Download 3-3 Solving Equations by Multiplying or Dividing

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Transcript 
Solving Equations by
Multiplying or Dividing
Objective: Solve equations using the
multiplication and division properties
of equality.
Minute Check
Solve each equation.
1. x – 3 = 5
Minute Check
Solve each equation.
1. x – 3 = 5
8
Minute Check
Solve each equation.
1. x – 3 = 5
2. y + 9 = 7
Minute Check
Solve each equation.
1. x – 3 = 5
2. y + 9 = 7
-2
Minute Check
Solve each equation.
1. x – 3 = 5
2. y + 9 = 7
3. 13 = m – 6
Minute Check
Solve each equation.
1. x – 3 = 5
2. y + 9 = 7
3. 13 = m – 6
19
Minute Check
Solve each equation.
1. x – 3 = 5
2. y + 9 = 7
3. 13 = m – 6
4. n – (-1) = 1
Minute Check
Solve each equation.
1. x – 3 = 5
2. y + 9 = 7
3. 13 = m – 6
4. n – (-1) = 1
0
Minute Check
Solve each equation.
1. x – 3 = 5
2. y + 9 = 7
3. 13 = m – 6
4. n – (-1) = 1
5. f + 4 = -5
Minute Check
Solve each equation.
1. x – 3 = 5
2. y + 9 = 7
3. 13 = m – 6
4. n – (-1) = 1
5. f + 4 = -5
-9
Solving Equations by
Multiplying or Dividing
Division Property of Equality
For any numbers a, b, and c, where c < >
0, if a = b, then a/c = b/c.
Solving Equations by
Multiplying or Dividing
Example
Solve 8y = 96. Check your solution.
Solving Equations by
Multiplying or Dividing
Example
Solve 8y = 96. Check your solution.
8y/ = 96/
Divide each side by 8.
8
8
Solving Equations by
Multiplying or Dividing
Example
Solve 8y = 96. Check your solution.
8y/ = 96/
Divide each side by 8.
8
8
y = 12
Solving Equations by
Multiplying or Dividing
Example
Solve 8y = 96. Check your solution.
8y/ = 96/
Divide each side by 8.
8
8
y = 12
Check: 8y = 96
Replace y with 12.
Solving Equations by
Multiplying or Dividing
Example
Solve 8y = 96. Check your solution.
8y/ = 96/
Divide each side by 8.
8
8
y = 12
Check: 8y = 96
Replace y with 12.
8(12) ? 96
Solving Equations by
Multiplying or Dividing
Example
Solve 8y = 96. Check your solution.
8y/ = 96/
Divide each side by 8.
8
8
y = 12
Check: 8y = 96
Replace y with 12.
8(12) ? 96
96 = 96
The solution is 12.
Solving Equations by
Multiplying or Dividing
Multiplication Property of Equality
For any numbers a, b, and c, if a = b, then ac = bc.
Solving Equations by
Multiplying or Dividing
Example 2
Solve y/-6 = 12. Check your solution.
Solving Equations by
Multiplying or Dividing
Example 2
Solve y/-6 = 12. Check your solution.
-6 * y/-6 = -6 * 12
Multiply each side by –6
Solving Equations by
Multiplying or Dividing
Example 2
Solve y/-6 = 12. Check your solution.
-6 * y/-6 = -6 * 12
Multiply each side by –6
y = -72
Solving Equations by
Multiplying or Dividing
Example 2
Solve y/-6 = 12. Check your solution.
-6 * y/-6 = -6 * 12
Multiply each side by –6
y = -72
Check: y/-6 = 12
Replace y with -72
Solving Equations by
Multiplying or Dividing
Example 2
Solve y/-6 = 12. Check your solution.
-6 * y/-6 = -6 * 12
Multiply each side by –6
y = -72
Check: y/-6 = 12
Replace y with -72
-72/ ? 12
-6
Solving Equations by
Multiplying or Dividing
Example 2
Solve y/-6 = 12. Check your solution.
-6 * y/-6 = -6 * 12
Multiply each side by –6
y = -72
Check: y/-6 = 12
Replace y with –72.
-72/ ? 12
-6
12 = 12
The solution is –72.
Solving Equations by
Multiplying or Dividing
Application:
Tom has a piece of rope that is 105 feet long. He wants to cut
the rope into 5 equal pieces. How long will each piece be?
Solving Equations by
Multiplying or Dividing
Application:
Tom has a piece of rope that is 105 feet long. He wants to cut
the rope into 5 equal pieces. How long will each piece be?
Let L represent the length of each piece.
Solving Equations by
Multiplying or Dividing
Application:
Tom has a piece of rope that is 105 feet long. He wants to cut
the rope into 5 equal pieces. How long will each piece be?
Let L represent the length of each piece.
105 = 5*L
Write an equation.
Solving Equations by
Multiplying or Dividing
Application:
Tom has a piece of rope that is 105 feet long. He wants to cut
the rope into 5 equal pieces. How long will each piece be?
Let L represent the length of each piece.
105 = 5*L
Write an equation.
105/5 = 5*L/5
Divide each side by 5.
Solving Equations by
Multiplying or Dividing
Application:
Tom has a piece of rope that is 105 feet long. He wants to cut
the rope into 5 equal pieces. How long will each piece be?
Let L represent the length of each piece.
105 = 5*L
Write an equation.
105/5 = 5*L/5
Divide each side by 5.
21 = L
The solution is 21.
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