Multiplication Equations 2-7 Multiplication Equations Warm Up Problem of the Day Lesson Presentation Course 1 Course 1

Warm Up Divide. 1. 2. 3. 4. 5. 6. 72 12 65 5 6 13 40 10 60 6 10 4 130 5 91 7 26 13

Problem of the Day Katie’s little brother is building a tower with blocks. He adds 6 blocks and then removes 4 blocks. If he adds 8 more blocks, the tower will have twice as many blocks as when he started. How many blocks did he start with? 10 blocks

Learn to solve whole-number multiplication equations.

Division is the inverse of multiplication Division is the inverse of multiplication. To solve an equation that contains multiplication, use division to “undo” the multiplication. 4m = 32 Caution ! 4m = 32 4m means “4  m.” 4 4 m = 8

Additional Example 1A: Solving Multiplication Equations Solve the equation. Check your answer. 5p = 75 p is multiplied by 5. 5p = 75 Divide both sides by 5 to undo the multiplication. 5 5 p = 15 Check 5p = 75 5(15)= 75 ? Substitute 15 for p in the equation. 75 = 75 ?  15 is the solution.

Additional Example 1B: Solving Multiplication Equations Solve the equation. Check your answer. 16 = 8r r is multiplied by 8. 16 = 8r Divide both sides by 8 to undo the multiplication. 8 8 2 = r Check 16 = 8r 16 = 8(2) ? Substitute 2 for r in the equation. 16 = 16 ?  2 is the solution.

Solve the equation. Check your answer. Check It Out: Example 1A Solve the equation. Check your answer. 8a = 72 a is multiplied by 8. 8a = 72 Divide both sides by 8 to undo the multiplication. 8 8 x = 9 Check 8a = 72 8(9)= 72 ? Substitute 9 for a in the equation. 72 = 72 ?  9 is the solution.

Solve the equation. Check your answer. Check It Out: Example 1B Solve the equation. Check your answer. 18 = 3w w is multiplied by 3. 18 = 3w Divide both sides by 3 to undo the multiplication. 3 3 6 = w Check 18 = 3w 18 = 3(6) ? Substitute 6 for w in the equation. 18 = 18 ?  6 is the solution.

Additional Example 2: Problem Solving Application The area of a rectangle is 56 square inches. Its length is 8 inches. What is its width?

Understand the Problem Additional Example 2 Continued 1 Understand the Problem The answer will be the width of the rectangle in inches. List the important information: The area of the rectangle is 56 square inches. The length of the rectangle is 8 inches. Draw a diagram to represent this information. w 56 8

Additional Example 2 Continued Make a Plan You can write and solve an equation using the formula for area. To find the area of a rectangle, multiply its length by its width. A = lw w 56 = 8w l

Additional Example 2 Continued Solve 3 56 = 8w w is multiplied by 8. 56 = 8w Divide both sides by 8 to undo the multiplication. 8 8 7 = w So the width of the rectangle is 7 inches.

Additional Example 2 Continued 4 Look Back Arrange 56 identical squares in a rectangle. The length is 8, so line up the squares in rows of 8. You can make 7 rows of 8, so the width of the rectangle is 7.

Check It Out: Example 2 The area of a rectangle is 48 square inches. Its width is 8 inches. What is its length?

Understand the Problem Check It Out: Example 2 1 Understand the Problem The answer will be the length of the rectangle in inches. List the important information: The area of the rectangle is 48 square inches. The width of the rectangle is 8 inches. Draw a diagram to represent this information. 48 8 l

Check It Out: Example 2 Continued Make a Plan You can write and solve an equation using the formula for area. To find the area of a rectangle, multiply its length by its width. A = lw w 48 = l8 l

Check It Out: Example 2 Continued Solve 3 48 = 8l l is multiplied by 8. 48 = 8l Divide both sides by 8 to undo the multiplication. 8 8 6 = l So the length of the rectangle is 6 inches.

