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Study Guide and Intervention

Integers and Absolute Value

NAME ______________________________________________ DATE ____________ PERIOD _____

2-12-1

©Glencoe/McGraw-Hill57Glencoe Pre-AlgebraLesson 2-1

Replace each ?with?or?to make a true sentence.

a. ?6 ??2b.3 ??4 Numbers on opposite sides of zero and the same distance from zero have the same absolute value. The symbol for absolute value is two vertical bars on either side of the number. ?2??2 and ??2??2

The set of integerscan be written {..., ?3,?2,?1, 0, 1, 2, 3, ...} where ... means continues indefinitely.

Two integers can be compared using an inequality, which is a mathematical sentence containing?or?.Replace each ?with?,?,or?to make a true sentence.

1.4 ??4

?2.8 ?12 ?3.?7 ??5 ?4.2 ?5 ?

5.?1 ?1 ?6.4 ??3 ?7.6 ?8 ?8.?2 ?12 ?

9.9 ??1 ?10.?6 ??6 ?11.5 ??3 ?12.?10 ?2 ?

Evaluate each expression.

13. ??6?614.?15?1515. ??12?1216.?21?21

17.?4? ? ?2?218.??8? ? ??3? 1119.??10? ? ??6?420.?12? ? ??4?16

ExercisesExercises

?2 is greater since it lies to the right of?6.

So write ?6

??2. 3 is greater since it lies to the right of ?4.

So write 3 ??4.

a.??4?b.??3???6? ?4??4??3???6? ?3 ?6 ?9??3??3,?6??6

Simplify.

2102223

242526272812345678y

A C

Example 1Example 1

Example 2Example 2

Use the integers graphed on the number line below for each question.

Evaluate each expression.

©Glencoe/McGraw-Hill58Glencoe Pre-Algebra

Skills Practice

Integers and Absolute Value

NAME ______________________________________________ DATE ____________ PERIOD _____

2-12-1

Replace each ?with?,?,or?to make a true sentence.

1.1 ?0

?2.-3 ?0 ?3.0 ??1 ?4.0 ?9 ?

5.?7 ?-7 ?6.2 ??2 ?7.?2 ?8 ?8.?4 ?4 ?

9.5 ?5 ?10.0 ??6 ?11.4 ?10 ?12.6 ??6 ?

13.3 ?7 ?14.?1 ??2 ?15.3 ?4 ?16.?3 ??4 ?

Order the integers in each set from least to greatest.

17.{4,?5, 0}18.{8,?2, 1}19.{?6,?3, 0}

{?5, 0, 4} {?2, 1, 8} {?6,?3, 0}

20.{?5, 5, 3,?1}21.{0,?3, 7,?2}22.{9,?11, 1, 0}

{?5,?1, 3, 5} {?3,?2, 0, 7} {?11, 0, 1, 9}

23.{12,?4, 3,?1}24.{?8, 15, 1,?10}25.{?12,?17,?20, 2}

{?4,?1, 3, 12} {?10,?8, 1, 15} {?20,?17,?12, 2}

Evaluate each expression.

26.?1?27.??10?28.??8?

1108

29.?10?30.?4????4?31.?9????5?

10 8 4

32.0 ???1?33.??6????5?34.??8????8?

1110

35.?12????3?36.??15???6?37.??13????7?

15 9 20

Evaluate each expression if a??3,b?0, and c?1.

38.?a??b39.?c??2 40.9 ??a?

33 6

41.?25??b42.10 ??b?43.??8???a?

25 10 11

Practice

Integers and Absolute Value

NAME ______________________________________________ DATE ____________ PERIOD _____

2-12-1

©Glencoe/McGraw-Hill59Glencoe Pre-Algebra

Replace each ?with ?,?,or?to make a true sentence.

1.0 ??5

?2.10 ??10 ?3.?8 ?3 ?4.11 ?11 ?

5.?18 ??18 ?6.?18 ?18 ?7.18 ??18 ?8.18 ?18 ?

