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

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

3. Gold classified as 24 karat is pure gold, while gold classified as 18 karat is only pure. 3434 1414 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. Course 2 4-12 Solving Equations Containing Fractions

4. 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.

5. Solve. Write the answer in simplest form. Additional Example 1A: Solving Equations by Adding or Subtracting A. x – 3737 = 5757 x – 3737 = 5757 3737 + 3737 = 5757 + 3737 Add to isolate x. x= 8787 = 1 1717 Simplify. Course 2 4-12 Solving Equations Containing Fractions

6. Solve. Write the answer in simplest form. Additional Example 1B: Solving Equations by Adding or Subtracting B. 3434 + y = 1818 3434 + y = 1818 3434 + y – 3434 = 1818 – 3434 Subtract to isolate y. y = 1818 – 6868 y =– 5858 Find a common denominator. Subtract. You can also isolate the variable y by adding the opposite of Helpful Hint 3434, – 3434, to both sides. Course 2 4-12 Solving Equations Containing Fractions

7. Solve. Write the answer in simplest form. Additional Example 1C: Solving Equations by Adding or Subtracting C. 5 12 +t = – 3838 5 12 + t =– 3838 = t– 9 24 – 10 24 t= – 19 24 Subtract to isolate t. Find a common denominator. Subtract. Course 2 4-12 Solving Equations Containing Fractions 5 12 + t –= – 3838 – 5 12 5 12

8. Solve. Write the answer in simplest form. Try This: Example 1A A. x – 3838 = 7878 x – 3838 = 7878 3838 + 3838 = 7878 + 3838 Add to isolate x. x = 10 8 = 1 1414 Simplify. Course 2 4-12 Solving Equations Containing Fractions

9. Solve. Write the answer in simplest form. Try This: Example 1B B. 3838 + y = 1414 3838 + y = 1414 3838 1414 3838 + y – = – 3838 Subtract to isolate y. 2828 y = – 3838 y =– 1818 Find a common denominator. Subtract. Course 2 4-12 Solving Equations Containing Fractions

10. Solve. Write the answer in simplest form. Try This: Example 1C C. 3 14 +t = – 2727 3 14 + t =– 2727 Subtract to isolate t. Find a common denominator. Subtract. Course 2 4-12 Solving Equations Containing Fractions 3 14 + t –= – 2727 – 3 14 3 14 t = – – 3 14 4 14 t= – 7 14 Simplify. t= – 1 2

11. Solve. Write the answer in simplest terms. Additional Example 2A: Solving Equations by Multiplying A. 3838 x = 1414 3838 x=. 8383 1414.8383 2 1 =x 2323 Multiply by the reciprocal of. 3838 Then simplify. 3838 = 1414 x = To undo multiplying by Remember! 3838, you can divide by 3838 or multiply by its reciprocal, 8383. Course 2 4-12 Solving Equations Containing Fractions

12. Additional Example 2B: Solving Equations by Multiplying B. 4x = 8989 8989 x=. 1414 8989. 1414 1 2 x = 2929 4x = 4 Multiply by the reciprocal of 4. Then simplify. Solve. Write the answer in simplest terms. Course 2 4-12 Solving Equations Containing Fractions

13. Solve. Write the answer in simplest terms. Try This: Example 2A A. 3434 x = 1212 3434 x=. 4343 1212.4343 2 1 =x 2323 Multiply by the reciprocal of. 3434 Then simplify. 3434 = 1212 x = Course 2 4-12 Solving Equations Containing Fractions

14. Try This: Example 2B B. 3x = 6767 6767 x=. 1313 6767. 1313 1 2 x = 2727 3x = 3 Multiply by the reciprocal of 3. Then simplify. Solve. Write the answer in simplest terms. Course 2 4-12 Solving Equations Containing Fractions

15. 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? Additional Example 3: Physical Science Application 3434 1515 Let w represent the total weight of the sample. 3434 w = 4 1515 3434 w · 4343 = 4 1515 · 4343 w = 21 5 · 4343 7 1 w = 28 5 or 5 3535 Write an equation. Multiply by the reciprocal of 3434 · Write 4 1515 as an improper fraction. Then simplify. The sample weighs 5 3535 ounces. Course 2 4-12 Solving Equations Containing Fractions

16. 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? Try This: Example 3 1414 1313 Let w represent the total weight of the sample. 1414 w = 5 1313 1414 w · 4141 = 5 1313 · 4141 w = 16 3 · 4141 w = 64 3 or 21 1313 Write an equation. Multiply by the reciprocal of 1414 · Write 5 1313 as an improper fraction. Then simplify. The sample weighs 21 1313 ounces. Course 2 4-12 Solving Equations Containing Fractions

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