2 7 Multiplication Equations Learn to solve wholenumber

2 -7 Multiplication Equations Learn to solve whole-number multiplication equations.

2 -7 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. ”

2 -7 Multiplication Equations Additional Example 1 A: Solving Multiplication Equations Solve the equation. Check your answer. 5 p = 75 p is multiplied by 5. 5 p = 75 5 5 Divide both sides by 5 to undo the multiplication. p = 15 Check 5 p = 75 ? 5(15)= 75 ? 75 = 75 Substitute 15 for p in the equation. 15 is the solution.

2 -7 Multiplication Equations Additional Example 1 B: Solving Multiplication Equations Solve the equation. Check your answer. 16 = 8 2= Check 8 r 8 r 8 r 16 = 8 r ? 16 = 8(2) ? 16 = 16 r is multiplied by 8. Divide both sides by 8 to undo the multiplication. Substitute 2 for r in the equation. 2 is the solution.

2 -7 Multiplication Equations Check It Out: Example 1 A Solve the equation. Check your answer. 8 a = 72 a is multiplied by 8. 8 a = 72 8 8 a=9 Divide both sides by 8 to undo the multiplication. 8 a = 72 ? 8(9)= 72 ? 72 = 72 Check Substitute 9 for a in the equation. 9 is the solution.

2 -7 Multiplication Equations Check It Out: Example 1 B Solve the equation. Check your answer. w is multiplied by 3. 18 = 3 w Check 18 = 3 w 3 3 6=w Divide both sides by 3 to undo the multiplication. 18 = 3 w ? 18 = 3(6) ? 18 = 18 Substitute 6 for w in the equation. 6 is the solution.

2 -7 Multiplication Equations Additional Example 2: Problem Solving Application The area of a rectangle is 56 square inches. Its length is 8 inches. What is its width?

2 -7 Multiplication Equations 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. 56 8 w

2 -7 Multiplication Equations Additional Example 2 Continued 2 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 56 = 8 w w l

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

2 -7 Multiplication Equations 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.

2 -7 Multiplication Equations Check It Out: Example 2 The area of a rectangle is 48 square inches. Its width is 8 inches. What is its length?

2 -7 Multiplication Equations 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 l 8

2 -7 Multiplication Equations Check It Out: Example 2 Continued 2 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 48 = l 8 w l

2 -7 Multiplication Equations Check It Out: Example 2 Continued 3 Solve 48 = 8 l 8 8 6=l l is multiplied by 8. Divide both sides by 8 to undo the multiplication. So the length of the rectangle is 6 inches.

2 -7 Multiplication Equations 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.