Download Addition, Subtraction, Multiplication, and Division Equations

Addition, Subtraction,
Multiplication, and Division
Equations
#39
INTODUCTION to Addition Equations
h + 14
82
h
?
h + 14
h
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.
INTODUCTION CONT.
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
Inverse operations undo each other.
Addition and subtraction are inverse
operations. If an equation contains addition,
solve it by subtracting from both sides to
“undo” the addition.
Example 1: Solving Addition Equations
Solve the equation. Check your answer.
x + 87 = 152
Example: 2
Solve each equation. Check your answers.
20 = 6 + n
Example: 3
For each exercise, write an addition equation. Then solve the
equation.
Sandy is thinking of a number. When 33 is added
to the number, the sum is equal to 55. What
number is Sandy thinking of?
Example: 4
For each exercise, write an addition equation. Then solve the
equation.
SheiKra is a roller coaster at Busch Gardens in
Tampa, Florida. You must be 54 inches tall to ride
SheiKra. Lisa is 5 inches short of this height
requirement. Find the height h of Lisa in inches.
Example: 5
For each exercise, write an addition equation. Then solve the
equation.
In Olympic archery, competitors use stabilizers to
help balance the bow. The main stabilizer is at most
36 inches in length. This is 7 inches more than its
minimum length. What is the minimum length of
the main stabilizer?
INTRODUCTION to Subtraction Equations
When Theodore Roosevelt became president of the United States, he was 42 years old. He was
27 years younger than Ronald Reagan was when Reagan became president. How old was
Reagan when he became president?
Let a represent Ronald Reagan’s age.
Ronald
Reagan’s age
a
–
27
=
Theodore
Roosevelt’s age
–
27
=
42
a – 27 = 42
+ 27 + 27
a
= 69
Ronald Reagan was 69 years old when he became
president.
Example 1: Solving Subtraction Equations
Solve y – 23 = 39. Check your answer.
Example 2: Solving Subtraction Equations
Solve 78 = s – 15. Check your answer.
Example: 3
Solve the equation. Check your answer.
57 = c – 13
Example: 4
Solve the equation. Check your answer.
Floridian Nancy Rios represented the United
States in windsurfing at the 2008 Olympics. In 10
races, her best finish was 22nd place. Her best
finish was 5 places ahead of her worst finish.
Solve the equation w - 5 = 22 to determine her
worst finish.
Example: 5
The Great Bay Scallop Search is one of Tampa Bay’s most popular
volunteer events each year. Volunteers snorkel to count scallops
and document the population trend.
In 2005, the search resulted in only one scallop!
This was 26 fewer scallops than were found in
1998. Write and solve a subtraction equation to
find the number of scallops found in 1998.
INTODUCTION to Multiplication Equations
Multiplication and division are inverse operations.
To solve an equation that contains multiplication,
use division to “undo” the multiplication.
4m = 32
4m = 32
4
4
m=8
Caution !
4m means “4  m.”
Example 1: Solving Multiplication Equations
Solve the equation. Check your answer.
5p = 75
Example 2: Solving Multiplication Equations
Solve the equation. Check your answer.
16 = 8r
Example 3: Problem Solving Application
The area of a rectangle is 56 square
inches. Its length is 8 inches. What
is its width?
Example 4
The area of a rectangle is 48 square
inches. Its width is 6 inches. What is
its length?
INTODUCTION to Division Equations
Recall that multiplication and division are
inverse operations. If an equation
contains division, solve it by multiplying
on both sides to “undo” the division.
Example 1: Solving Division Equations
Solve the equation. Check your answer.
x
=5
7
Example 2: Solving Division Equations
Solve the equation. Check your answer.
13 = p
6
Example 3
Solve the equation. Check your answer.
y =3
12
Example 4
Solve the equation. Check your answer.
m
21= 3
Example 5: Application
At Elk Meadows Park an aspen tree is onethird the height of a pine tree.
height of aspen = height of pine
3
The aspen tree is 14 feet tall. How tall is the
pine tree?
Example 6
Jamie weighs one-half as much as her father.
Jamie’s weight = father’s weight
2
Jamie weighs 95 pounds. How many pounds
does her father weigh?
Example 7
A rectangular garden is split into 3 equal sections.
Each section has an area of 100 square feet. What
is the area of the entire garden?