Pre-Algebra Unit 1

Rational Numbers

Name: ___________________________ Period: _______

Common Core State Standards CC.8.NS.1 - Understand informally that every number has a decimal expansion; the

rational numbers are those with decimal expansions that terminate in 0’s or eventually repeat. Know that other numbers are called irrational.

CC.8.EE.7 - Solve linear equations in one variable

CC.8.EE.7b - Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

Scope and Sequence Day 1 Lesson 1-1 Day 7 Lesson 1-5

Day 2 Lesson 1-2 Day 8 Lesson 1-5

Day 3 Lesson 1-3 Day 9 Lesson 1-6

Day 4 Lesson 1-4 Day 10 Lesson 1-6

Day 5 Lesson 1-4 Day 11 Review

Day 6 Quiz / Tech Lab Day 12 Test

IXL Modules

SMART Score of 80 is required Due the day of the exam

Lesson 1 8.D.1 Identify rational and irrational numbers

8.D.2 Simplify Fractions

8.D.6 Convert between decimals and fractions or mixed numbers

Lesson 2-3 8.E.1 Reciprocals and multiplicative inverses

8.E.5 Multiply and divide rational numbers

8.E.6 Multiply and divide rational numbers: word problems

8.E.9 Evaluate variable expressions involving rational numbers

Lesson 4 8.E.2 Add and subtract rational numbers

8.E.3 Add and subtract rational numbers: word problems

Lesson 5 8.U.4 Solve one-step linear equations

Lesson 6 8.U.5 Solve two-step linear equations

Lesson 1-1

Rational Numbers

Warm-Up

Vocabulary

A rational number is any number that can be written as a ____________ , where n and d ared

n

____________ and d 0.=/

The goal of simplifying fractions is to make the numerator and the denominator relatively prime. Relatively prime numbers have no ____________ ____________ other than 1.

Examples: Simplifying Fractions

Simplify:

8016

- 2918

2718

- 3517

Decimals that ____________ or ____________ are rational numbers.

Examples: Writing Decimals as Fractions

Write each decimal as a fraction in simplest form.

5.37

0.622

8.75

0.2625

To write a fraction as a decimal, divide the ____________ by the ____________. You can use ____________ division.

Examples: Writing Fractions as Decimals Write the fraction as a decimal

911

720

915 940

Lesson 1-2

Multiplying Rational Numbers

Warm-Up

Examples: Multiplying a Fraction and an Integer

Multiply. Write the answer in simplest form.

-8( )76

2(5 )31

-3( )85

4(9 )52

Caution: A fraction in lowest terms, or simplest form, when the numerator and denominator

have no ____________ ____________.

Examples: Multiplying Fractions

Multiply. Write the answer in simplest form.

( )81

76

- ( )32

29

( )53

85

- ( )87

74

Examples: Multiplying Decimals

Multiply.

2(-0.51)

(-0.4)(-3.75)

3.1 (0.28)

(-0.4)(-2.53)

Examples: Application

Joy completes of her painting each day. How much of her painting does she complete in a 7120

day week?

Mark runs mile each day. What is the total distance he runs in a 5-day week?71

Lesson 1-3

Dividing Rational Numbers

Warm-Up

Vocabulary

A number and its reciprocal have a product of 1. To find the reciprocal of a fraction,

____________ the numerator and the denominator. Remember that an ____________ can be

written as a fraction with a denominator of 1.

*** Flip the second fraction and multiply ***

Examples: Dividing Fractions

Divide. Write the answer in simplest form.

511 ÷ 2

1

2 283 ÷

715 ÷ 4

3

4 352 ÷

When dividing a decimal by a decimal, multiply both numbers by a ____________ of 10 so you

can divide by a __________ number. To decide which power of 10 to multiply by, look at the

denominator. The number of decimal places is the number of zeros to write after the 1.

Examples: Dividing Decimals

Find 0.384 0.24÷

Find 0.585 0.25÷

Examples: Evaluating Expressions with Fractions and Decimals

Evaluate the expression for the given value of the variable.

for n = 0.15n5.25

k for k = 5÷ 54

for b = 0.75b2.55

u for u = 9÷ 74

Examples: Problem Solving Application

A cookie recipe calls for cup of oats. You have cup of oats. How many batches of cookies21

43

can you bake using all of the oats you have?

A ship will use of its total fuel load for a typical round trip. If there is of a total fuel61

85

load on board now, how many complete trips can be made?

Lesson 1-4

Adding and Subtracting with Unlike Denominators

Warm-Up

There are two methods that can be used to add and subtract rational numbers with

____________ denominators.

Method 1 - Find a common denominator by ____________ one denominator by the other

denominator.

Method 2 - Find the ____________ ____________ denominator (LCD).

Examples: Adding and Subtracting Fractions with Unlike Denominators

Add using method 1.

+ 81

72

Subtract using method 2.

1 - 161

85

Add using method 1.

+ 31

85

Add using method 2.

2 +61

43

Examples: Evaluating Expressions with Rational Numbers

Evaluate t - for t = 54

65

Evaluate - h for h = -54 7

12

Examples: Consumer Application

Two dancers are making necklaces from ribbon for their costumes. They need pieces

measuring 13 inches and 12 inches. How much ribbon will be left over after the pieces are43

87

cut from a 36-inch length?

Fred and Jose are building a treehouse. They need to cut a 6 foot and a 4 foot piece of43 5

12

wood from a 12 foot board. How much of the board will be left?.

Lesson 1-5

Solving Equations with Rational Numbers

Warm-Up

Examples: Solving Equations with Decimals Solve and Check.

m + 4.6 = 9

8.2p = -32.8

= 15x1.2

m + 9.1 = 3

5.5b = 75.9

= 90y4.5

Examples: Solving Equations with Fractions

Solve and Check

n + = -72

73

y - =61

32

x =65

85

n + = -91

95

y - =21

43

x =83 6

19

Examples: Solving Word Problems Using Equations

Mr. Rios wants to prepare a dessert, but only has 2 tablespoons of sugar. If each serving32

has tablespoon, how many servings can he make for the party?32

Rick’s car holds the amount of gas as his wife’s van. If the car’s gas tank can hold32

231

gallons, how much gas can the tank in the minivan hold?

Lesson 1-6

Solving Two-Step Equations

Warm-Up

Sometimes more than one ____________ operation is needed to solve an equation. Before

solving, ask yourself, “What is being done to the ____________, and in what order?” Then

work backward to ____________ the operations.

Examples: Problem Solving Application

The mechanic’s bill to repair Mr. Wong’s car was $650. The mechanic charges $45 per hour for labor, and the parts that were used cost $443. How many hours did the mechanic work on the car?

The mechanic’s bill to repair your car was $850. The mechanic charges $35 per hour for labor, and the parts that were used cost $275. How many hours did the mechanic work on your car?

Examples: Solving Two-Step Equations

Solve and Check

+ 7 = 223n

= 93y−4

+ 8 = 184n

= 72y−7