4-12

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

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

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

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

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

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

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

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

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

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

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

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

17. 4-12 Solving Equations Containing Fractions 1 5 3 4 w = 4 Course 2 Additional Example 3: Physical Science Application The amount of copper in brass is of the total weight. If a sample contains 4ounces of copper, what is the total weight of the sample? 3 4 1 5 Let w represent the total weight of the sample. Write an equation. 3 4 4 3 4 3 1 5 w · · = 4 3 4 Multiply by the reciprocal of · 1 5 7 Write 4 as an improper 21 5 4 3 w = · fraction. 1 28 5 3 5 w = or 5 Then simplify. 3 5 The sample weighs 5 ounces.

18. 4-12 Solving Equations Containing Fractions 1 3 1 4 w = 5 Course 2 Try This: Example 3 The amount of copper in zinc is of the total weight. If a sample contains 5ounces of zinc, what is the total weight of the sample? 1 4 1 3 Let w represent the total weight of the sample. Write an equation. 1 4 4 1 4 1 1 3 w · · = 5 1 4 Multiply by the reciprocal of · 1 3 Write 5 as an improper 16 3 4 1 w = · fraction. 64 3 1 3 w = or 21 Then simplify. 1 3 The sample weighs 21 ounces.

19. 4-12 Solving Equations Containing Fractions 12 7 5 7 or 1 16 9 7 9 or 1 Course 2 Insert Lesson Title Here Lesson Quiz Solve. Write each answer in simplest form. 1. 2. 3. 4. 3 8 5 8 1 x – = 5 32 7 16 19 32 y + = x 4 3 7 = 1 3 3 4 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