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1-10 Solving Equations by Dividing Dividing by a number is the inverse of multiplying by that number. To solve an equation that contains multiplication, use division to “undo” the multiplication. 4m = 32 4m = 32 4 4 m=8 Holt CA Course 1 Caution ! 4m means “4 m.” 1-10 Solving Equations by Dividing Additional Example 1A: Solving Equations by Dividing Solve the equation. Check your answer. 5p = 75 p is multiplied by 5. 5p = 75 5 5 p = 15 Divide both sides by 5 to undo the multiplication. Check 5p = 75 ? 5(15)= 75 ? 75 = 75 Holt CA Course 1 Substitute 15 for p in the equation. 15 is the solution. 1-10 Solving Equations by Dividing Additional Example 1B: Solving Equations by Dividing Solve the equation. Check your answer. 16 = 16 = 8 2= 8r 8r 8 r r is multiplied by 8. Divide both sides by 8 to undo the multiplication. Check 16 = 8r ? 16 = 8(2) ? 16 = 16 Holt CA Course 1 Substitute 2 for r in the equation. 2 is the solution. 1-10 Solving Equations by Dividing Check It Out! Example 1A Solve the equation. Check your answer. 8a = 72 a is multiplied by 8. 8a = 72 8 8 a=9 Divide both sides by 8 to undo the multiplication. Check 8a = 72 ? 8(9)= 72 ? 72 = 72 Holt CA Course 1 Substitute 9 for a in the equation. 9 is the solution. 1-10 Solving Equations by Dividing Check It Out! Example 1B Solve the equation. Check your answer. 18 = 3w w is multiplied by 3. 18 = 3w 3 3 6=w Divide both sides by 3 to undo the multiplication. Check 18 = 3w ? 18 = 3(6) ? 18 = 18 Holt CA Course 1 Substitute 6 for w in the equation. 6 is the solution. 1-10 Solving Equations by Dividing Additional Example 2: Problem Solving Application The area of a rectangle is 56 square inches. Its length is 8 inches. What is its width? Remember! For a rectangle, area = length width Holt CA Course 1 1-10 Solving Equations by Dividing 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 Holt CA Course 1 w 1-10 Solving Equations by Dividing 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 = 8w w l Holt CA Course 1 1-10 Solving Equations by Dividing Additional Example 2 Continued 3 Solve 56 = 8w 56 = 8w 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. Holt CA Course 1 1-10 Solving Equations by Dividing 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. Holt CA Course 1 1-10 Solving Equations by Dividing Check It Out! Example 2 The area of a rectangle is 48 square inches. Its width is 8 inches. What is its length? Holt CA Course 1 1-10 Solving Equations by Dividing Check It Out! Example 2 Continued 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 Holt CA Course 1 8 1-10 Solving Equations by Dividing 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 = l8 w l Holt CA Course 1 1-10 Solving Equations by Dividing Check It Out! Example 2 Continued 3 Solve 48 = 8l 48 = 8l 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. Holt CA Course 1 1-10 Solving Equations by Dividing 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. Holt CA Course 1