Warm Up Divide. 1. 2. 3. 4. 5. 6.

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

2. Learn to solve whole-number multiplication equations.

3. 4 4 Multiplication and division are inverse operations. To solve an equation that contains multiplication, use division to “undo” the multiplication. 4m = 32 Caution ! 4m = 32 4m means “4  m.” m = 8

4. 5 5 ? 5(15)= 75 ? 75 = 75 Additional Example 1A: Solving Multiplication Equations Solve the equation. Check your answer. 5p = 75 p is multiplied by 5. Divide both sides by 5 to undo the multiplication. 5p = 75 p = 15 Check 5p = 75 Substitute 15 forp in the equation.  15 is the solution.

5. 8 8 ? 16 = 8(2) ? 16 = 16 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. 2 = r Check 16 =8r Substitute 2 forr in the equation.  2 is the solution.

6. 8 8 ? 8(9)= 72 ? 72 = 72 Check It Out: Example 1A Solve the equation. Check your answer. a is multiplied by 8. 8a = 72 8a = 72 Divide both sides by 8 to undo the multiplication. a = 9 Check 8a = 72 Substitute 9 fora in the equation.  9 is the solution.

7. 3 3 ? 18 = 3(6) ? 18 = 18 Check It Out: Example 1B Solve the equation. Check your answer. w is multiplied by 3. 18 = 3w 18 = 3w Divide both sides by 3 to undo the multiplication. 6 = w Check 18 =3w Substitute 6 forw in the equation.  6 is the solution.

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

9. 1 Understand the Problem Additional Example 2 Continued 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

10. Make a Plan 2 Additional Example 2 Continued 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

11. 3 Solve 8 8 Additional Example 2 Continued 56= 8w w is multiplied by 8. 56= 8w Divide both sides by 8 to undo the multiplication. 7= w So the width of the rectangle is 7 inches.

12. 4 Additional Example 2 Continued 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.

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

14. 1 Understand the Problem Check It Out: Example 2 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. 8 48 l

15. Make a Plan 2 Check It Out: Example 2 Continued 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

16. 3 Solve 8 8 Check It Out: Example 2 Continued 48= 8l l is multiplied by 8. 48= 8l Divide both sides by 8 to undo the multiplication. 6= l So the length of the rectangle is 6 inches.

17. 4 Check It Out: Example 2 Continued 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.

18. Learn to solve whole-number division equations.

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

20. 35 x x x = 5 = 5 = 5 = 5 7 7 7 7 x is divided by 7. x 7 = 7 5 7 Check ? ? 5 = 5 Additional Example 1A: Solving Division Equations Solve the equation. Check your answer. Multiply both sides by 7 to undo the division. x = 35 Substitute 35 for x in the equation. 35 is the solution. 

21. 78 p p p 13 = 13 = 13 = 13 = 6 6 6 6 p is divided by 6. p 6 13 = 6 6 Check ? ? 13 = 13 Additional Example 1B: Solving Division Equations Solve the equation. Check your answer. Multiply both sides by 6 to undo the division. 78 = p Substitute 78 for p in the equation. 78 is the solution. 

22. 18 x x x = 9 = 9 = 9 = 9 2 2 2 2 x is divided by 2. x 2 = 2 9 2 Check ? ? 9 = 9 Check It Out: Example 1A Solve the equation. Check your answer. Multiply both sides by 2 to undo the division. x = 18 Substitute 18 for x in the equation. 18 is the solution. 

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

24. h 3 14 = 3 3 h Substitute 14 for height of aspen. h is divided by 3. 14 = 3 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. Multiply both sides by 3 to undo the division. 42 = h The pine tree is 42 feet tall.

25. w 95 = 2 Substitute 95 for Jamie’s weight. w is divided by 2. w 2 2 95 = 2 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. Multiply both sides by 2 to undo the division. 190 = w Jamie’s father weighs 190 pounds.