1-4 Integers and Absolute Value Open your notebook and write today’s date. We are doing sec 1.4 today

1-4 Integers and Absolute Value

Open your notebook

and write today’s date.

We are doing sec 1.4 today.


Warm UpEvaluate each expression for the given

values of the variables.

1. 2x – 3y for x = 17 and y = 6

2. 5(x + 3) + 4y for x = 3 and y = 2

3. 5x – 4y for x = 0.3 and y = 0.2


Warm UpEvaluate each expression for the given

values of the variables.

1. 2x – 3y for x = 17 and y = 6

2. 5(x + 3) + 4y for x = 3 and y = 2

3. 5x – 4y for x = 0.3 and y = 0.2

16

38

0.7


Learn to compare and order integers and to evaluate expressions containing absolute value.


Vocabularyintegeroppositeadditive inverseabsolute value


Integers are the set of whole numbers and their opposites. Opposites, or additive inverses, are numbers that are the same distance from 0, but on opposite sides of 0 on the number line.


Use <, >, or = to compare the scores.

Additional Example 1A: Sports Application

Aaron’s score is 4, and Felicity’s score is –1.

Place the scores on the number line.

–1 < 4

–5 –4 –3 –2 –1 0 1 2 3 4 5

••

–1 is to the left of 4.



Additional Example 1B: Sports Application

List the golf scores in order from the lowest to the highest. The scores are –4, 2, 5, and –3.

Place the scores on the number line and read them from left to right.

In order from the lowest score to the highest score, the scores are –4, –3, 2, and 5.

–5 –4 –3 –2 –1 0 1 2 3 4 5

• • ••



Check It Out: Additional Example 1A

Fran’s score is –2, and Joaquin’s score is –3.

Place the scores on the number line.

–3 < –2

–5 –4 –3 –2 –1 0 1 2 3 4 5

• •

–3 is to the left of –2.


Write the integers 7, –12, and 13 in order from least to greatest.

Check It Out: Additional Example 2

13 > –12, 13 > 7, and –12 < 7

Compare each pair of integers.

–12, 7, and 13.–12 is less than both 7 and 13.


Find the additive inverse of each integer.

Additional Example 3: Finding Additive Inverses

A. 6

–6

B. –14

–6 is the same distance from 0 as 6 is on the number line.

14 14 is the same distance from 0 as –14 is on the number line.

C. 0.5

–0.5 –0.5 is the same distance from 0 as 0.5 is on the number line.


Both 4 and –4 are 4 units from 0.

–5 –4 –3 –2 –1 0 1 2 3 4 5

A number’s absolute value is its distance from 0 on a number line. Absolute value is always positive or 0 because distance cannot be negative. “The absolute value of –4” is written as |–4|. Additive inverses have the same absolute value.

4 units 4 units

–4 = 4 = 4.


00

88

88


0

0

or


Simplify each expression.

Additional Example 4: Simplifying Absolute-Value Expressions

A. –8 + –5

–8 is 8 units from 0.

8 + 5 = 13

–8 = 8

–5 is 5 units from 0.–5 = 5

B. 5 – 6




Check It Out: Additional Example 4

A. –2 + –9

–2 is 2 units from 0.

2 + 9 = 11

–2 = 2


B. 1 – 1

0 is 0 units from 0. 0 = 0


Try these problems.

Write the integers in order from least to greatest.

1. –17, –26, 23

2. 0, 5, –4


3. The sum of 3 and the additive inverse of –8

4. |–4| + |–2|

5. At the end of the course, your golf score was –2. Your friend’s score was 7. Use <, >, or = to compare the scores.


Answers

Write the integers in order from least to greatest.

1. –17, –26, 23

2. 0, 5, –4


3. The sum of 3 and the additive inverse of –8

4. |–4| + |–2|

5. At the end of the course, your golf score was –2. Your friend’s score was 7. Use <, >, or = to compare the scores.

–26, –17, 23

–4, 0, 5

11

6

–2 < 7


1. Which of the following represents the given integers in order from least to greatest?

–24, 16, –13

A. –24, 16, –13

B. –24, –13, 16

C. –13, 16, –24

D. 16, –13, –24

Try this problem.


1. Which of the following represents the given integers in order from least to greatest?

–24, 16, –13

A. –24, 16, –13

B. –24, –13, 16

C. –13, 16, –24

D. 16, –13, –24

Answer


3. Evaluate the sum of 5 and the additive inverse of –14.

A. –19

B. –9

C. 9

D. 19

Try this problem.


3. Evaluate the sum of 5 and the additive inverse of –14.

A. –19

B. –9

C. 9

D. 19

Answer


4. Evaluate |–6| + |–12|.

A. –6

B. 6

C. 12

D. 18

Try this problem.


4. Evaluate |–6| + |–12|.

A. –6

B. 6

C. 12

D. 18

Answer

Documents

1-4 Integers and Absolute Value Open your notebook and write today’s date. We are doing sec 1.4 today