7th Grade Math Chapter 3

Applying Rational Numbers

Name: ___________________________ Period: _______

Common Core State Standards

CC.7.NS.1 - Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

CC.7.NS.2 - Apply and extend previous understandings of multiplication and division of fractions to multiply and divide rational numbers.

CC.7.EE.4 - Use variables to represent quantities in a real-world or mathematical problem, and

construct simple equations and inequalities to solve problems by reasoning about the quantities.

Scope and Sequence Day 1 Lesson 3-1 Day 11 Lesson 3-6

Day 2 Lesson 3-1 Day 12 Lesson 3-6

Day 3 Lesson 3-2 Day 13 Lesson 3-7

Day 4 Lesson 3-2 Day 14 Lesson 3-7

Day 5 Lesson 3-3 Day 15 Lesson 3-8

Day 6 Lesson 3-3 Day 16 Lesson 3-8

Day 7 Lesson 3-4 Day 17 Review Day 1

Day 8 Quiz Day 18 Review Day 2

Day 9 Lesson 3-5 Day 19 Test

Day 10 Lesson 3-5

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IXL Modules

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

Lesson 1 7.E.1 Add and subtract decimals

7.E.2 Add and subtract decimals: word problems

Lesson 2 7.E.3 Multiply decimals

7.E.4 Multiply decimals and whole numbers: word problems

Lesson 3 7.E.5 Divide decimals

7.E.6 Divide decimals and whole numbers: word problems

Lesson 4 7.E.7 Estimate sums, differences and products of decimals

7.E.8 Add, subtract, multiply and divide decimals: word problems

7.E.10 Maps with decimal distances

7.E.11 Evaluate numerical expressions involving decimals

Lesson 5 7.G.1 Add and subtract fractions

7.G.2 Add and subtract fractions: word problems

7.G.3 Add and subtract mixed numbers

7.G.4 Add and subtract mixed numbers: word problems

7.G.5 Estimate sums and differences of mixed numbers

Lesson 6 7.G.7 Multiply fractions and whole numbers

7.G.9 Multiply fractions

7.G.10 Multiply mixed numbers

7.G.11 Multiply fractions and mixed numbers: word problems

Lesson 7 7.G.12 Divide fractions

7.G.13 Divide mixed numbers

7.G.14 Divide fractions and mixed numbers: word problems

2 

Lesson 8 7.G.15 Estimate products and quotients of fractions and mixed

numbers

7.G.16 Add, subtract, multiply and divide fractions and mixed numbers:

word problems

7.G.17 Maps with fractional distances

7.G.18 Evaluate numerical expressions involving fractions

3 

Lesson 3-1

Adding and Subtracting Decimals

Warm-Up

4 

Examples: Adding Decimals

Add. Estimate to check whether each answer is reasonable

4.55 + 11.3

6.44 + 16

-8.33 + (-10.972)

6.78 + 13.2

4.21 + 34

-7.89 + (-13.852)

Examples: Subtracting Decimals

Subtract.

5.34 - 2.08

28 - 15.911

3.57 - 1.46

34 - 12.462

5 

Examples: Application

During one month in the United States, 492.23 million commuter trips were taken on buses, and 26.331 million commuter trips were taken on light rail. What was the total number of trips taken on buses and light rail? Estimate to check whether your answer is reasonable.

In 1999, 143.66 million bushels of corn were grown in the United States. In 2000, the harvest yielded 169.831 million bushels. What was the total production for those two years? Estimate to check whether your answer is reasonable.

6 

Lesson 3-2

Multiplying Decimals

Warm-Up

7 

Examples: Multiplying Integers by Decimals

Multiply.

7 x 0.1

-3 x 0.03

2.45 x 35

8 x 0.3

-2 x 0.04

3.65 x 15

Examples: Multiplying Decimals by Decimals

Multiply. Estimate to check whether each answer is reasonable.

2.4 x 1.8

-3.84 x 0.9

3.2 x 1.6

-2.96 x 0.7

8 

Examples: Application

To find your weight on another planet, multiply the relative gravitational pull of the planet and your weight. The relative gravitational pull on Mars is 0.38. What would a person who weighs 85 pounds on Earth weigh on Mars.

Jet fuel weighs approximately 6.2 pounds per gallon. If a plane was serviced with 1,012 gallons of fuel, how many pounds of fuel were used?

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Lesson 3-3

Dividing Decimals

Warm-Up

When you divide two numbers, you can multiply __________ __________ by the same power

of ten __________ changing the final answer.

By multiplying both numbers by the same power of ten, you can make the divisor an

__________. Dividing by an integer is much __________ than dividing by a decimal.

Examples: Dividing Decimals by Decimals

Divide.

8.28 ÷ 4.6

18.48 ÷ (-1.75)

6.45 ÷ 0.5

16.48 ÷ (-2.06)

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Examples: Dividing Integers by Decimals Divide. Estimate to check whether each answer is reasonable.

