1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

2. Warm Up
Add or subtract.
7 10
5 10 1 5 1. +
3 8
5 16 1 16 2.
2 – 1
8.4
– 0.05
2.35

3. Problem of the Day
A computer word is made of strings of 0’s and 1’s. How many different words can be formed using 3 characters? (An example is 010.)‏ 8

4. Learn to solve equations with rational numbers.

5. Additional Examples 1A: Solving Equations with Decimals
Solve.
m = 9
Use the Subtraction Property of Equality. Subtract 4.6 from both sides.
m = 9
– 4.6 =
4.4 m =
Once you have solved an equation it is a good idea to check your answer. To check your answer, substitute your answer for the variable in the original equation.
Remember!

6. Additional Examples 1B: Solving Equations with Decimals
Solve.
8.2p = –32.8 –
8.2p 8.2 =
Use the Division Property of Equality. Divide both sides by 8.2 –4 p =

7. Additional Examples 1C: Solving Equations with Decimals
Solve.
= 15
x 1.2
x 1.2
= 1.2 • 15
1.2 •
Use the Multiplication Property of Equality. Multiply both sides by 1.2
x = 18

8. Check It Out: Example 1A & 1B
Solve. A.
m = 3
Use the Subtraction Property of Equality. Subtract 9.1 from both sides.
m = 3
–9.1 =
–6.1 m = B.
5.5b = 75.9
Use the Division Property of Equality. Divide both sides by 5.5 = b
13.8 b =

9. C. Solve. Check It Out: Example 1C y 4.5 = 90
Use the Multiplication Property of Equality. Multiply both sides by 4.5
y 4.5
= 4.5 • 90
4.5 •
y = 405

10. Additional Example 2A: Solving Equations with Fractions
Solve.
2 7
3 7
n +
= –
n – = – –
2 7
3 7
2 7
Subtract from both sides.
2 7
n = –
5 7

11. Additional Example 2B: Solving Equations with Fractions
Solve.
1 6
2 3 y – =
1 6 =
2 3 – + y
Add to both sides.
1 6 = y
4 6
1 6 +
Find a common denominator; 6. y =
5 6
Simplify.

12. Additional Example 2C: Solving Equations with Fractions
Solve.
5 6
5 8 x = 3
5 6 =
5 8 x
6 5 •
Multiply both sides by .
6 5 4 x =
3 4
Simplify.

13. Solve. Check It Out: Example 2A 1 9 5 9 n + = –
1 9
5 9
n +
= –
Subtract from both sides.
1 9
n – = – –
1 9
5 9
1 9
n = –
2 3
Simplify – .
6 9

14. Solve. Check It Out: Example 2B 1 2 3 4 y – = 1 2 = 3 4 – + y
1 2
3 4 y – =
1 2 =
3 4 – + y
Add to both sides.
1 2 = y
3 4
2 4 +
Find a common denominator; 4. y
= 1
1 4
Simplify.

15. Solve. Check It Out: Example 2C 3 8 = 6 19 x 2 3 8 = 6 19 x 8 3 •
3 8 =
6 19 x 2
3 8 =
6 19 x
8 3 •
Multiply both sides by .
8 3 1 x =
16 19
Simplify.

16. = 2 Additional Example 3: Solving Word Problems Using Equations
Mr. Rios wants to prepare a dessert, but only has 2 tablespoons of sugar. If each serving of the dessert has tablespoon of sugar, how many servings can he make for the party?
2 3
Write an equation:
Amount needed for each dessert
Amount of sugar
Total servings  = s
2 3  = 2

17. Additional Example 3 Continued
Now solve the equation.
2 3 
= 2 s
2 3
= 2  s  
3 2
Multiply both sides by .
3 2
8 3 s = 
3 2
24 6
, or 4 s =
Simplify.
Mr. Rios can make 4 servings.

18. Ratio of car’s tank to van’s tank
Check It Out: Example 3
Rick’s car holds the amount of gasoline as his
wife’s van. If the car’s gas tank can hold
gallons of gasoline, how much gasoline can the tank in the minivan hold?
2 3 2 31
Write an equation:
Van’s gas tank
Ratio of car’s tank to van’s tank
Capacity of car’s tank • =
2 3
31 2 g • =

19. Check It Out: Example 3 Continued
Now solve the equation.
2 3
31 2 g • =
Multiply both sides by .
3 2
31 2
2 3 = g •
3 2
g =
93 4
Simplify.
1 4
g = 23
The van’s gas tank holds 23 gallons of gasoline.
1 4

20. Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems

21. Lesson Quiz: Part I
Solve.
1. x – 23.3 = 17.8
x = 41.1
2 3
3 4
j = –15
5 12
2. j = –14
3 5 1 15
y =
3. 9y = d
3 8 1 2
d = 9 4. = 2 4

22. Lesson Quiz: Part II
2 5 5.
Tamara can mow acre in one hour. If her yard is 2 acres, how many hours will it take her to mow the entire yard?
5 hours

23. Lesson Quiz for Student Response Systems
1. Solve.
a – 36 = 44.9
A. a = 36.7
B. a = 49.2
C. a = 59.9
D. a = 80.9

24. Lesson Quiz for Student Response Systems
2. Solve.
c + = –11
A. c = 12 C. c = 11
B. c = –12 D. c = 11
3 4
4 5
11 20
4 5
11 20
3 4

25. Lesson Quiz for Student Response Systems
3. Solve.
8e =
A. e = 8 C. e =
B. e = 5 D. e =
2 3
2 3
1 12
1 3
3 20

26. Lesson Quiz for Student Response Systems
4. Solve.
= 3
A. h = 9 C. h = 11
B. h = 10 D. h = 12
h 3
5 6
1 2
1 2
1 2
1 2