9.?120 ??95 ?10.35 ??12 ?11.?35 ?12 ?12.41 ?17 ?

Order the integers in each set from least to greatest.

13.{?14,?6,?22, 0}14.{?3, 19, 0,?5}15.{?7, 20,?21, 7}

{?22,?14,?6, 0} {?5,?3, 0, 19} {?21,?7, 7, 20}

16.{15,?1, 4,?3}17.{0,?1, 2,?3, 4}18.{55, 0,?60, 12}

{?3,?1, 4, 15} {?3,?1, 0, 2, 4} {?60, 0, 12, 55}

19.{?48,?30,?49,?8, 3,?4}20.{27,?9, 3, 0,?2, 29}

{?49,?48,?30,?8,?4, 3}{?9,?2, 0, 3, 27, 29}

Evaluate each expression.

21.??7?22.?14?23.??11?

7 14 11

24.??9???6?25.??18????8?26.??12???1?

3 10 13

27.?8 ?4?28.?23???18?29.??16????22?

4 5 38

Evaluate each expression if a??3,b?0, and c?1.

30.?a???c?31.?a???c?32.?ab??c

2 4 1

33.5 ??ac?34.c???5?35.c??5?

2 6 6

36.WEATHERAt 6:15 a.m. the temperature was ?8°F. At 12:15 p.m. the temperature

was ?12°F. At 6:16 p.m. the temperature was ?10°F. Order the temperatures from least to greatest. ?12°F,?10°F,?8°F

Lesson 2-1

Glencoe/McGraw-Hill

58

Glencoe Pre-Algebra

Skills PracticeIntegers and Absolute Value

NAME ______________________________________________ DATE ____________ PERIOD _____

2-12-1

Replace each lwith , ,or to make a true sentence.

1.1 l0

2.-3 l0

3.0 l21

4.0 l9

5.27 l-7

6.2 l22

7.22 l8

8.24 l4

9.5 l5

10.0 l26

11.4 l10

12.6 l26

13.3 l7

14.21 l22

15.3 l4

16.23 l24

Order the integers in each set from least to greatest.

17.{4,25, 0}18.{8,22, 1}19.{26,23, 0}

{ 5, 0, 4} { 2, 1, 8} { 6, 3, 0}

20.{25, 5, 3,21}21.{0,23, 7,22}22.{9,211, 1, 0}

{ 5, 1, 3, 5} { 3, 2, 0, 7} { 11, 0, 1, 9}

23.{12,24, 3,21}24.{28, 15, 1,210}25.{212,217,220, 2}

{ 4, 1, 3, 12} { 10, 8, 1, 15} { 20, 17, 12, 2}

Evaluate each expression.

26.u1u27.u210u28.u28u

1108

29.u10u30.u4u1 u24u31.u9u2 u25u

10 8 4

32.0 1u21u33.u26u1 u25u34.u28u2 u28u

1110

35.u12u1 u23u36.u215u2 u6u37.u213u1 u27u

15 9 20

Evaluate each expression if a 3,b 0, and c 1.

38.uau2b39.ucu12 40.9 2uau

33 6

41.u25u2b42.10 2ubu43.u28u1 uau

25 10 11

Study Guide and InterventionIntegers and Absolute Value NAME ______________________________________________ DATE ____________ PERIOD _____

2-12-1

Glencoe/McGraw-Hill

57

Glencoe Pre-Algebra

Lesson 2-1

Replace each lwith or to make a true sentence.

a. 6 l 2b.3 l 4 Numbers on opposite sides of zero and the same distance from zero have the same absolute value. The symbol for absolute value is two vertical bars on either side of the number. u 2 u

52 and

u 2 2 u 52

The set of integerscan be written {..., 23,22,21, 0, 1, 2, 3, ...} where ... means continues indefinitely.

Two integers can be compared using an inequality, which is a mathematical sentence containing,or..

Replace each lwith , ,or to make a true sentence.

