Chapter 1 Operations with Whole Numbers. 1-1: Mathematical Expression

Chapter 1

Operations with Whole Numbers

1-1: Mathematical Expression

Variable

A variable is a symbol used to represent one or more numbers. The number that the variable represents is called the value of the variable. Examples:

b + 903 X n18 – my ÷ 24

Variable and Numerical Expressions

An expression such as b + 90

Is called a variable expression.

An expression such as 3 X 2

Is called a numerical expression.

Multiplication Symbols

We can used a raised dot as a multiplication symbol. 9 x 7 can be written as 9·72 x a x b can be written as 2·a·b

In a variable expression we can use the raised dot or omit the multiplication symbol.

3 x n can be written as 3·n3·n can be written as 3n 2 x a x b can be written as 2·a·b

2·a·b can be written as 2ab

EquationWhen a mathematical sentence uses an equal sign, it is called an equation. An equation tells us that two expressions name the same number. The expression to the left of the equal sign is the left side of the equation. The expression to the right of the equal sign is called the right side.

5 5 = 0

4 + 5 = 9

18 ÷ 9 = 2

2 · 4 = 8

An Equation is like a balance scale. Everything must be equal on both sides.

10 5 + 5=


12 6 + 6=


7 n + 2=


7 n + 2=

5

Substitution

When a number is substituted for a variable in a variable expression and the operation is carried out, we say that the variable has been evaluated.

If n = 6, evaluate 3 · n If n = 6, 3 · 6 = 18

If x = 2, evaluate 3 + x If x = 2, 3 + 2 = 5

If y = 9, evaluate 18 ÷ y If y = 9, 18 ÷ 9 = 2

x = 10; y = 20. Evaluate

1. x 52. y x + 503. 50 x + y4. 50 + y x5. y 10 6. xy

10 5 = 5

20 10 + 50 = 60

50 10 + 20 = 60

50 + 20 10 = 60

20 10 = 10

10 · 20 = 200

1-2: Properties of Addition and Multiplication

The Set of Numbers

Counting numbers1, 2, 3, 4, 5, . . .

Whole numbers0, 1, 2, 3, 4, . . .

Commutative Property of Addition and Multiplication

The order in which two whole numbers are added or multiplied does not change their sum or their product.

3 + 4 = 7 and 4 + 3 = 7

3 x 4 = 12 and 4 x 3 = 12

a + b = b + a

a x b = b x a

Associative Property of Addition and Multiplication

Add6 + 5 + 7 =

1. (6 + 5) + 7 =2. 6 + (5 + 7) =3. (6 + 7) + 5 =

Multiply9 x 2 x 5 =

4. (9 x 2) x 5 =5. 9 x (2 x 5) =6. (9 x 5) x 2 =

1818

9090

18

90

Exercise

Simplify Using the Commutative and Associative Properties

1. 13 + 8 + 7

2. 5 x 7 x 2

Addition Property of Zero

• 7 + 0 = • a + 0 = • 8 + 0 = • c + 0 = • 2 + 0 =

7a8

c2

Multiplication Property of One

• 7 x 1 = • a x 1 = • 8 x 1 = • c x 1 = • 2 x 1 =

7a8c2

Multiplication Property of Zero

• 7 x 0 = • a x 0 = • 8 x 0 = • c x 0 = • 2 x 0 =

00000

1-4: The Distributive Property

The fee for each person entering the state park is $4. If the person rents a bicycle, he has to pay an additional $2. How much will a group of 12 people have to spend if each will enter the park and each will rent a bicycle?

12 · (4 + 2)

Two Methods:= 12 · 6 = 72

= (12 · 4) + (12 · 2) = 48 + 24 = 72

The fee for each person entering the state park is $4. If the person has a coupon, he gets a $2 discount. How much will a group of 12 people have to spend if each will enter the park with a coupon?

