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4-6 Solving Equations Containing Fractions California Standards AF1.1 Write and solve one-step linear equations in one variable. Also covered: NS2.1, NS2.2, NS2.4 Holt CA Course 1 4-6 Solving Equations Containing Fractions The goal when solving equations that contain fractions is the same as when working with other kinds of numbers—to get the variable by itself on one side of the equation. Holt CA Course 1 4-6 Solving Equations Containing Fractions Example 1A: Solving Equations by Adding or Subtracting Solve. Write the answer in simplest form. x – 3= 5 7 7 x– 3 =5 7 7 x – 3 + 3= 5+ 3 7 7 7 7 1 x = 8 =1 7 7 Holt CA Course 1 3 Since 7 is subtracted from x, 3 add 7 to both sides. Simplify. 4-6 Solving Equations Containing Fractions Example 1B: Solving Equations by Adding or Subtracting Solve. Write the answer in simplest form. 3 5 + t = 8 12 3 + t = 5 12 8 5– 3 3 3 + t– = 12 8 8 8 t = 10 – 9 24 24 t= Holt CA Course 1 1 24 3 Since 8 is added to t, subtract 3 from both sides. 8 Find a common denominator. Subtract. 4-6 Solving Equations Containing Fractions Example 2A: Solving Equations by Multiplying Solve. Write the answer in simplest form. 3x 1 = 8 4 3 =1 x 8 4 2 1 8 8 3x = 41 3 3 8 x =2 3 Multiply by the reciprocal of 3 . 8 Then simplify. Caution! To undo multiplying by 3 , you can divide by 3 8 8 or multiply by its reciprocal, . 3 Holt CA Course 1 8 4-6 Solving Equations Containing Fractions Additional Example 2B: Solving Equations by Multiplying Solve. Write the answer in simplest form. 4y = 8 9 4y = 8 9 2 81 1 = 4y 4 9 41 y= 2 9 Holt CA Course 1 Multiply by the reciprocal of 4. Then simplify. 4-6 Solving Equations Containing Fractions Example 3: Physical Science Application The amount of copper in brass is 3 of the total weight. If a 4 1 sample contains 4 ounces of copper, what is the total 5 weight of the sample? Let w represent the total weight of the sample. 3w = 41 5 4 3w 4 Write an equation. 4 = 4 1 43 3 Multiply by the reciprocal of 3 · 5 1 Write 4 as an improper 5 7 w = 21 4 5 fraction. 31 w = 28 or 5 3 5 5 Then simplify. The sample weighs 5 3 ounces. 5 Holt CA Course 1 4 4-6 Solving Equations Containing Fractions Check It Out! Example 1 Solve. Write the answer in simplest form. 3 7 x – 8= 8 x– 3 =7 8 8 x – 3 + 3= 7+ 3 8 8 8 8 3 3 Since 8 is subtracted from x, add 8 to both sides. 1 x = 10 = 1 4 8 Holt CA Course 1 Simplify. 4-6 Solving Equations Containing Fractions Check It Out! Example 2 Solve. Write the answer in simplest form. 3y = 6 7 3y = 6 7 2 1 3y = 6 1 3 7 31 y= 2 7 Holt CA Course 1 Multiply by the reciprocal of 3. Then simplify. 4-6 Solving Equations Containing Fractions Check It Out! Example 3 The amount of copper in zinc is 1 4 of the total weight. If a 1 sample contains 53 ounces of copper, what is the total weight of the sample? Let w represent the total weight of the sample. 1w = 51 3 4 1w 4 Write an equation. 4 = 51 4 1 3 Multiply by the reciprocal of 1 · 1 1 Write 5 as an improper 3 w = 16 4 3 fraction. 1 w = 64 or 21 1 3 3 Multiply. The sample weighs 21 1 ounces. 3 Holt CA Course 1 4