1. Solving Fraction Equations: Addition and Subtraction
5-10
Solving Fraction Equations: Addition and Subtraction
Course 1
Warm Up
Problem of the Day
Lesson Presentation

2. Solving Fraction Equations: Addition and Subtraction
Course 1
5-10
Solving Fraction Equations: Addition and Subtraction
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

3. Solving Fraction Equations: Addition and Subtraction
Course 1
5-10
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

4. Learn to solve equations by adding and subtracting fractions.
Course 1
5-10
Solving Fraction Equations: Addition and Subtraction
Learn to solve equations by adding and subtracting fractions.

5. Additional Example 1A: Solving Equations by Adding and Subtracting
Course 1
5-10
Solving Fraction Equations: Addition and Subtraction
Additional Example 1A: Solving Equations by Adding and Subtracting
Solve the equation. Write the solution in simplest form. 3 5 __
A. x = 14 3 5 __
x = 14
Subtract from both sides to undo addition. 3 5 __ 3 5 __ 3 5 __
– – 5
______ ______ 5 __ 3 5 __
Rename 14 as 5 __
x = – 5 2 5 __
x = 8
Subtract.

6. Additional Example 1B: Solving Equations by Adding and Subtracting
Course 1
5-10
Solving Fraction Equations: Addition and Subtraction
Additional Example 1B: Solving Equations by Adding and Subtracting
Solve the equation. Write the solution in simplest form. 2 9 __ 1 3 __
B = x – 4 2 9 __ 1 3 __
3 = x – 4
Add to both sides to undo the
subtraction. 1 3 __ 1 3 __ 1 3 __
______ ________ 2 9 __ 3 9 __
= x
Find a common denominator. 5 9 __
7 = x
Add.

7. Additional Example 1C: Solving Equations by Adding and Subtracting
Course 1
5-10
Solving Fraction Equations: Addition and Subtraction
Additional Example 1C: Solving Equations by Adding and Subtracting
Solve the equation. Write the solution in simplest form. 1 6 __ 7 12 __
C = 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
Rename as 7 12 __
5 = m
Subtract.

8. Additional Example 1D: Solving Equations by Adding and Subtracting
Course 1
5-10
Solving Fraction Equations: Addition and Subtraction
Additional Example 1D: Solving Equations by Adding and Subtracting
Solve the equation. Write the solution in simplest form. 4 5 __ 3 10 __
D. 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 =
Find a common denominator. 3 10 __ 8 10 __
w =
Add. 11 10 __ 1 10 __ 11 10 __
w = 3
3 = 1 10 __
w = 4

9. Solving Fraction Equations: Addition and Subtraction
Course 1
5-10
Solving Fraction Equations: Addition and Subtraction
Try This: Example 1A
Solve the equation. Write the solution in simplest form. 5 8 __
A. x = 12 5 8 __
x = 12
Subtract from both sides to undo addition. 5 8 __ 5 8 __ 5 8 __
– – 3
______ ______ 8 __ 5 8 __
Rename 12 as 8 __
x = – 3 3 8 __
x = 8
Subtract.

10. Solving Fraction Equations: Addition and Subtraction
Course 1
5-10
Solving Fraction Equations: Addition and Subtraction
Try This: Example 1B
Solve the equation. Write the solution in simplest form. 3 8 __ 1 4 __
B = x – 3 3 8 __ 1 4 __
2 = x – 3 1 4 __ 1 4 __
Add to both sides to undo the
subtraction. 1 4 __
______ ______ 3 8 __ 2 8 __
= x
Find a common denominator. 5 8 __
5 = x
Add.

11. Solve the equation. Write the solution in simplest form.
Course 1
5-10
Solving Fraction Equations: Addition and Subtraction
Try This: Example 1C
Solve the equation. Write the solution in simplest form. 2 5 __ 7 10 __
C = 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 __
= m
Rename as 7 10 __
4 = m
Subtract.

12. Solve the equation. Write the solution in simplest form.
Course 1
5-10
Solving Fraction Equations: Addition and Subtraction
Try This: Example 1D
Solve the equation. Write the solution in simplest form. 1 3 __ 5 6 __
D. 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 =
Find a common denominator. 5 6 __ 2 6 __
w =
Add. 7 6 __ 1 6 __ 7 6 __
w = 5
5 = 1 6 __
w = 6

13. Additional Example 2: Application
Course 1
5-10
Solving Fraction Equations: Addition and Subtraction
Additional Example 2: Application 1 4 __
Linda’s dog weighs pounds. If Linda’s dog weighs pounds less than Ian’s dog, how much does Ian’s dog weigh? 1 2 __ 1 2 __ 1 4 __
d – = 85
Let d represent the weight of Ian’s dog. 1 2 __ 1 2 __ 1 2 __
Add to both sides to undo the
subtraction.
________ ________ 3 4 __
d = 102

14. Additional Example 2 Continued
Course 1
5-10
Solving Fraction Equations: Addition and Subtraction
Additional Example 2 Continued
Check 1 2 __ 1 4 __
d – = 85 3 4 __ 1 2 __ ? 1 4 __ 3 4 __
– = 85
Substitute for d. 3 4 __ 2 4 __ ? 1 4 __
– = 85
Find a common denominator. 3 4 __ 1 4 __ ? 1 4 __
85 = 85
is the solution. 3 4 __
Ian’s dog weighs pounds.

15. Solving Fraction Equations: Addition and Subtraction
Course 1
5-10
Solving Fraction Equations: Addition and Subtraction
Try This: Example 2 2 3 __
Jimmy’s cat weighs 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 – = 13
Let c represent the weight of Vicki’s cat. 1 6 __ 1 6 __ 1 6 __
Add to both sides to undo the
subtraction.
_______ ________ 5 6 __
c = 17

16. Solving Fraction Equations: Addition and Subtraction
Course 1
5-10
Solving Fraction Equations: Addition and Subtraction
Try This: Example 2
Check 1 6 __ 2 3 __
c – 4 = 13 5 6 __ 1 6 __ ? 2 3 __ 5 6 __
– 4 = 13
Substitute for c. 5 6 __ 1 6 __ ? 4 6 __
– 4 = 13
Find a common denominator. 5 6 __ 4 6 __ ? 4 6 __
13 = 13
is the solution. 5 6 __
Vicki’s cat weighs pounds.

17. Solving Fraction Equations: Addition and Subtraction
Course 1
5-10
Solving Fraction Equations: Addition and Subtraction
Lesson Quiz
Solve each equation. Write the solution in simplest form.
1. x – 3 = x = 11
= x – = x –
5. Marco needs to work 40 hours per week. He has worked 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 __
hours