12 · (4 2)

Two Methods:= 12 · 2 = 24

= (12 · 4) (12 · 2) = 48 24 = 24

Simplify using the distributive property.1. (11 · 4) + (11 · 6)

=11 · (4 + 6) = 11 · 10 = 110

2. 13 · 15= (13 · 10) + (13 · 5) = 130 + 65 = 195

Simplify using the distributive property.1. 6 ( 20 + 4) 2. 4 ( 80 – 6)3. (4 x 12) + (4 x 8)4. (33 x 90) + (33 x 10)5. (23 x 104) – (23 x 4)6. (56 x 11) – (6 x 11)7. 35 (10 + 2)8. 33 ( 100 – 3)9. 12 x 2210. 32 x 811. 9 x 12012. 7 x 896

144304

80

3300

2300

550

420

3201

264

256

1080

6272

Test: 1-1, 1-2, 1-3, 1-4

1-5: Order of Operations

Grouping Symbols: Show which operations need to be performed first.

[ ]( )

When one pair of grouping symbols is enclosed in another, we ALWAYS perform the operation enclosed in the INNER pair of symbols FIRST.

(14 + 77) ÷ 7

[3 + (4 · 5)] · 10

Simplify(14 + 77) ÷ 7

91 ÷ 7

13

Simplify[3 + (4 · 5)] · 10

20 ] · 10

23

[3 +

· 10

230

For expressions that are written without grouping symbols like,

8 + 3 – 9 x 2 ÷ 3

Rule1. Do all multiplication and divisions in order

from left to right.2. Then do all additions and subtractions in

order from left to right.

Simplify72 – 24 ÷ 3

8 72 –

64




Simplify8 + 3 – 9 x 2 ÷ 3

18 8 + 3 –

–




÷ 3

6

5

11

Solve1. 12 ( 18 + 36)2. (100 – 16) ÷ 73. 4[(6 + 17)2]

1-6: A Problem Solving Model

Plan for Solving Word Problems1. Read the problem carefully. Make sure you understand what it says.

You may need to read it more than once.2. Use questions like these in planning the solution:

a. What is asked for?b. What facts are given?c. Are enough facts given? If not, what else is needed? d. Are unnecessary facts given? If so, what are they? e. Will a sketch or diagram help?

3. Determine which operations or operations can be used to solve the problem.

4. Carry out the operations carefully.5. Check your results with the facts given in the problem. Give the

answer.

The Golden Gate Bridge has a span of 4200 feet. The Brooklyn Bridge has a span of 1595 feet. How much longer is the span of the Golden Gate Bridge?

a. What number or numbers does the problem ask for?b. Are enough facts given? If not, what else is needed?c. Are unnecessary facts given? If so, what are they?d. What operation or operations would you use to find the

answer?

How many 30-second ads can a politician buy with $528,000?


answer?

Paula washed 5 cars and Jim washed 4. Paula charged $3 for each car. Jim charged $4. How much money did Paula earn?


answer?

Mike can type a page in 7 min. How many pages can he type in 45 min?


answer?

1-7: Problem Solving Applications

During the four quarters of a basketball game, the Hoopsters scored 16 points, 21 points, 19 points, and 17 points. How many points did the Hoopsters score during the game?


answer?

Simon had $165 in his checking account. He wrote checks for $32, $19, and $47. How much did Simon have left in his account?


answer?

The temperature was 15°C at 8am. By noon, the temperature had increased by 13°. What was the temperature at noon?


answer?

Test: 1-5, 1-6, 1-7Next: Chapter 11

Chapter 11

Operations with Integers

11-1: Negative Numbers

Objective: To represent negative numbers on the number line.

HW: P. 368: 1-39 ODD; 40-43 ALL; Read 11-2

The Number Line

Natural Numbers = {1, 2, 3, …}Whole Numbers = {0, 1, 2, …}Integers = {…, -2, -1, 0, 1, 2, …}

-5 0 5

Definition

Positive number – a number greater than zero.

0 1 2 3 4 5 6

DefinitionNegative number – a number less than zero.

