4 3 8 1 4 + y – =
Subtract to isolate y. 2 8 y = – 3
Find a common denominator. y = – 1 8
Subtract.

12. Solving Equations Containing Fractions
Course 2
4-12
Solving Equations Containing Fractions
Try This: Example 1C
Solve. Write the answer in simplest form. 3 14 2 7 C. +
t = – 3 14 + t = – 2 7 3 14 + t – = 2 7
Subtract to isolate t.
t = – – 3 14 4
Find a common denominator. t = – 7 14
Subtract. t = – 1 2
Simplify.

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

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

15. Solving Equations Containing Fractions
Course 2
4-12
Solving Equations Containing Fractions
Try This: Example 2A
Solve. Write the answer in simplest terms. 3 4 1 2 x A. = 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 =

16. Solving Equations Containing Fractions
Course 2
4-12
Solving Equations Containing Fractions
Try This: Example 2B
Solve. Write the answer in simplest terms. 6 7
B. 3x = 6 7
3x =
Multiply by the reciprocal of 3. 2 . 1 3 6 7 . 1 3
Then simplify. 3 x = 1 2 7
x =

17. Additional Example 3: Physical Science Application
Course 2
4-12
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.

18. Solving Equations Containing Fractions
Course 2
4-12
Solving Equations Containing Fractions
Try This: Example 3
The amount of copper in zinc is of the total weight. If a sample contains 5 ounces of zinc, 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.

19. Insert Lesson Title Here
Course 2
4-12
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 1
x – = 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