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Understanding Integers: Comparing, Ordering, and Opposites in Real-Life Situations

This guide delves into the concepts of integers, including comparing integers, identifying opposites, and ordering scores relevant in practical applications, such as sports. Through various examples and guided practice, learners will be equipped to handle scenarios involving profit and loss, temperature changes, and competitive scores. The step-by-step approach ensures comprehension and retention, while a range of practice problems helps solidify the understanding of these fundamental math concepts.

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Understanding Integers: Comparing, Ordering, and Opposites in Real-Life Situations

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  1. EXAMPLE 1 StandardizedTest Practice

  2. EXAMPLE 1 StandardizedTest Practice SOLUTION The shuttle’s computers take over at T– 31 seconds. The correct answer is B.

  3. GUIDED PRACTICE for Example 1 Write the integer that represents the situation. 1.a$15 profit ANSWER 15 2. a9point decrease ANSWER – 9 3. a loss of5yards ANSWER – 5

  4. EXAMPLE 2 Identifying Opposites Find the opposite of –3.

  5. EXAMPLE 2 Identifying Opposites Find the opposite of –3.

  6. EXAMPLE 2 Identifying Opposites Find the opposite of –3. ANSWER The opposite of –3 is 3.

  7. EXAMPLE 3 EXAMPLE 3 Comparing Integers Comparing Integers Compare –8 and –5.

  8. EXAMPLE 3 EXAMPLE 3 Comparing Integers Comparing Integers Compare –8 and –5.

  9. EXAMPLE 3 EXAMPLE 3 Comparing Integers Comparing Integers Compare –8 and –5. ANSWER Because –8 is to the left of –5 on the number line, –8 <–5.

  10. EXAMPLE 3 EXAMPLE 4 Ordering Integers Comparing Integers Sports In a golf tournament, the player with the lowest score wins. The table shows the scores of several golfers (including the winner) in a recent Masters Tournament. Who won? SOLUTION ANSWER Phil Mickelson won with the lowest score of –9.

  11. for Examples 2, 3, and 4 GUIDED PRACTICE Find the opposite of the integer. ANSWER 4. 8 –8 ANSWER 5. –7 7 0 6. 0 ANSWER ANSWER 1 7. –1

  12. for Examples 2, 3, and 4 GUIDED PRACTICE Copy and complete the statement using < or >. 8. –2 ? 2 ANSWER < 9. 0 ? –1 ANSWER > 10. –8 ? –9 > ANSWER 11. –5 ? –4 ANSWER <

  13. for Examples 2, 3, and 4 GUIDED PRACTICE What If? 12. Suppose the scores in another golf tournament are –14, 4, –5, 0, and –16. Which score is the lowest? ANSWER –16

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