Use Integers and Rational Numbers Warm Up Lesson Presentation Lesson Quiz

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

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

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

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

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

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

Example 2 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 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.

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

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 Yes No –2 –1.2 3 Rational number? Integer? Whole number? Number ANSWER –2, –1.2, 0, 3 (Ordered the numbers from least to greatest).

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

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

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

Example 4 For the given value of a, find –a. a. If a = – 2.5, then – a = –(– 2.5) = 2.5. b. If a = , 3 4 3 4 then – a = – .

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

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

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.

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 Hypothesis: a number is a rational number ANSWER Conclusion: the number is positive – false The number –1 is a counterexample, because –1 is a rational number but not positive.

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

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

Lesson Quiz 3. The table shows the boiling-point temperature of some elements. Order the elements from lowest boiling-point temperature to highest. Element Temperature Hydrogen – 2593°C Mercury 357°C Nitrogen – 196°C Oxygen – 183°C ANSWER Hydrogen, Nitrogen, Oxygen, Mercury