0 1 2 3 4 5 6-1-2-3-4-5-6

Put the appropriate sign: > OR < OR =1. – 6 ____ 9

2. 2 ____ – 1

3. 12 ____ – 9

4. – 12 ___ 9

Use a number line and arrow to represent each integer.1. 3, starting at 0

2. – 3, starting at 0

3. 3, starting at – 1

4. – 3 starting at 2

Negative Numbers Are Used to Measure Temperature

0102030

-10-20-30-40-50

Negative Numbers Are Used to Measure Under Sea Level

Negative Numbers Are Used to Show Debt

Let’s say your parents bought a car but had to get a loan from the bank for $5,000. When counting all their money they add in –$5,000 to show they still owe the bank.

TemperatureSea Level

$Slope of a Line

FootballDirections on a #

Line

Cold

Example +─

-5 -4 -3 -2 -1 0 1 2 3 4 5

BelowDebt

DownhillYards Lost

Left

HotAboveProfitUphill

Yards GainedRight

DefinitionOpposite Numbers – numbers that are the same distance from zero in the opposite direction

0 1 2 3 4 5 6-1-2-3-4-5-6

Hint

If you don’t see a negative or positive sign in front of a number it is positive.

9+

Absolute Value: Absolute value is the distance from zero.

• The absolute value of 2 is 2 because 2 is 2 units away from 0.

• The absolute value of – 2 is 2 because – 2 is 2 units away from 0.

0 2-2

Absolute value is ALWAYS a POSITIVE number.

Absolute Value

Bars are used to show absolute value.

l -2 l = 2

l 2 l = 2

11-2: Adding Integers

Objective: To add positive and negative integers.

HWP. 373: 9 – 34 ALL (Tonight)

P. 374: 1-7 ALL; Read 11-3 (Tomorrow Night)

The Number Line

Natural Numbers = {1, 2, 3, …}Whole Numbers = {0, 1, 2, …}Integers = {…, -2, -1, 0, 1, 2, …}

-5 0 5

One Way to Add Integers Is With a Number Line

0 1 2 3 4 5 6-1-2-3-4-5-6

When the number is positive, countto the right.

When the number is negative, countto the left.

+–


6 7 8 9 101112543210

+

+6 + (+ 4) = + 10

+

The sum of two positive integers is a positive integer.


-6 -5 -4 -3 -2 -1 0-7-8-9-10-11-12

–– 6 + (– 4) = – 10

–

The sum of two negative integers is a negative integer.

0 1 2 3 4 5 6-1-2-3-4-5-6

+

–

+6 + (– 4) = +2

The sum of a positive and a negative integer is:1. Positive if the positive number has the greater

absolute value.2. Negative if the negative number has that greater

absolute value.3. Zero if both number have the same absolute value.

0 1 2 3 4 5 6-1-2-3-4-5-6

+

–

+3 + (–5) = –2




0 1 2 3 4 5 6-1-2-3-4-5-6+

–

+6 + (– 6) = 0




SHORT CUTAdding integers with the same sign

Positive + Positive: Add and make the sign

6 + 4 = 10

6 7 8 9 101112543210

+

+

positive.

SHORT CUTAdding integers with the same sign

Negative + Negative: Add and make the sign

– 6 + (– 4) = – 10negative.

-6 -5 -4 -3 -2 -1 0-7-8-9-10-11-12

–

–

Adding Integers with the Same Sign

1. -7 + -9 =2. 4 + 7 =3. -6 + -7 = 4. 5 + 9 =5. -9 + -9 =

-16

-18 14

-1311

SHORT CUTAdding integers with the different signs

Subtract and take the sign of the absolute value.

