Addition, Subtraction, Multiplication, and Division Equations

#39

The equation h + 14 = 82 can be represented as a balanced scale.

h + 14 82

To find the value of h, you need h by itself on one side of the scale.

h ?

To get h by itself, first take away 14 from the left side of the scale. Now the scale is unbalanced.

h 68To rebalance the scale, take away 14 from the other side.

h + 14 82

INTODUCTION to 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 –14h = 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.

INTODUCTION CONT.

Solve the equation. Check your answer.Example 1: Solving Addition Equations

x + 87 = 152

Example: 2

20 = 6 + n

Solve each equation. Check your answers.

Example: 3

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?

For each exercise, write an addition equation. Then solve the equation.

Example: 4

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.

For each exercise, write an addition equation. Then solve the equation.

Example: 5

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?

For each exercise, write an addition equation. Then solve the equation.

Ronald Reagan’s age

Theodore Roosevelt’s age– = 27

Let a represent Ronald Reagan’s age.

a – =27 42

a – 27 = 42+ 27 + 27

a = 69

Ronald Reagan was 69 years old when he became president.

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?

INTRODUCTION to Subtraction Equations

Solve y – 23 = 39. Check your answer.

Example 1: Solving Subtraction Equations

Solve 78 = s – 15. Check your answer.

Example 2: Solving Subtraction Equations

Example: 3

57 = c – 13

Solve the equation. Check your answer.

Example: 4

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.

Solve the equation. Check your answer.

Example: 5

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.

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.

Multiplication and division are inverse operations. To solve an equation that contains multiplication, use division to “undo” the multiplication.

4m = 324m = 324 4 m = 8

Caution !

4m means “4 m.”

INTODUCTION to Multiplication Equations

5p = 75Solve the equation. Check your answer.

Example 1: Solving Multiplication Equations

16 = 8rSolve the equation. Check your answer.

Example 2: Solving Multiplication Equations

The area of a rectangle is 56 square inches. Its length is 8 inches. What is its width?

Example 3: Problem Solving Application

Example 4

The area of a rectangle is 48 square inches. Its width is 6 inches. What is its length?

Recall that multiplication and division are inverse operations. If an equation contains division, solve it by multiplying on both sides to “undo” the division.

INTODUCTION to Division Equations

Solve the equation. Check your answer.Example 1: Solving Division Equations

x7 = 5

Solve the equation. Check your answer.Example 2: Solving Division Equations

p613 =

Solve the equation. Check your answer.Example 3

y12= 3

Solve the equation. Check your answer.Example 4

m321=

At Elk Meadows Park an aspen tree is one-third the height of a pine tree.

Example 5: Application

height of aspen = height of pine3

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?