5-4 Solving Fraction Equations: Addition and Subtraction
Warm Up
Lesson Presentation
Problem of the Day
Lesson Quizzes
5-4 Solving Fraction Equations: Addition and Subtraction
Warm UpSolve.
1. x – 15 = 9
2. x + 21 = 34
3. 17 = x – 11
4. 22 = x – 34
x = 24
x = 13
x = 28
x = 56
5-4 Solving Fraction Equations: 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
5-4 Solving Fraction Equations: Addition and Subtraction
Learn to solve equations by adding and subtracting fractions.
5-4 Solving Fraction Equations: Addition and Subtraction
Additional Example 1A: Solving Equations by Adding and Subtracting
Solve each equation. Write the solution in simplest form.
3
5__
x + 5 = 143
5__
3
5__ – 5 – 5
3
5__
______ ______
x = 13 – 53
5__5
5__
x = 82
5__
Subtract 5 from both sides to undo addition.
3
5__
Regroup 14 as 13 . 5
5__
Subtract.
x + 5 = 14
5-4 Solving Fraction Equations: Addition and Subtraction
Additional Example 1B: Solving Equations by Adding and Subtracting
Solve each equation. Write the solution in simplest form.
2
9__
3 = x – 42
9__
1
3__ + 4 + 4
1
3__
______ ________
3 + 4 = x3
9__2
9__
7 = x5
9__
Add 4 to both sides to undo the
subtraction.
1
3__
Find a common denominator.
Add.
1
3__
1
3__
3 = x – 4
5-4 Solving Fraction Equations: Addition and Subtraction
Additional Example 1C: Solving Equations by Adding and Subtracting
Solve each equation. Write the solution in simplest form.
1
6__
6 = m +1
6__
7
12__ – –
7
12__
______ ______
6 – = m7
12__2
12__
5 = m7
12__
Subtract from both sides to undo the
addition.
7
12__
Find a common denominator.
Subtract.
7
12__
7
12__
5 – = m7
12__14
12__
Regroup 6 as 5 + . 2
12__ 12
12__ 2
12__
6 = m +
5-4 Solving Fraction Equations: Addition and Subtraction
Additional Example 1D: Solving Equations by Adding and Subtracting
Solve each equation. Write the solution in simplest form.
4
5__
w – = 34
5__
4
5__ + + 4
5__
_____ _____
w = 3 +4
5__3
10__
w = 3 +3
10__
Add to both sides to undo subtraction.
4
5__
Find a common denominator.
Add.
3
10__
3
10__
8
10__
w = 3
w = 4
11
10__
1
10__
Regroup 3 = 3 + 1 11
10__ 1
10__
w – = 3
5-4 Solving Fraction Equations: Addition and Subtraction
Check It Out: Example 1A
Solve each equation. Write the solution in simplest form.
5
8__
x + 3 = 125
8__
5
8__ – 3 – 3
5
8__
______ ______
x = 11 – 35
8__8
8__
x = 83
8__
Subtract 3 from both sides to undo addition.
5
8__
Regroup 12 as 11 . 8
8__
Subtract.
x + 3 = 12
5-4 Solving Fraction Equations: Addition and Subtraction
Check It Out: Example 1B
Solve each equation. Write the solution in simplest form.
3
8__
2 = x – 33
8__
1
4__ + 3 + 3
1
4__
______ ______
2 + 3 = x2
8__3
8__
5 = x5
8__
Add 3 to both sides to undo the
subtraction.
1
4__
Find a common denominator.
Add.
1
4__
1
4__
2 = x – 3
5-4 Solving Fraction Equations: Addition and Subtraction
Check It Out: Example 1C
Solve each equation. Write the solution in simplest form.
2
5__
5 = m +2
5__
7
10__ – –
7
10__
______ ______
5 – = m7
10__4
10__
4 = m
7
10__
Subtract from both sides to undo the
addition.
7
10__
Find a common denominator.
Subtract.
7
10__
7
10__
4 – = m
7
10__
14
10__ Regroup 5 as 4 + .
4
10__ 10
10__ 4
10__
5 = m +
5-4 Solving Fraction Equations: Addition and Subtraction
Check It Out: Example 1D
Solve each equation. Write the solution in simplest form.1
3__
w – = 51
3__
1
3__ + +
1
3__
_____ _____
w = 5 +1
3__5
6__
w = 5 +5
6__
Add to both sides to undo subtraction. 1
3__
Find a common denominator.
Add.
5
6__
5
6__
2
6__
w = 5
w = 6
7
6__
1
6__
Regroup 5 = 5 + 1 7
6__ 1
6__
w – = 5
5-4 Solving Fraction Equations: Addition and Subtraction
Additional Example 2: Application1
4__
1
2__
d – 17 = 851
2__
1
2__ + 17 + 17
1
2__
________ ________
1
4__
d = 1023
4__
Let d represent the weight of Ian’s dog.
Add 17 to both sides to undo the
subtraction.
1
2__
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?
5-4 Solving Fraction Equations: Addition and Subtraction
Additional Example 2 Continued
Check
d – 17 = 85 1
2__ 1
4__
3
4__102 – 17 = 85
1
2__ 1
4__?
3
4__102 – 17 = 85
2
4__ 1
4__?
85 = 85 ? 1
4__1
4__
Substitute 102 for d. 3
4__
Find a common denominator.
102 is the solution. 3
4__
Ian’s dog weighs 102 pounds.3
4__
5-4 Solving Fraction Equations: Addition and Subtraction
Check It Out: Example 22
3__
1
6__
c – 4 = 131
6__
1
6__ + 4 + 4
1
6__
_______ ________
2
3__
c = 175
6__
Let c represent the weight of Vicki’s cat.
Add 4 to both sides to undo the
subtraction.
1
6__
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?
5-4 Solving Fraction Equations: Addition and Subtraction
Check It Out: Example 2 Continued
Check
c – 4 = 13 1
6__ 2
3__
5
6__ 17 – 4 = 13
1
6__ 2
3__?
5
6__ 17 – 4 = 13
1
6__ 4
6__?
13 = 13 ? 4
6__4
6__
Substitute 17 for c. 5
6__
Find a common denominator.
17 is the solution. 5
6__
Vicki’s cat weighs 17 pounds.5
6__
5-4 Solving Fraction Equations: Addition and Subtraction
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
5-4 Solving Fraction Equations: Addition and Subtraction
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?
Lesson Quiz
34__ 5
12__ x = 6
16__ 5
8__
710__ 1
2__3
4__
58__
x = 438__
x = 412__ x = 6
14__
8 hours38__
45__
5-4 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.
5-4 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.
5-4 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.
5-4 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.
5-4 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.