Check It Out: Example 2 Continued 4 Look Back Arrange 48 identical squares in a rectangle. The width is 8, so line up the squares in columns of 8. You can make 6 columns of 8, so the length of the rectangle is 6.

Lesson Quiz 1. 10y = 300 2. 2y = 82 3. 63 = 9y 4. 78 = 13x y = 30 y = 41 y = 7 x = 6 5. The area of a board game is 468 square inches. Its width is 18 inches. What is the length? 26 inches

2-8 Division Equations Warm Up Problem of the Day Lesson Presentation Course 1 Course 1

2-8 Division Equations Warm Up 1. 5x = 20 2. 7n = 84 3. 18 = y – 4 Course 1 Warm Up Solve. 1. 5x = 20 2. 7n = 84 3. 18 = y – 4 4. 21 = n + 3 x = 4 n = 12 y = 22 n = 18 Course 1

If 11 is 4 less than 3 times a number, what is the number? Problem of the Day If 11 is 4 less than 3 times a number, what is the number? 5

Learn to solve whole-number division equations.

Multiplication is the inverse of division Multiplication is the inverse of division. When an equation contains division, use multiplication to “undo” the division.

Solve the equation. Check your answer. Additional Example 1A: Solving Division Equations Solve the equation. Check your answer. x 7 = 5 x is divided by 7. x 7 = 5 7  x 7 = 7  5 Multiply both sides by 7 to undo the division. x = 35 Check x 7 = 5 35 7 = 5 ? Substitute 35 for x in the equation. 5 = 5 ?  35 is the solution.

Solve the equation. Check your answer. Additional Example 1B: Solving Division Equations Solve the equation. Check your answer. p 6 13 = p is divided by 6. p 6 13 = 6  p 6 6  13 = Multiply both sides by 6 to undo the division. 78 = p Check p 6 13 = ? 78 6 13 = Substitute 78 for p in the equation. 13 = 13 ? 78 is the solution. 

Solve the equation. Check your answer. Check It Out: Example 1A Solve the equation. Check your answer. x 2 = 9 x is divided by 2. x 2 = 9 2  x 2 = 2  9 Multiply both sides by 2 to undo the division. x = 18 Check x 2 = 9 18 2 = 9 ? Substitute 18 for x in the equation. 9 = 9 ?  18 is the solution.

Solve the equation. Check your answer. Check It Out: Example 1B Solve the equation. Check your answer. p 4 72 = p is divided by 4. p 4 72 = 4  p 4 4  72 = Multiply both sides by 4 to undo the division. 288 = p Check p 4 72 = ? 288 4 72 = Substitute 288 for p in the equation. 72 = 72 ? 288 is the solution. 

The aspen tree is 14 feet tall. How tall is the pine tree? Additional Example 2: Application At Elk Meadows Park an aspen tree is one-third the height of a pine tree. height of pine height of aspen = 3 The aspen tree is 14 feet tall. How tall is the pine tree? Let h represent the height of the pine tree. Substitute 14 for height of aspen. h is divided by 3. h 3 14 = 3  h 3 3  14 = Multiply both sides by 3 to undo the division. 42 = h The pine tree is 42 feet tall.

Jamie weighs one-half as much as her father. Check It Out: Example 2 Jamie weighs one-half as much as her father. father’s weight Jamie’s weight = 2 Jamie weighs 95 pounds. How many pounds does her father weigh? Let w represent her father’s weight. Substitute 95 for Jamie’s weight. w is divided by 2. w 2 95 = 2  w 2 2  95 = Multiply both sides by 2 to undo the division. 190 = w Jamie’s father weighs 190 pounds.

Solve each equation. Check your answers. Lesson Quiz Solve each equation. Check your answers. x 10 1. = 7 2. 8 = 3. = 11 4. = 7 x = 70 x 4 x = 32 x 9 x = 99 x 15 x = 105 5. The area of Sherry’s flower garden is one- fourth the area of her vegetable garden. The area of the flower garden is 17 square feet. Let x represent the area of her vegetable garden. Find the area of her vegetable garden? 68 square feet