Problem of the Day Janie’s score is 3 times the sum of 1 and Maria’s score on the final exam. Maria scored 12 points. Whose score is higher? Janie

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

Vocabulary integer opposite additive inverse absolute value

Integers are the set of whole numbers and their opposites 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.

Additional Example 1A: Sports Application Use <, >, or = to compare the scores. Aaron’s score is 4, and Felicity’s score is –1. Place the scores on the number line. –5 –4 –3 –2 –1 0 1 2 3 4 5 • • –1 < 4 –1 is to the left of 4.

Additional Example 1B: Sports Application Use <, >, or = to compare the scores. 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. –5 –4 –3 –2 –1 0 1 2 3 4 5 • • • • In order from the lowest score to the highest score, the scores are –4, –3, 2, and 5.

Check It Out: Additional Example 1A Use <, >, or = to compare the scores. Fran’s score is –2, and Joaquin’s score is –3. Place the scores on the number line. • –5 –4 –3 –2 –1 0 1 2 3 4 5 • –3 < –2 –3 is to the left of –2.

Check It Out: Additional Example 1B Use <, >, or = to compare the scores. List the golfer’s scores in order from the lowest to the highest. The scores are –3, 1, 0, and –2. Place the scores on the number line and read them from left to right. –5 –4 –3 –2 –1 0 1 2 3 4 5 • • • • In order from the lowest score to the highest score, they are –3, –2, 0, and 1.

Additional Example 2: Ordering Integers Write the integers 8, –5, and 4 in order from t least to greatest. Compare each pair of integers. 8 > –5, 8 > 4, and –5 < 4 –5 is less than both 4 and 8. –5, 4, and 8.

Check It Out: Additional Example 2 Write the integers 7, –12, and 13 in order from greatest to least. Compare each pair of integers. 13 > –12, 13 > 7, and –12 < 7 –12 is less than both 7 and 13. 13, 7, and -12.

Additional Example 3: Finding Additive Inverses Find the additive inverse of each integer. A. 6 –6 –6 is the same distance from 0 as 6 is on the number line. B. –14 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.

Check It Out: Additional Example 3 Find the additive inverse of each integer. A. 12 –12 –12 is the same distance from 0 as 12 is on the number line. B. –1.9 1.9 1.9 is the same distance from 0 as –1.9 is on the number line. C. 1 –1 –1 is the same distance from 0 as 1 is on the number line.

Both 4 and –4 are 4 units from 0. 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 –5 –4 –3 –2 –1 0 1 2 3 4 5 –4 = 4 = 4. Both 4 and –4 are 4 units from 0.

Additional Example 4: Simplifying Absolute-Value Expressions Simplify each expression. A. –8 + –5 –8 = 8 –8 is 8 units from 0. –5 = 5 –5 is 5 units from 0. 8 + 5 = 13 B. 5 – 6 –1 = 1 –1 is 1 units from 0.

Check It Out: Additional Example 4 Simplify each expression. A. –2 + –9 –2 = 2 –2 is 2 units from 0. –9 = 9 –9 is 9 units from 0. 2 + 9 = 11 B. 1 – 1 0 = 0 0 is 0 units from 0.

Lesson Quizzes Lesson Quiz for Student Response Systems

Lesson Quiz for Student Response Systems 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

Lesson Quiz for Student Response Systems 2. Which of the following represents the given integers in order from least to greatest? 23, 0, –90 A. –90, 0, 23 B. –90, 23, 0 C. 0, 23, –90 D. 0, –90, 23

Lesson Quiz for Student Response Systems 3. Evaluate the sum of 5 and the additive inverse of –14. A. –19 B. –9 C. 9 D. 19

Lesson Quiz for Student Response Systems 4. Evaluate |–6| + |–12|. A. –6 B. 6 C. 12 D. 18