1. Solving Multiplication and Division Equations 1-4
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra

2. 1-4 Solving Multiplication and Division Equations Warm Up Solve.
Pre-Algebra
Warm Up
Solve.
1. x  3 = 9
x = 12
n = 7
2. 16 = n + 9
k = 6
k = 1
4. 47 = t  19
t = 66
5. 15 = x + 2
x = 13

3. Problem of the Day
Jackie went shopping for a new wardrobe. She bought seven new shirts and four new pairs of pants. She made sure that they can all be worn together in combinations. How many outfits can she put together? 28

4. Learn to solve equations using multiplication and division.

5. Vocabulary Division Property of Equality
Multiplication Property of Equality

6. DIVISION PROPERTY OF EQUALITY
You can solve a multiplication equation using the Division Property of Equality.
DIVISION PROPERTY OF EQUALITY
Words
Numbers
Algebra
You can divide both sides of an equation by the same nonzero number, and the equation will still be true.
4 • 3 = 12
x = y
4 • 3 = 12
x = y 2 2 z z
12 = 6 2

7. Additional Example 1: Solving Equations Using Division
Solve 8x = 32.
8x = 32
8x = 32
Divide both sides by 8. 8 8
1x = 4
1 • x = x
x = 4
Check
8x = 32
8(4) = 32 ?
Substitute 4 for x.
32 = 32 ? 

8. Try This: Example 1 Solve 9x = 36. 9x = 36 9x = 36
Divide both sides by 9. 9 9
1x = 4
1 • x = x
x = 4
Check
9x = 36
9(4) = 36 ?
Substitute 4 for x.
36 = 36 ? 

9. MULTIPLICATION PROPERTY OF EQUALITY
You can solve a division equation using the Multiplication Property of Equality.
MULTIPLICATION PROPERTY OF EQUALITY
Words
Numbers
Algebra
You can multiply both sides of an equation by the same number, and the statement will still be true.
2 • 3 = 6
x = y
4 •
2 • 3 = z
x = y
8 • 3 = 24

10. Additional Example 2: Solving Equations Using Multiplication7
Solve = 7. n 7 =
7 •
7 •
Multiply both sides by 7.
n = 49
Check n 7
= 7 49 7
= 7 ?
Substitute 49 for n.
7 = 7 ? 

11. Try This: Example 2 n 4 Solve = 16 n 4 = 16 4 • 4 •=
4 •
4 •
Multiply both sides by 4.
n = 64
Check n 4
= 16 64 4
= 16 ?
Substitute 64 for n.
16 = 16 ? 

12. Additional Example 3: Food Application
Joe has enough flour to bake one sheet cake but would rather make cookies. How many dozen cookies can he make?
Dessert
Apple crisp
Bread pudding
Cookies (1 doz.)
Pumpkin pie
Sheet cake
Tiramisu
Cups of Flour
1.5 4 2 1 8 3

13. = =  • Additional Example 3 Continued
cups of flour for 1 dozen cookies
number of dozen cookies
cups of flour in 1 cake  = • = 2 c 8
2c = 8
Write the equation.
2c = 8
Divide both sides by 2. 2 2
c = 4
Joe can make 4 dozen cookies with the same amount of flour that he would need for 1 sheet cake.

14. = = • Try This: Example 3 cups of flour for bread pudding
number of bread pudding desserts
cups of flour in 1 cake =  • = 4 b 8
4b = 8
Write the equation.
4b = 8
Divide both sides by 4. 4 4
c = 2
Joe can make 2 bread pudding desserts with the same amount of flour that he would need for 1 sheet cake.

15. = =  • Additional Example 4: Money Application 1 4 x 50 x = 50 1 4
Meg has saved $50, which is one-fourth of the amount she needs for a school trip. What is the total amount she needs?
fraction of amount raised so far 
total amount needed =
amount raised so far 1 4 • = x 50
x = 50 1 4
Write the equation.
x = 1 4
Multiply both sides by 4.
4 •
4 •
x = 200
Meg needs $200 total.

16. = = • Try This: Example 4  1 x 750 8 1 x = 750 8 1 8 • x = 750 8 • 8
The school library needs money to complete a new collection. So far, the library has raised $750, which is only one-eighth of what they need. What is the total amount needed?
fraction of total amount raised so far
total amount needed =
amount raised so far  1 8 • = x
750
x = 750 1 8
Write the equation.
x = 1 8
8 •
8 •
Multiply both sides by 8.
x = 6000
The library needs to raise a total of $6000.

17. Sometimes it is necessary to solve equations by using two inverse operations. For instance, the equation 6x  2 = 10 has multiplication and subtraction.
Variable term
6x  2 = 10
Multiplication
Subtraction
To solve this equation, add to isolate the term with the variable in it. Then divide to solve.

18. Additional Example 5: Solving a Simple Two-Step Equation
Solve 3y – 7 = 20.
Step 1:
3y – 7 = 20
Add 7 to both sides to isolate the term with y in it.
+ 7
+ 7
3y = 27
Step 2:
3y = 27
Divide both sides by 3. 3 3
y = 9

19. Try This: Example 5
Solve 4y + 5 = 29.
Step 1:
4y + 5 = 29
Subtract 5 from both sides to isolate the term with y in it.
– 5
– 5
4y = 24
Step 2:
4y = 24
Divide both sides by 4. 4 4
y = 6

20. Lesson Quiz Solve. 1. = 3 2. 16t = 112 k k = 18 3. = 14 6
= 3
2. 16t = 112
= 14
4. 3n + 17 = 29
5. Joan is making a scrapbook of her pictures. She wants to put three pictures on each page. She has 63 photos. Write and solve an equation to find how many pages she will need for all of the photos. k 6
k = 18
t = 7 b 9
b = 126
n = 4
3x = 63; 21 pages