6 + (– 4 ) = 2

LARGER

0 1 2 3 4 5 6-1-2-3-4-5-6

+

–



3 + (– 7 ) = – 4

LARGER

0 1 2 3 4 5 6-1-2-3-4-5-6+

–



3 + (– 5 ) = – 2

LARGER

0 1 2 3 4 5 6-1-2-3-4-5-6

+

–

1) – 4 + 5

4) 7 + (– 1)

3) – 33 + 7

6) 2 + (–15) + (– 2)

2) 12 + – 15

5) – 8 + 3

1 – 3 – 26

6 – 5 – 15

Adding Integers with Different Signs

Adding Integers with Different Signs

1. -7 + 9 =2. 4 + (-7) =3. (-3) + (+4) =4. 6 + -7 = 5. 5 + -9 =6. -9 + 9 =

2

0

- 4

-11

- 3

Additive Inverse

The sum of any number and its additive inverse is

3 + (– 3 ) = 0zero.

0 1 2 3 4 5 6-1-2-3-4-5-6

+

–

11-3: Subtracting Integers

Objective: To subtract positive and negative integers.

HW: P. 376: 1-21 ODD; 23 – 30 ALL; Read 11-4

Subtracting Integers 3 5

When you subtract 5, it is like adding its opposite, 5.

3 + ( 5 ) =

0 1 2 3 4 5 6-1-2-3-4-5-6

+

–

2

1 ( 4 )When you subtract 4, it is like adding its opposite, 4.

1 + 4 =

Subtracting Integers

0 1 2 3 4 5 6-1-2-3-4-5-6

–

+

3

Subtracting IntegersKeep, Change, Change1.Keep the first number2.Change subtraction sign to addition3.Change the second number’s sign to its opposite.4.Follow the addition rules.

9+ (– 9) – 54 – 4 ==

(– 10)+ 10 177 – 7 ==

Subtract Positive Integers

Find 2 – 15.

2 – 15 = 2 + (–15)= –13

Keep, Change, Change1.Keep the first number2.Change subtraction sign to addition3.Change the second number’s sign to its opposite.4.Follow the addition rules.

A. AB. BC. CD. D

A. –34

B. –8

C. 8

D. 34

Find 13 – 21.

Subtract Positive Integers

Find –13 – 8.

–13 – 8 = –13 + (–8)= –21


1. A2. B3. C4. D

A. –20

B. –2

C. 2

D. 20

Find –9 – 11.

Find 12 – (–6).

12 – (–6) = 12 + 6= 18


1. A2. B3. C4. D

A. –13

B. –5

C. 5

D. 13

Find 9 – (–4).

Find –21 – (–8).

Subtract Negative Integers

–21 – (–8) = –21 + 8= –13


A. AB. BC. CD. D

A. –23

B. –11

C. 11

D. 23

Find 17 – (–6).

ALGEBRA Evaluate g – h if g = –2 and h = –7.

Evaluate an Expression

g – h = –2 – (–7) Replace g with –2 and h with –7.

= –2 + 7 To subtract –7, add 7.

= 5 Simplify.

A. AB. BC. CD. D

A. –10

B. –2

C. 2

D. 10

ALGEBRA Evaluate m – n if m = –6 and n = 4.

Use Integers to Solve a Problem

GEOGRAPHY In Mongolia, the temperature can fall to –45ºC in January. The temperature in July may reach 40ºC. What is the difference between these two temperatures?

To find the difference in temperatures, subtract the lower temperature from the higher temperature.

Answer: The difference between the temperatures is 85ºC.

40 – (–45) = 40 + 45 To subtract –45, add 45.

= 85 Simplify.

A. AB. BC. CD. D

A. –26

B. –4

C. 4

D. 26

TEMPERATURE On a particular day in Anchorage, Alaska, the high temperature was 15ºF and the low temperature was –11ºF. What is the difference between these two temperatures for that day?

1) 8 – 13

4) – 25 – 5

3) 4 – (–19)

6) 54 – 14

2) 14 – 7

5) 13 – 7

– 5 23

– 30 6 40

7

Subtract Integers

Adding integersPositive + Positive: Add and make the sign positive.

