Download Ch. 2.5-Addition Equations

2-5
AdditionEquations
Equations
2-5 Addition
Warm Up
Problem of the Day
Lesson Presentation
Course
1
Course 11
Course
2-5 Addition Equations
Problem of the Day
After Renee used 40 m of string for her kite
and gave 5 m to her sister for her wagon,
she had 8 m of string left. How much string
did she have to start with?
53 m
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2-5 Addition Equations
Learn to solve whole-number addition
equations.
Course 1
2-5 Addition Equations
h + 14
82
h
?
h + 14
h
Course 1
82
68
The equation h + 14 = 82 can be
represented as a balanced scale.
To find the value of h, you need h
by itself on one side of the scale.
To get h by itself, first take away
14 from the left side of the scale.
Now the scale is unbalanced.
To rebalance the scale, take away
14 from the other side.
2-5 Addition Equations
Taking away 14 from both sides of the scale is
the same as subtracting 14 from both sides of
the equation.
h + 14 = 82
–14 –14
h = 68
Subtraction is the inverse, or opposite, of
addition. If an equation contains addition,
solve it by subtracting from both sides to
“undo” the addition.
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2-5 Addition Equations
Additional Example 1A: Solving Addition Equations
Solve the equation. Check your answer.
x + 87 = 152
x + 87 = 152
– 87 – 87
87 is added to x.
Subtract 87 from both
sides to undo the addition.
x = 65
Check x + 87 = 152
?
Substitute 65 for x in the
equation.
65 + 87 = 152
?
152 = 152  65 is the solution.
Course 1
2-5 Addition Equations
Additional Example 1B: Solving Addition Equations
Solve the equation. Check your answer.
72 = 18 + y
72 = 18 + y
–18 –18
54 =
y
Check 72 = 18 + y
?
72 = 18 + 54
?
72 = 72 
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18 is added to y.
Subtract 18 from both
sides to undo the addition.
Substitute 54 for y in the
equation.
54 is the solution.
2-5 Addition Equations
Check It Out: Example 1A
Solve the equation. Check your answer.
u + 43 = 78
u + 43 = 78
– 43 – 43
u
43 is added to u.
Subtract 43 from both
sides to undo the addition.
= 35
Check u + 43 = 78
?
35 + 43 = 78
?
78 = 78 
Course 1
Substitute 35 for u in the
equation.
35 is the solution.
2-5 Addition Equations
Check It Out: Example 1B
Solve the equation. Check your answer.
68 = 24 + g
68 = 24 + g
–24
–24
44 =
g
Check 68 = 24 + g
?
68 = 24 + 44
?
68 = 68 
Course 1
24 is added to g.
Subtract 24 from both
sides to undo the addition.
Substitute 44 for g in the
equation.
44 is the solution.
2-5 Addition Equations
Additional Example 2: Social Studies Application
Johnstown, Cooperstown, and Springfield are located
in that order in a straight line along a highway. It is
12 miles from Johnstown to Cooperstown and 95 miles
from Johnstown to Springfield. Find the distance d
between Cooperstown and Springfield.
distance between
Johnstown and
Springfield
=
95
=
95 = 12 + d
–12
–12
83 =
d
distance between
Johnstown and
Cooperstown
12
+
distance between
Cooperstown and
Springfield
+
d
12 is added to d.
Subtract 12 from both sides to undo
the addition.
It is 83 miles from Cooperstown to Springfield.
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2-5 Addition Equations
Check It Out: Example 2
Patterson, Jacobsville, and East Valley are located in
that order in a straight line along a highway. It is 17
miles from Patterson to Jacobsville and 35 miles from
Patterson to East Valley. Find the distance d between
Jacobsville and East Valley.
distance between
Patterson and East
Valley
=
35
=
35 = 17 + d
–17 –17
18 =
d
distance between
Patterson and
Jacobsville
17
+
distance between
Jacobsville and
East Valley
+
d
17 is added to d.
Subtract 17 from both sides to
undo the addition.
It is 18 miles from Jacobsville to East Valley.
Course 1