Solving Fraction Equations Addition and Subtraction Warm Up
Solving Fraction Equations: Addition and Subtraction Warm Up Problem of the Day Lesson Presentation Lesson Quizzes
Solving Fraction Equations: 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
Solving Fraction Equations: Addition and Subtraction Learn to solve equations by adding and subtracting fractions.
Solving Fraction Equations: Addition and Subtraction Additional Example 1 A: 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 ______ 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: Addition and Subtraction Additional Example 1 B: 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 ______ 2 3 3 __ + 4 __ = x 9 9 + 4 __ 5 __ 7 =x 9 1 __ Add 4 to both sides to undo the 3 subtraction. Find a common denominator. Add.
Solving Fraction Equations: Addition and Subtraction Additional Example 1 C: 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 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: Addition and Subtraction Additional Example 1 D: Solving Equations by Adding and Subtracting Solve each equation. Write the solution in simplest form. 4 3 __ __ w– =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 4 __ Add to both sides to undo subtraction. 5 4 __ 5 8 __ 10 Find a common denominator. Add. Regroup 3 1 11 __ __ =3+1 10 10
Solving Fraction Equations: Addition and Subtraction Check It Out: Example 1 A Solve each equation. Write the solution in simplest form. 5 8 x + 3 __ = 12 x+3 5 __ = 12 8 5 5 – 3 __ ______ 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: Addition and Subtraction Check It Out: Example 1 B Solve each equation. Write the solution in simplest form. 3 1 __ __ 2 =x– 3 8 4 1 __ 4 ______ +3 3 8 2 __ + 3 __ = x 5 __ 5 =x 8 1 4 ______ + 3 __ 1 __ to both sides to undo the 4 subtraction. Add 3 Find a common denominator. Add.
Solving Fraction Equations: Addition and Subtraction Check It Out: Example 1 C 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 10 7 4 __ = m 10 Find a common denominator. Subtract.
Solving Fraction Equations: Addition and Subtraction Check It Out: Example 1 D 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 6 1 __ Add to both sides to undo subtraction. 3 Find a common denominator. Add. 1 7 __ __ Regroup 5 =5+1 6 6
Solving Fraction Equations: Addition and Subtraction Additional Example 2: Application 1 __ Linda’s dog weighs 85 pounds. If Linda’s dog weighs 4 1 __ 17 pounds less than Ian’s dog, how much does Ian’s 2 dog weigh? 1 1 d – 17__ = 85 __ 2 4 1 1 __ __ + 17 2 2 ________ 3 __ d = 102 4 Let d represent the weight of Ian’s dog. 1 __ to both sides to undo the 2 subtraction. Add 17
Solving Fraction Equations: 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 85 Ian’s dog weighs 102 Substitute 102 3 __ for d. 4 Find a common denominator. 3 __ 102 is the solution. 4 3 __ pounds. 4
Solving Fraction Equations: 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
Solving Fraction Equations: Addition and Subtraction Check It Out: Example 2 Continued 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 Substitute 17 5 __ for c. 6 Find a common denominator. 5 __ 17 is the solution. 6 5 __ pounds. 6
Solving Fraction Equations: Addition and Subtraction Lesson Quizzes Standard Lesson Quiz for Student Response Systems
Solving Fraction Equations: Addition and Subtraction Lesson Quiz Solve each equation. Write the solution in simplest form. 1 3 __ __ 5 3 5 __ __ __ x=6 1. x – 3 = 2 2. x + 6 = 11 x = 4 6 8 12 4 8 1 7 4 x = 4 __ 3. 1__ = x – 2 __ 2 10 5 1 1 x = 6 __ 3 __ __ 4. 5 =x– 4 2 4 5. Marco needs to work 40 hours per week. He has worked 5 31__ hours so far this week. How many hours does he need 8 to work on Friday to meet his 40 -hour requirement? 3 8 __ hours 8
Solving Fraction Equations: Addition and Subtraction Lesson Quiz for Student Response Systems 1. Solve the equation and identify the solution in simplest form. A. C. B. D.
Solving Fraction Equations: Addition and Subtraction Lesson Quiz for Student Response Systems 2. Solve the equation and identify the solution in simplest form. A. C. B. D.
Solving Fraction Equations: Addition and Subtraction Lesson Quiz for Student Response Systems 3. Solve the equation and identify the solution in simplest form. A. C. B. D.
Solving Fraction Equations: Addition and Subtraction Lesson Quiz for Student Response Systems 4. Solve the equation and identify the solution in simplest form. A. C. B. D.
Solving Fraction Equations: Addition and Subtraction 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.
- Slides: 22