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## 5-5

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**Solving Fraction Equations: Addition and Subtraction**5-5 Course 1 Warm Up Problem of the Day Lesson Presentation**Solving Fraction Equations: Addition and Subtraction**5-5 Course 1 Warm Up Solve. 1.x – 15 = 9 2.x + 21 = 34 3. 17 = x – 11 4. 22 = x – 34 x = 24 x = 13 x = 28 x = 56**Solving Fraction Equations: Addition and Subtraction**5-5 Course 1 Problem of the Day If a newborn baby weighs two pounds plus three-fourths its own weight, how much does it weigh? 8 pounds**Solving Fraction Equations: Addition and Subtraction**5-5 Course 1 Learn to solve equations by adding and subtracting fractions.**Solving Fraction Equations: Addition and Subtraction**5-5 3 5 3 3 3 2 5 3 3 __ __ __ __ __ __ __ __ __ 5 5 5 5 5 5 5 5 5 Subtract 5 from both sides to undo addition. Regroup 14 as 13 . Course 1 Additional Example 1A: Solving Equations by Adding and Subtracting Solve each equation. Write the solution in simplest form. x + 5 = 14 x + 5 = 14 – 5 – 5 ______ ______ x = 13 – 5 x = 8 Subtract.**Solving Fraction Equations: Addition and Subtraction**5-5 2 1 3 1 1 1 1 2 2 5 __ __ __ __ __ __ __ __ __ __ 9 3 3 9 9 9 3 3 3 9 Add 4 to both sides to undo the subtraction. Course 1 Additional Example 1B: Solving Equations by Adding and Subtracting Solve each equation. Write the solution in simplest form. 3 = x – 4 3 = x – 4 + 4 + 4 ______ ________ 3 + 4 = x Find a common denominator. 7= x Add.**Solving Fraction Equations: Addition and Subtraction**5-5 7 7 1 1 2 7 12 2 2 7 14 7 7 7 7 __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ 12 12 12 12 12 6 6 12 12 12 12 12 12 12 12 Course 1 Additional Example 1C: Solving Equations by Adding and Subtracting Solve each equation. Write the solution in simplest form. 6 = m + 6 = m + Subtract from both sides to undo the addition. – – ______ ______ 6 – = m Find a common denominator. 5 – = m Regroup 6 as 5 + . 5 = m Subtract.**Solving Fraction Equations: Addition and Subtraction**5-5 3 1 4 1 4 4 4 11 8 3 4 3 3 4 11 __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ 5 10 10 5 10 5 10 10 5 10 5 5 10 10 10 Course 1 Additional Example 1D: Solving Equations by Adding and Subtracting Solve each equation. Write the solution in simplest form. w – = 3 w – = 3 + + Add to both sides to undo subtraction. _____ _____ Find a common denominator. w = 3 + w = 3 + Add. 3 = 3 + 1 w = 3 w = 4**Solving Fraction Equations: Addition and Subtraction**5-5 5 8 5 5 5 3 8 5 5 __ __ __ __ __ __ __ __ __ 8 8 8 8 8 8 8 8 8 Subtract 3 from both sides to undo addition. Regroup 12 as 11 . Course 1 Check It Out: Example 1A Solve each equation. Write the solution in simplest form. x + 3 = 12 x + 3 = 12 – 3 – 3 ______ ______ x = 11 – 3 x = 8 Subtract.**Solving Fraction Equations: Addition and Subtraction**5-5 3 1 2 1 1 1 1 3 3 5 __ __ __ __ __ __ __ __ __ __ 8 4 4 8 8 8 4 4 4 8 Add 3 to both sides to undo the subtraction. Course 1 Check It Out: Example 1B Solve each equation. Write the solution in simplest form. 2 = x – 3 2 = x – 3 + 3 + 3 ______ ______ 2 + 3 = x Find a common denominator. 5 = x Add.**Solving Fraction Equations: Addition and Subtraction**5-5 7 7 2 2 4 7 10 4 4 7 14 7 7 7 7 __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ 10 10 10 10 10 5 5 10 10 10 10 10 10 10 10 Course 1 Check It Out: Example 1C Solve each equation. Write the solution in simplest form. 5 = m + 5 = m + Subtract from both sides to undo the addition. –– ______ ______ 5 – = m Find a common denominator. 4 – = m Regroup 5 as 4 + . 4 = m Subtract.**Solving Fraction Equations: Addition and Subtraction**5-5 5 1 1 1 1 1 1 7 2 5 1 5 5 1 7 __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ 3 6 6 3 6 3 6 6 3 6 3 3 6 6 6 Course 1 Check It Out: Example 1D Solve each equation. Write the solution in simplest form. w – = 5 w – = 5 + + Add to both sides to undo subtraction. _____ _____ Find a common denominator. w = 5 + w = 5 + Add. 5 = 5 + 1 w = 5 w = 6**Solving Fraction Equations: Addition and Subtraction**5-5 1 1 1 3 1 1 1 1 __ __ __ __ __ __ __ __ 2 4 4 2 2 2 4 2 Course 1 Additional Example 2: Application Linda’s dog weighs 85 pounds. If Linda’s dog weighs 17 pounds less than Ian’s dog, how much does Ian’s dog weigh? Let d represent the weight of Ian’s dog. d – 17 = 85 + 17 + 17 Add 17 to both sides to undo the subtraction. ________ ________ d = 102**Solving Fraction Equations: Addition and Subtraction**5-5 3 1 1 1 1 3 1 1 1 3 3 3 2 __ __ __ __ __ __ __ __ __ __ __ __ __ 4 4 4 2 4 4 4 4 4 4 2 4 4 Course 1 Additional Example 2 Continued Check d – 17 = 85 ? 102 – 17 = 85 Substitute 102 for d. ? Find a common denominator. 102 – 17 = 85 ? 102 is the solution. 85 = 85 Ian’s dog weighs 102 pounds.**Solving Fraction Equations: Addition and Subtraction**5-5 2 1 1 5 1 2 1 1 __ __ __ __ __ __ __ __ 6 3 3 6 6 6 6 6 Course 1 Check it Out: Example 2 Jimmy’s cat weighs 13 pounds. If Jimmy’s cat weighs 4 pounds less than Vicki’s cat, how much does Vicki’s cat weigh? Let c represent the weight of Vicki’s cat. c – 4 = 13 + 4 + 4 Add 4 to both sides to undo the subtraction. _______ ________ c = 17**Solving Fraction Equations: Addition and Subtraction**5-5 5 1 2 4 2 5 1 4 4 5 5 5 1 __ __ __ __ __ __ __ __ __ __ __ __ __ 3 6 3 6 6 6 6 6 6 6 6 6 6 Course 1 Check it Out: Example 2 Check c – 4 = 13 ? 17 – 4 = 13 Substitute 17 for c. ? Find a common denominator. 17 – 4 = 13 ? 17 is the solution. 13 = 13 Vicki’s cat weighs 17 pounds.**Solving Fraction Equations: Addition and Subtraction**5-5 x = 6 x = 4 x = 4 x = 6 1 3 5 5 5 7 1 3 3 1 1 3 __ __ __ __ __ __ __ __ __ __ __ __ 8 2 4 12 8 6 2 4 4 8 8 10 Course 1 Lesson Quiz Solve each equation. Write the solution in simplest form. 1.x – 3 = 2 2.x + 6 = 11 3. 1 = x – 2 4. 5 = x – 5. Marco needs to work 40 hours per week. He has worked 31 hours so far this week. How many hours does he need to work on Friday to meet his 40-hour requirement? 4 __ 5 8 hours