2-6 Solving Equations with Rational Numbers

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

2-6 Solving Equations with Rational Numbers

Warm UpAdd or subtract.

+ 15

1

116

1

1. 5 10

2. 5 16

2 – 1

3. 4.8 + 3.6

4. 2.4 – 0.05

8.4

2.35

7 10

3 8

2-6 Solving Equations with Rational Numbers

Coefficient

The numerical factor of a term that contains a variable.

coefficient 3x variable

2-6 Solving Equations with Rational Numbers

MA.8.A.6.4 Perform operations on real numbers (including…rational numbers…)…using real-world problems…

Sunshine State Standards

2-6 Solving Equations with Rational Numbers

m + 4.6 = 9

m + 4.6 = 9Use the Subtraction Property of Equality. Subtract 4.6 from both sides.

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!

Additional Examples 1A: Solving Equations with Decimals

Solve.

4.4 m =– 4.6 = – 4.6

2-6 Solving Equations with Rational Numbers

8.2p = –32.8

–4p =

Use the Division Property of Equality. Divide both sides by 8.2.

–32.8 8.2

8.2p 8.2

=

Additional Examples 1B: Solving Equations with Decimals

Solve.

2-6 Solving Equations with Rational Numbers

Additional Examples 1C: Solving Equations with Decimals

x = 18

Use the Multiplication Property of Equality. Multiply both sides by 1.2.

= 15x 1.2

x 1.2

= 1.2 • 15 1.2 •

Solve.

2-6 Solving Equations with Rational Numbers

m + 9.1 = 3

Check It Out: Example 1A and 1B

m + 9.1 = 3

–6.1 m =–9.1 –9.1

Solve each equation.A.

B. – 3.1p = 15.5

15.1 –3.1

–3.1 –3.1

=p

–5p =

2-6 Solving Equations with Rational Numbers

2 7

= –3 7

n +

Additional Example 2A: Solving Equations with Fractions

n – + = – –2 7

3 7

27

27

n = – 5 7

Subtract from both sides.2 7

Solve.

2-6 Solving Equations with Rational Numbers

1 6 = 2

3y –

Additional Example 2B: Solving Equations with Fractions

Find a common denominator, 6.

y = 5 6

=y 4 6

1 6

+

1 6

= 2 3

–1 6

+ 1 6

+y Add to both sides.1 6

Solve.

2-6 Solving Equations with Rational Numbers

5 6 =

5 8x

6 5••

6 5

5 6

= 5 8

x

Simplify.

Additional Example 2C: Solving Equations with Fractions

Multiply by the reciprocal.

x =3 4

3

4

Solve.

5 6

Divide both sides by . 5 6

= 5 8

x ÷ 5 6

5 6÷

2-6 Solving Equations with Rational Numbers

1 3

= 5 8

m –

Check It Out: Example 2A

Solve each equation.

m – + = +1 3

5 8

13

13

m = 23 24

m = + 8 24

15 24

m – = 5 8

13

2-6 Solving Equations with Rational Numbers

3 8 x = 6

19

Check It Out: Example 2BSolve each equation.

= 6 19

3 8

x

÷3 8

3 8

x = 6 19 ÷

3 8

•8 3

3 8

x = 6 19

8 3

•2

1

16 19

x =

2-6 Solving Equations with Rational Numbers

Write an equation:

Total servings

Amount needed for each dessert

Amount of sugar

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

2 3

s2 3

2 3 = 2

2-6 Solving Equations with Rational Numbers

Now solve the equation.Additional Example 3 Continued

Mr. Rios can make 4 servings.

2 3 = 2 s 3

22 3

3 2

2 3

= 2s 2 3

24 6 , or 4 s =

8 3s = 3

2

Multiply both sides by the reciprocal.

Simplify.

2 3

Divide both sides by . 2 3

= 22 3s ÷ 2

32 3÷

2-6 Solving Equations with Rational Numbers

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 16

gallons of gasoline, how much gasoline can the tank in the minivan hold?

3 5

21

• =Amount of gas in van

Three-fifths Amount of gas in car

2-6 Solving Equations with Rational Numbers

Check It Out: Example 3 Continued

3 5

=x •

33 2

=x • •5 3

x = 33 • 5 2 • 3

3 5

= 33 2

x ÷ 3 5

3 5÷

1 216

3 5

=x • 33 2

1

11

155 2

, or=

So, the tank in the minivan can hold gallons of gas.

271 2

271 2

2-6 Solving Equations with Rational Numbers

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

2-6 Solving Equations with Rational Numbers

Lesson Quiz: Part I

Solve.

1. x – 23.3 = 17.8

2. j + = –14

3. 9y =

4.

115

y =

x = 41.1

3 5

2 3

3 4

j = –155 12

d4 = 2 3

812

d = 9

2-6 Solving Equations with Rational Numbers

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?

Lesson Quiz: Part II

5.

5 hours

2 5

2-6 Solving Equations with Rational Numbers

1. Solve.

a – 36 = 44.9

A. a = 36.7

B. a = 49.2

C. a = 59.9

D. a = 80.9

Lesson Quiz for Student Response Systems

2-6 Solving Equations with Rational Numbers

2. Solve.

c + = –11

A. c = 12 C. c = 11

B. c = –12 D. c = 11

Lesson Quiz for Student Response Systems

11

2011

20

4 5

3 4

3 4

4 5

2-6 Solving Equations with Rational Numbers

3. Solve.

8e =

A. e = 8 C. e =

B. e = 5 D. e =

Lesson Quiz for Student Response Systems

2 3

1 3

1 12

3 20

2 3

2-6 Solving Equations with Rational Numbers

4. Solve.

= 3

A. h = 9 C. h = 11

B. h = 10 D. h = 12

Lesson Quiz for Student Response Systems

1 2

1 2

1 2

1 2

h 3

5 6