advertisement

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