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