6 + 4 = 10

Negative + Negative: Add and make the sign negative. – 6 + (– 4) = – 10 Positive + Negative: Subtract and take the sign of the LARGER absolute value. 6 + (– 4 ) = 2

Negative + Positive: Subtract and take the sign of the LARGER absolute value. – 3 + 2 = – 1

Subtracting IntegersKeep, Change, Change1.Keep the first number2.Change subtraction sign to addition3.Change the second number’s sign to its opposite.4.Follow the addition rules.

9+ (– 9) – 54 – 4 ==

(– 10)+ 10 177 – 7 ==

1) 16 – 14

4) – 12 + 16

7) – 19 – 1

10) 3 – 13

3) 99 + 11

6) – 23 + 15

9) – 447 – 23

12) 39 – 42

2) 9 + 26

5) – 22 + 18

8) – 14 – 16

11) 23 – 8

2 35 110

4 – 4 – 8

– 20 – 30 – 470

– 10 – 15 – 3

Subtract and Add Integers

1) 23 + 4

4) – 18 + 12

7) – 18 – (–12)

10) 18 + (– 12) + 5

3) 9 – (– 2)

6) 24 + (– 17)

9) – 15 – 0

12) – 14 + 0 + 13

2) – 4 – 2

5) – 24 + (–11)

8) 52 – (–30)

11) – 2 (–10) + 15

27 – 6 11

– 6 – 35 7

– 6 82 – 15

11 – 17 – 1

Subtract and Add Integers

1) a + ( – 12)

4) b + c

7) x – 7

10) x – (– z)

3) c + 23

6) a + b

9) y - x

12) x – z – y

2) – 20 + b

5) a + c

8) x - z

11) | y – z |

0 – 35 13

– 25 2 – 3

– 15 3 15

– 19 18 – 4

a = 12, b = – 15, c = – 10

x = –8, y = 7, z = – 11

Test: 11-1, 11-2, 11-3

11-4: Products with one negative number.

ObjectiveTo multiply a positive number and a negative number.

HWP. 379: 1-25 ODD; 26-33 ALL; Read 11-5

Multiplying Integers

• Same sign always has a positive answer.

• Different sign always has a negative answer.

• When multiplying by zero, you get zero, no matter what the sign is.

9 ● 3 = 27– 9 ● (– 3) = 27

9 ● (– 3) = – 27– 9 ● 3 = – 27

9 ● 0 = 0– 9 ● 0 = 0

Lesson 6 Ex1Multiply Integers with Different Signs

Find 5(–4).

Answer: –20

5(–4) = –20 The integers have different signs. This product is negative.

A. AB. BC. CD. D

A. –15

B. –2

C. 2

D. 15

Find 3(–5).

Lesson 6 Ex2Multiply Integers with Different Signs

Find –3(9).

Answer: –27

–3(9) = –27 The integers have different signs. This product is negative.

1. A2. B3. C4. D

A. –35

B. 2

C. 12

D. 35

Find –5(7).

Lesson 6 Ex3Multiply Integers with the Same Sign

Find –6(–8).

Answer: 48

–6(–8) = 48 The integers have the same sign. This product is

positive.

1. A2. B3. C4. D

A. –28

B. –11

C. 11

D. 28

Find –4(–7).

Lesson 6 Ex4Find (–8)2.

Answer: 64

Multiply Integers with the Same Sign

(–8)2 = (–8)(–8) There are two factors of –8.

= 64 The product is positive.

A. AB. BC. CD. D

A. –25

B. –10

C. 10

D. 25

Find (–5)2.

Lesson 6 Ex5Find –2(–5)(–6).

Answer: –60

Multiply Integers with the Same Sign

–2(–5)(–6) = [–2(–5)](–6)Associative Property

= 10(–6)–2(–5) = 10= –60The product is

negative.

A. AB. BC. CD. D

A. 84

B. –14

C. 14

D. –84

Find –7(–3)(–4).

• Explain what Product means.

