Preview Warm Up California Standards Lesson Presentation

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

California Standards AF1.1 Write and solve one-step linear equations in one variable.

Dividing by a number is the inverse of multiplying by that number 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 Caution ! 4m = 32 4m means “4  m.” 4 4 m = 8

Additional Example 1A: Solving Equations by Dividing 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 Equations by Dividing 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 a = 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? Remember! For a rectangle, area = length  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 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 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 Solve each equation. 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