1.4 l24

2.8 l12

3.27 l25

4.2 l5

5.21 l1

6.4 l23

7.6 l8

8.22 l12

9.9 l21

10.26 l26

11.5 l23

12.210 l2

Evaluate each expression.

13. u 26u
6

14.u15u

15

15.u212u

12

16.u21u

21

17.u4u2 u2u

2

18.u28u1 u23u

11

19.u210u2 u26u

4

20.u12u1 u24u

16

ExercisesExercises

22 is greater since it lies to the right of26.

So write 26

22. 3 is greater since it lies to the right of 24.

So write 3

24.
a. 4 b. 3 6 u 2 4 u 54
u 2 3 u 1 u 6 u 53 16
59
u23u53,u6u56

Simplify.

210
22
23
24
25
26
27
28
1 2 3 4 5 6 7 8 10 2 3 1 2 3

2 units

2 units

Example

1

Example

1

Example

2

Example

2 Use the integers graphed on the number line below for each question.Evaluate each expression.

©Glencoe/McGraw-HillA2Glencoe Pre-Algebra

Answers(Lesson 2-1)

Glencoe/McGraw-Hill

60

Glencoe Pre-Algebra

How are integers used to model real-world situations?Do the activity at the top of page 56 in your textbook.

Write your answers below.

a.What does a value of27 represent?

7 inches below normal

b.Which city was farthest from its normal rainfall?

Jackson, MS

c.How could you represent 5 inches above normal rainfall? 5 R eading to Learn MathematicsIntegers and Absolute Value NAME ______________________________________________ DATE ____________ PERIOD _____

2-12-1

Pre-ActivityReading the Lesson

Helping You Remember6.Absolute is a word that is used frequently in the English language. a.Find the definition of absolutein a dictionary. Write the definition that most closely relates to mathematics. independent of arbitrary standards of measurement b.Explain how the English definition can help you remember the meaning of absolute valuein mathematics. The absolute value of an integer is independent of the sign of thenumber.1-5. See students' work. Write a definition and give an example of each new vocabulary word or phrase.

Vocabulary Definition Example

1.negative number2.integers3.coordinate4.inequality5.absolute value

PracticeIntegers and Absolute Value

NAME ______________________________________________ DATE ____________ PERIOD _____

2-12-1

Glencoe/McGraw-Hill

59

Glencoe Pre-Algebra

Replace each lwith , ,or to make a true sentence.

1.0 l25

2.10 l210

3.28 l3

4.11 l11

5.218 l218

6.218 l18

7.18 l218

8.18 l18

9.2120 l295

10.35 l212

11.235 l12

12.41 l17

Order the integers in each set from least to greatest.

13.{214,26,222, 0}14.{23, 19, 0,25}15.{27, 20,221, 7}

{ 22, 14, 6, 0} { 5, 3, 0, 19} { 21, 7, 7, 20}

16.{15,21, 4,23}17.{0,21, 2,23, 4}18.{55, 0,260, 12}

{ 3, 1, 4, 15} { 3, 1, 0, 2, 4} { 60, 0, 12, 55}

19.{248,230,249,28, 3,24}20.{27,29, 3, 0,22, 29}

49,
48,
30,
8, 4, 3} { 9, 2, 0, 3, 27, 29}

Evaluate each expression.

21.u27u22.u14u23.u211u

7 14 11

24.u29u2 u6u25.u218u2 u28u26.u212u1 u1u

3 10 13

27.u8 24u28.u23u2 u18u29.u216u1 u222u

4 5 38

Evaluate each expression if a 3,b 0, and c 1.

30.uau2 ucu31.uau1 ucu32.uabu1c

2 4 1

33.5 2uacu34.c1u25u35.c1u5u

2 6 6

36.WEATHERAt 6:15 a.m. the temperature was 28°F. At 12:15 p.m. the temperature

was 212°F. At 6:16 p.m. the temperature was 210°F. Order the temperatures from least to greatest.

12°F,210°F,28°F

Lesson 2-1

©Glencoe/McGraw-HillA3Glencoe Pre-Algebra

Answers(Lesson 2-1)

Answers

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