Warm Up

1. Use Integers and Rational Numbers Warm Up Lesson Presentation Lesson Quiz

2. > ANSWER 6 5 9 8 2. ? < ANSWER Warm-Up Complete the statement using <, >, or =. 1. 1.3 ? 1.03

3. 3.Order from least to greatest: , 0.04, , 0.45 1 1 2 2 3 3 0.04, , 0.45, ANSWER 7 7 4. A hobby store has balsa wood strips in three thicknesses (in inches): , , and . Which strip is the thickest? 3 5 1 16 8 32 3 ANSWER -inch strip 16 Warm-Up Complete the statement using <, >, or =.

4. ANSWER On the number line,–3is to the right of– 4.So, –3 > – 4. Example 1 Graph– 3and– 4on a number line. Then tell which number is greater.

5. 0 4 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 ANSWER On the number line,4is to the right of0.So, 4 > 0. Guided Practice Graphthe numbers on a number line. Then tell which number is greater. 1.4and0

6. –5 2 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 ANSWER On the number line,2is to the right of–5.So, 2 > –5. Guided Practice 2.2and–5

7. –1 –6 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 ANSWER On the number line,–1is to the right of–6.So, –1 > –6. Guided Practice 3.–1and–6

8. Tell whether each of the following numbers is a whole number, an integer, or a rational number:5, 0.6, –2 , and –24. 2 3 Example 2

9. Example 3 ASTRONOMY A star’s color index is a measure of the temperature of the star. The greater the color index, the cooler the star. Order the stars in the table from hottest to coolest. SOLUTION Begin by graphing the numbers on a number line.

10. ANSWER From hottest to coolest, the stars are Shaula, Rigel, Denebola, and Arneb. Example 3 Read the numbers from left to right:– 0.22, – 0.03, 0.09, 0.21.

11. Number Whole number? Integer? Rational number? 3 Yes Yes Yes ANSWER –1.2 No No Yes –2, –1.2, 0, 3 (Ordered the numbers from least to greatest). –2 No Yes Yes 0 Yes Yes Yes Guided Practice Tell whether each number in the list is a whole number, an integer, or a rational number.Then order the numbers from least to greatest. 4. 3, –1.2, –2,0

12. Number Whole number? Integer? Rational number? 5. 4.5, – , – 2.1, 0.5 4.5 No No Yes 3 No No Yes – 3 3 4 4 4 No No Yes –2 .1 0.5 No No Yes ANSWER – 2.1, – , 0.5 , – 2.1.(Ordered the numbers from least to greatest). Guided Practice

13. ANSWER Number Whole number? Integer? Rational number? –2.8, –1.5, – 0.31, 3.6 (Ordered the numbers from least to greatest). 3.6 No No Yes –1.5 No No Yes –0.31 No No Yes –2.8 No No Yes Guided Practice 6. 3.6, –1.5, –0.31, – 2.8

14. 2 7. , 1.75, – , 0 3 Number Whole number? Integer? Rational number? 1 No No Yes 6 1.75 No No Yes 1 1 2 6 6 No No Yes – 3 0 Yes Yes Yes ANSWER 2 – , 0 , , 1.75. (Ordered the numbers from leastto greatest). 3 Guided Practice

15. 3 3 b.Ifa = , 4 4 then – a = – . Example 4 For the given value ofa, find –a. a. Ifa=– 2.5, then – a = –(– 2.5) = 2.5.

16. 2 2 3 3 2 2 . then | a| = |– | = – (– ) = a.Ifa = – , 3 3 Example 5 For the given value ofa, find | a |. b.Ifa= 3.2, then|a| = |3.2| = 3.2.

17. ANSWER ANSWER 4 4 4 9 9 9 – 10. a = – 5.3, 5.3 7, 7 ANSWER , Guided Practice For the given value of a, find –aand |a|. 9. a = – 7 8. a = 5.3

18. Example 6 Identify the hypothesis and the conclusion of the statement “If a number is a rational number, then the number is an integer.” Tell whether the statement is true or false. If it is false, give a counterexample. SOLUTION Hypothesis: a number is a rational number Conclusion: the number is an integer The statement is false. The number 0.5 is a counterexample, because 0.5 is a rational number but not an integer.

19. ANSWER Hypothesis: a number is a rational number Guided Practice Identify the hypothesis and the conclusion of the statement. Tell whether the statement is true or false. If it is the false, give a counterexample. 11. If a number is a rational number, then the number is positive Conclusion: the number is positive –false The number –1 is a counterexample, because –1 is a rational number but not positive.

20. 12. If the absolute value of a number is a positive, then the number is positive. ANSWER Hypothesis: the absolute value of a number is positive Guided Practice Conclusion: the number is positive –false The number –2 is a counterexample, because the absolute value of –2 is 2, but –2 isnegative.

21. ANSWER –3 > –5 1 3 4 2. Tell whether each number is a whole number, an integer, or a rational number: –2.24, 6, , –16. 1 3 4 ANSWER –2.24 :rational number; 6: whole number, integer, rationalnumber ; :rational number; –16 : integer, rational number Lesson Quiz 1. Graph – 3 and –5 on a number line.Then tell which number is greater.

22. ANSWER Hydrogen, Nitrogen, Oxygen, Mercury Lesson Quiz 3. The table shows the boiling-point temperature of some elements. Order the elements from lowest boiling-point temperature to highest.