Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

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

Problem of the Day If a newborn baby weighs two pounds plus three-fourths its own weight, how much does it weigh? 8 pounds

Learn to solve equations by adding and subtracting fractions.

Additional Example 1A: Solving Equations by Adding and Subtracting Solve each equation. Write the solution in simplest form. 3 5 __ x + 5 = 14 3 5 __ x + 5 = 14 Subtract 5 from both sides to undo addition. 3 5 __ 3 5 __ 3 5 __ – 5 – 5 ______ ______ 5 __ 3 5 __ Regroup 14 as 13 . 5 __ x = 13 – 5 2 5 __ x = 8 Subtract.

Additional Example 1B: Solving Equations by Adding and Subtracting Solve each equation. Write the solution in simplest form. 2 9 __ 1 3 __ 3 = x – 4 2 9 __ 1 3 __ 3 = x – 4 Add 4 to both sides to undo the subtraction. 1 3 __ 1 3 __ 1 3 __ + 4 + 4 ______ ________ 2 9 __ 3 9 __ 3 + 4 = x Find a common denominator. 5 9 __ 7 = x Add.

Additional Example 1C: Solving Equations by Adding and Subtracting Solve each equation. Write the solution in simplest form. 1 6 __ 7 12 __ 6 = m + 1 6 __ 7 12 __ 6 = m + 7 12 __ 7 12 __ 7 12 __ Subtract from both sides to undo the addition. – – ______ ______ 2 12 __ 7 12 __ 6 – = m Find a common denominator. 14 12 __ 7 12 __ 2 12 __ 12 __ 2 12 __ 5 – = m Regroup 6 as 5 + . 7 12 __ 5 = m Subtract.

Additional Example 1D: Solving Equations by Adding and Subtracting Solve each equation. Write the solution in simplest form. 4 5 __ 3 10 __ w – = 3 4 5 __ 3 10 __ w – = 3 4 5 __ 4 5 __ 4 5 __ + + Add to both sides to undo subtraction. _____ _____ 3 10 __ 4 5 __ w = 3 + Find a common denominator. 3 10 __ 8 10 __ w = 3 + Add. 11 10 __ 1 10 __ 11 10 __ w = 3 Regroup 3 = 3 + 1 1 10 __ w = 4

Check It Out: Example 1A Solve each equation. Write the solution in simplest form. 5 8 __ x + 3 = 12 5 8 __ x + 3 = 12 Subtract 3 from both sides to undo addition. 5 8 __ 5 8 __ 5 8 __ – 3 – 3 ______ ______ 8 __ 5 8 __ Regroup 12 as 11 . 8 __ x = 11 – 3 3 8 __ x = 8 Subtract.

Check It Out: Example 1B Solve each equation. Write the solution in simplest form. 3 8 __ 1 4 __ 2 = x – 3 3 8 __ 1 4 __ 2 = x – 3 1 4 __ 1 4 __ Add 3 to both sides to undo the subtraction. 1 4 __ + 3 + 3 ______ ______ 3 8 __ 2 8 __ 2 + 3 = x Find a common denominator. 5 8 __ 5 = x Add.

Solve each equation. Write the solution in simplest form. Check It Out: Example 1C Solve each equation. Write the solution in simplest form. 2 5 __ 7 10 __ 5 = m + 2 5 __ 7 10 __ 5 = m + 7 10 __ 7 10 __ 7 10 __ Subtract from both sides to undo the addition. – – ______ ______ 4 10 __ 7 10 __ 5 – = m Find a common denominator. 14 10 __ 7 10 __ 4 10 __ 10 __ 4 10 __ 4 – = m Regroup 5 as 4 + . 7 10 __ 4 = m Subtract.

Solve each equation. Write the solution in simplest form. Check It Out: Example 1D Solve each equation. Write the solution in simplest form. 1 3 __ 5 6 __ w – = 5 1 3 __ 5 6 __ w – = 5 1 3 __ 1 3 __ 1 3 __ + + Add to both sides to undo subtraction. _____ _____ 5 6 __ 1 3 __ w = 5 + Find a common denominator. 5 6 __ 2 6 __ w = 5 + Add. 7 6 __ 1 6 __ 7 6 __ w = 5 Regroup 5 = 5 + 1 1 6 __ w = 6

Additional Example 2: Application 1 4 __ 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? 1 2 __ 1 2 __ 1 4 __ d – 17 = 85 Let d represent the weight of Ian’s dog. 1 2 __ 1 2 __ 1 2 __ + 17 + 17 Add 17 to both sides to undo the subtraction. ________ ________ 3 4 __ d = 102

Additional Example 2 Continued Check 1 2 __ 1 4 __ d – 17 = 85 3 4 __ 1 2 __ ? 1 4 __ 3 4 __ 102 – 17 = 85 Substitute 102 for d. 3 4 __ 2 4 __ ? 1 4 __ 102 – 17 = 85 Find a common denominator. 3 4 __ 1 4 __ ? 1 4 __ 85 = 85 102 is the solution. 3 4 __ Ian’s dog weighs 102 pounds.

Check It Out: Example 2 2 3 __ 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? 1 6 __ 1 6 __ 2 3 __ c – 4 = 13 Let c represent the weight of Vicki’s cat. 1 6 __ 1 6 __ 1 6 __ + 4 + 4 Add 4 to both sides to undo the subtraction. _______ ________ 5 6 __ c = 17

Check It Out: Example 2 Continued 1 6 __ 2 3 __ c – 4 = 13 5 6 __ 1 6 __ ? 2 3 __ 5 6 __ 17 – 4 = 13 Substitute 17 for c. 5 6 __ 1 6 __ ? 4 6 __ 17 – 4 = 13 Find a common denominator. 5 6 __ 4 6 __ ? 4 6 __ 13 = 13 17 is the solution. 5 6 __ Vicki’s cat weighs 17 pounds.

Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

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? 3 4 __ 5 12 __ x = 6 1 6 __ 5 8 __ x = 4 3 8 __ 7 10 __ x = 4 1 2 __ 4 3 4 __ 1 2 __ x = 6 1 4 __ __ 5 5 8 __ 3 8 __ 8 hours

Lesson Quiz for Student Response Systems 1. Solve the equation and identify the solution in simplest form. A. C. B. D.

Lesson Quiz for Student Response Systems 2. Solve the equation and identify the solution in simplest form. A. C. B. D.

Lesson Quiz for Student Response Systems 3. Solve the equation and identify the solution in simplest form. A. C. B. D.

Lesson Quiz for Student Response Systems 4. Solve the equation and identify the solution in simplest form. A. C. B. D.

Lesson Quiz for Student Response Systems 5. Jim needs to work 35 hours to complete his project. He has worked hours so far. How many hours more does he have to work to complete the project? A. C. B. D.