4 ÷ 1.25

-24 ÷ (-2.5)

6 ÷ 1.25

-22 ÷ (-2.5)

Examples: Transportation Application

Eric paid $229.25 to rent a car. The fee to rent the car was $32.75 per day. For how long did Eric rent the car?

Jace took a trip in which he drove 350 miles. During the trip his truck used 12.5 gallons of gas. What was his truck’s gas mileage.

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Lesson 3-4

Solving Equations Containing Decimals

Warm-Up

Examples: Solving Equations by Adding and Subtracting Solve.

n - 2.75 = 8.3

a + 32.66 = 42

n - 1.46 = 4.7

a + 27.51 = 36

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Examples: Solving Equations by Multiplying and Dividing Solve.

= 5.4x4.8

9 = 3.6d

= 2.4x3.5

9 = 2.5d

Examples: Problem Solving Application

A board-game box is 2.5 inches tall. A toy store has shelving measuring 15 inches vertically in which to store the boxes. How many boxes can be stacked in the space?

A canned good is 4.5 inches tall. A grocery store has shelving measuring 18 inches vertically in which to store the cans. How many cans can be stacked in the space?

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Lesson 3-5

Adding and Subtracting Fractions

Warm-Up

Examples: Adding or Subtracting Fractions with Like Denominators

Add. Write the answer in simplest form.

+ 85

81

- 911

411

+ 65

61 - 7

10410

To add or subtract fractions with __________, you must rewrite the fractions with a

__________ denominator.

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Two Ways to Find a Common Denominator

● Find the LCM (least common multiple) of the denominators.

● Multiply the denominators.

Examples: Adding and Subtracting Fractions with Unlike Denominators

Add. Write the answer in simplest form.

+ 65

87

- 32

43

:

- + 72

31 + 5

265

:

- 52

21

- + 53

21

15 

Examples: Astronomy Application

In one Earth year, Jupiter completes about of its orbit around the Sun, while Mars112

completes about of its orbit. How much more of its orbit does Mars complete than Jupiter?21

It takes Michelle hour to drive to work. It takes Luke hour to drive to work. How much512 2

1 longer does it take Luke to drive to work?

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Lesson 3-6

Multiplying Fractions and Mixed Numbers

Warm-Up

To multiply fractions, multiply the ____________ to find the product’s ____________. Then

multiply the ____________ to find the product’s ____________.

Examples: Multiplying Fractions

Multiply. Write the answer in simplest form.

-12 x 43

x 31

83

x (- )53

41 -16 x 4

1

x 61

96

(- ) x 73

21

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Examples: Multiplying Mixed Numbers

Multiply. Write the answer in simplest form.

x 152

32

4 x 251

71

6 x 432

52 x 25

331

3 x 163

31

3 x 161

31

Examples: Transportation Application

In 2001, the car toll on the George Washington Bridge was $6.00. In 1995 the toll was of32

that toll. What was the toll in 1995?

In 2002, the fee to park in a parking garage was $4.00. In 2000 the fee was of the fee in43

2002. What was the fee in 2000?

18 

Lesson 3-7

Dividing Fractions and Mixed Numbers

Warm-Up

Two numbers are reciprocals or multiplicative inverses if their ____________ is 1.

Dividing a number is the same as multiplying by its ____________.

Examples: Dividing Fractions

Divide. Write each answer in simplest form.

61 ÷ 9

6

1283 ÷

53 ÷ 2

1 343 ÷

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Examples: Dividing Mixed Numbers

Divide. Write each answer in simplest form.

5 132 ÷ 4

1

243 ÷ 2

1

8 32 ÷ 27

13 3 132 ÷ 2

1

153 ÷ 5

2

7 51 ÷ 5

18

20 

Examples: Social Studies Application

The life span of a golden dollar coin is 30 years, while paper currency lasts and average of 1 years. How many times longer will the golden dollar stay in circulation?21

The average life of a queen ant is approximately 3 years. The life span of a worker ant is 73

year. How many times longer will the queen ant live?

21 

Lesson 3-8

Solving Equations Containing Fractions

Warm-Up

The goal when solving equations that contain fractions is the ____________ as when working

with other kinds of numbers - to isolate the variable on one side of the equation.

Examples: Solving Equations by Adding or Subtracting

Solve. Write the answer in simplest form.

x - = 73

75

+ r = -94

21

x - = 83

87 + t = -3

14 72

Examples: Solving Equations by Multiplying

22 

Solve. Write each answer in simplest form.

x = 83

41

4x = 98

x = 43

21 3x = 7

6

Examples: Physical Science Application

The amount of copper in brass is of the total weight. If a sample contains 4 ounces of43

51

copper, what is the total weight of the sample?

The amount of copper in zinc is of the total weight. If a sample contains 5 ounces of41

31

copper, what is the total weight of the sample?

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