1) 8 (–12)

4) –6 (–6)

3) –6 (–5)

6) –9 (1)(–5)

2) 25 (–2)

5) –4 (–2)(–8)

– 96 – 50 30

36 – 64 45

Multiply Integers

Lesson 6 Ex6Use Integers to Solve a Problem

MINES A mine elevator descends at a rate of 300 feet per minute. How far below the earth’s surface will the elevator be after 5 minutes?

If the elevator descends 300 feet per minute, then after 5 minutes, the elevator will be 300(5) or 1,500 feet below the surface. Thus, the elevator will descend to 1,500 feet below the earth’s surface.

Answer: After five minutes, the elevator will be 1,500 feet below the earth’s surface.

A. AB. BC. CD. D

A. –$468

B. $468

C. –$84

D. $84

RETIREMENT Mr. Rodriguez has $78 deducted from his pay every month and placed in a savings account for his retirement. What integer represents a change in his savings account for these deductions after six months?

Lesson 6 Ex7ALGEBRA Evaluate abc if a = –3, b = 5, and c = –8.

Answer: 120

Evaluate Expressions

abc = (–3)(5)(–8) Replace a with –3, b with 5, and c with –8.

= (–15)(–8) Multiply –3 and 5.

= 120 Multiply –15 and –8.

A. AB. BC. CD. D

A. –48

B. –4

C. 0

D. 48

ALGEBRA Evaluate xyz if x = –6, y = –2, and z = 4.

End of Lesson 6

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Lesson 7 MenuFive-Minute Check (over Lesson 2-6)

Main Idea

California Standards

Example 1: Look For a Pattern

Lesson 7 MI/Vocab• Solve problems by looking for a pattern.

Look For a Pattern

HAIR Lelani wants to grow an 11-inch ponytail to cut off and donate to a program that makes wigs for children with cancer. She has a 3-inch ponytail now, and her hair grows about one inch every two months. How long will it take for her ponytail to reach 11 inches?

Explore You know the length of Lelani’s ponytail now. You know how long Lelani wants her ponytail to grow and you know how fast her hair grows. You need to know how long it will take for her ponytail to reach 11 inches.Plan Look for a pattern. Then extend the pattern to find the solution.

Lesson 7 Ex1Look For a Pattern

Solve After the first two months, Lelani’s ponytail will be 3 inches + 1 inch, or 4 inches. Her hair grows according to the pattern below.

3 in. 4 in. 5 in. 6 in. 7 in. 8 in. 9 in. 10 in. 11 in.

Answer: 16 months

+1 +1 +1 +1 +1 +1 +1 +1

It will take eight sets of two months, or 16 months total, for Lelani’s ponytail to reach 11 inches.Check Lelani’s ponytail grew from 3 inches to 11 inches, a difference of eight inches, in 16 months. Since one inch of growth requires two months and 8 × 2 = 16, the answer is correct.

A. AB. BC. CD. D

A. 3.5 mi

B. 15 mi

C. 16.5 mi

D. 19.5 mi

RUNNING Samuel ran 2 miles on his first day of training to run a marathon. On the third day, Samuel increased the length of his run by 1.5 miles. If this pattern continues for every other day, how many miles will Samuel run on the 27th day?

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Lesson 8 MI/Vocab• Divide integers.

Dividing Integers

• Same sign always has a positive answer.

• Different sign always has a negative answer.

• When you divide 0 by number, no matter what the sign is, you get 0.

27 ÷ 3 = 9– 27 ÷ (– 3) = 9

27 ÷ (– 3) = – 9– 27 ÷ 3 = – 9

0 ÷ 3 = 0 0 ÷ (–3) = 0

Lesson 8 Ex1Dividing Integers with Different Signs

Find 51 ÷ (–3).

Answer: –17

51 ÷ (–3) = –17

A. AB. BC. CD. D

A. –4

B. 4

C. 27

D. 45

Find 36 ÷ (–9).

Lesson 8 Ex2Dividing Integers with Different Signs

Answer: –11

The integers have different signs. The quotient is

negative.

