Addition Subtraction Multiplication and Division Equations 39 INTODUCTION

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 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. Shei. Kra is a roller coaster at Busch Gardens in Tampa, Florida. You must be 54 inches tall to ride Shei. Kra. 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 a – 27 = Theodore Roosevelt’s age – 27 = 42 a – 27 = 42 + 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 22 nd 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. 4 m = 32 4 4 m=8 Caution ! 4 m means “ 4 m. ”

Example 1: Solving Multiplication Equations Solve the equation. Check your answer. 5 p = 75

Example 2: Solving Multiplication Equations Solve the equation. Check your answer. 16 = 8 r

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?