Fraction Equations 5 4 Solving Addition and Subtraction

Fraction Equations: 5 -4 Solving Addition and Subtraction Learn to solve equations by adding and subtracting fractions.

Fraction Equations: 5 -4 Solving 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

Fraction Equations: 5 -4 Solving 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.

Fraction Equations: 5 -4 Solving 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.

Fraction Equations: 5 -4 Solving 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

Fraction Equations: 5 -4 Solving 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

Fraction Equations: 5 -4 Solving 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.

Fraction Equations: 5 -4 Solving 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.

Fraction Equations: 5 -4 Solving 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

Fraction Equations: 5 -4 Solving 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 2 1 4 d – 17__ = 85 __ 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

Fraction Equations: 5 -4 Solving 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

Fraction Equations: 5 -4 Solving 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

Fraction Equations: 5 -4 Solving 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