1. 2-7 Warm Up Problem of the Day Lesson Presentation
Solving Equations with Rational Numbers
Course 3
Warm Up
Problem of the Day
Lesson Presentation

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. Learn to solve equations with rational numbers.

4. Additional Examples 1A: Solving Equations with Decimals.
Solve.
m = 9
m = 9
Subtract 4.6 from both sides.
– 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!

5. Additional Examples 1B: Solving Equations with Decimals
Solve.
8.2p = –32.8 –
8.2p 8.2 =
Divide both sides by 8.2 –4 p =

6. Additional Examples 1C: Solving Equations with Decimals
Solve.
= 15
x 1.2
x 1.2
= 1.2 • 15
1.2 •
Multiply both sides by 1.2
x = 18

7. Check It Out: Example 1A & 1B
Solve. A.
m = 3
m = 3
Subtract 9.1 from both sides.
–9.1 =
–6.1 m = B.
5.5b = 75.9 = b
Divide both sides by 5.5
13.8 b =

8. C. Solve. Check It Out: Example 1C y 4.5 = 90 y 4.5 = 4.5 • 90 4.5 •
Multiply both sides by 4.5
y = 405

9. Additional Example 2A: Solving Equations with Fractions
Solve.
2 7
3 7
n +
= –
n – = – –
2 7
3 7 27
Subtract from both sides.
2 7
n = –
5 7

10. 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.

11. 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.

12. Solve. Check It Out: Example 2A 1 9 5 9 n + = –
Subtract from both sides.
1 9
n – = – –
1 9
5 9 19
n = –
2 3
Simplify – .
6 9

13. Solve. Check It Out: Example 2B 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.

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

15. Lesson Quiz: Part 1
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

16. 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