Find

1. A2. B3. C4. D

0%0%0%0%

A B C D

A. –5

B. 5

C. 36

D. 54

Lesson 8 KC 2

Lesson 8 Ex3Dividing Integers with Same Sign

Find –12 ÷ (–2).

Answer: 6

–12 ÷ (–2) = 6 The integers have the same sign. The quotient is

positive.

1. A2. B3. C4. D

0%0%0%0%

A B C D

A. –32

B. –16

C. –3

D. 3

Find –24 ÷ (–8).

• Explain what quotient means.

Lesson 8 Ex4ALGEBRA Evaluate –18 ÷ x if x = –2.

Answer: 9

Dividing Integers with Same Sign

–18 ÷ x = –18 ÷ (–2) Replace x with –2. = 9 Divide. The quotient is

positive.

A. AB. BC. CD. D

A B C D

0% 0%0%0%

A. –63

B. 63

C. 7

D. –7

ALGEBRA Evaluate g ÷ h if g = –21 and h = –3.

7) 50 ÷ – 5

10) – 26 13

9) – 21 – 7

12) 36 ÷ 4

8) – 100 ÷ (– 10)

11) 84 –12

– 103

– 2 – 7 9

10

Divide Integers

Lesson 8 Ex5

Answer: The car’s acceleration is –4 feet per second squared.

Subtract 80 from 40.

= –4 Divide.

PHYSICS You can find an object’s acceleration with the expression ,

where Sf = final speed, Ss = starting speed, and t = time. If a car was traveling at

80 feet per second and, after 10 seconds, is traveling at 40 feet per second,

what was its acceleration?

A. AB. BC. CD. D

A B C D

0% 0%0%0%

A. –20ºF

B. –4ºF

C. 12ºF

D. 4ºF

WEATHER The temperature at 4:00 P.M. was 52ºF. By 8:00 P.M., the temperature had gone down to 36ºF. What is the average change in temperature per hour?

Lesson 3 Ex1Naming Points Using Ordered Pairs

Write the ordered pair that names point R. Then state the quadrant in which the point is located.

Answer: R is (–2, 4). R is in Quadrant II.

A. AB. BC. CD. D

A. (–3, –1); Quadrant III

B. (2, 1); Quadrant I

C. (3, 1); Quadrant I

D. (3, –1); Quadrant IV

Write the ordered pair that names point M. Then name the quadrant in which the point is located.

1. A2. B3. C4. D

Graph and label the point G(–2, –4).

A. B.

C. D.

G

G

G

G

Lesson 3 Ex3GEOGRAPHY Use the map of Utah shown below. In which quadrant is Vernal located.

Answer: Quadrant I

Locate an Ordered Pair

1. A2. B3. C4. D

A. Quadrant I

B. Quadrant II

C. Quadrant III

D. Quadrant IV

GEOGRAPHY Use the map of Utah. In which quadrant is Tremonton located.

Lesson 3 Ex4Which of the cities labeled on the map is located in Quadrant IV?

Answer: Bluff

Identify Quadrants

A. AB. BC. CD. D

A. Tremonton

B. Vernal

C. Bluff

D. Cedar City

Name a city from the map of Utah that is located in Quadrant III.

Dave goes to the video store to rent a movie. The cost per movie is $3.50. Make a table that shows the amount Dave would pay for renting 1, 2, 3, and 4 movies.

Melanie read 14 pages of a detective novel each hour. Write an equation using two variables to show how many pages p she read in h hours.

Let p represent the number of pages readLet h represent the number of hours.

Equation p = 14 ● h

Equation p = 14 h

On an average day, Nancy can pick 2 rows of strawberries per hour. The table shows the number of rows she can pick in a given number of hours. Complete the table.

Number of hours worked Number of rows picked

1 2

2 4

3 ?

4 ?

5 ?

Let t stand for the number of hours worked. Write an expression for the number of rows picked.

Let r stand for the number of rows picked. Write an expression for the number of hours worked.

6

8

10

2t

r ÷ 2

Documents

Chapter 1 Operations with Whole Numbers. 1-1: Mathematical Expression