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ALGEBRA 1

ALGEBRA 1. 2.1 Integers & Rational Numbers. Vocabulary. Whole numbers : Counting numbers starting with 0 Integers : positive and negative counting numbers and 0 Rational numbers : a number that can be written as a/b where a and b are both integers.

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ALGEBRA 1

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  1. ALGEBRA 1 2.1 Integers & Rational Numbers

  2. Vocabulary Whole numbers: Counting numbers starting with 0 Integers: positive and negative counting numbers and 0 Rational numbers: a number that can be written as a/b where a and b are both integers

  3. Opposites: two numbers that are the same distance from 0 on a number line but on opposite sides Absolute value: the distance between a number and 0 on the number line Vocabulary

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

  5. GUIDED PRACTICE 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. 1. Graph4 and 0 on a number line. Then tell which number is greater.

  6. GUIDED PRACTICE –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–4.So, 2 > –5. 2. Graph2 and -5 on a number line. Then tell which number is greater.

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

  8. EXAMPLE 2 Classify numbers Number Whole number? Integer? Rational number? 2 5 Yes Yes Yes 3 0.6 No No Yes No No Yes –2 –24 No Yes Yes Tell whether each of the following numbers is a whole number, an integer, or a rational number: 5, 0.6, -2 and -24.

  9. GUIDED PRACTICE 1. Tell whether each of the following numbers is a whole number, an integer, or a rational number. Then order the numbers from least list to greatest. 3, –1.2, –2,0 –2, –1.2, 0, 3 (Ordered the numbers from least to greatest).

  10. GUIDED PRACTICE 4.5, – , – 2.1, 0.5 – 2.1, – ,0.5 ,– 2.1.(Order the numbers from least to greatest). Number Whole number? Integer? Rational number? 3 3 4 4 3 4 4.5 No No Yes No No Yes – –2 .1 No No Yes 0.5 No No Yes 2. Tell whether each of the following numbers is a whole number, an integer, or a rational number. Then order the numbers from least list to greatest.

  11. GUIDED PRACTICE Number Whole number? Integer? Rational number? 3.6 No No Yes –1.5 No No Yes –0.31 No No Yes –2.8 No No Yes 3. Tell whether each of the following numbers is a whole number, an integer, or a rational number. Then order the numbers from least list to greatest. 3.6, –1.5,–0.31, – 2.8 –2.8, –1.5, – 0.31, 3.6 (Ordered the numbers from least to greatest).

  12. GUIDED PRACTICE 2 1 3 6 4. Tell whether each of the following numbers is a whole number, an integer, or a rational number. Then order the numbers from least list to greatest. – , 0 , , 1.75. (Order the numbers from leastto greatest).

  13. EXAMPLE 3 Order rational numbers 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.

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

  15. EXAMPLE 4 Find opposites of numbers b.Ifa = ,then – a = – . 3 3 4 4 a. Ifa=– 2.5, then –a=2.5.

  16. EXAMPLE 5 Find absolute values of numbers a.Ifa = – , then|a|= || = 2 2 2 3 3 -3 b.Ifa= 3.2,then|a|=|3.2|= 3.2.

  17. GUIDED PRACTICE For the given value of a, find –a and |a|. 1. a = 5.3 If a = 5.3, then –a = – 5.3 |a| = |5.3| = 5.3 2. a = -7 If a = -7, then –a = 7|a| = |-7| = 7 3. a = If a = -4/9, then –a = 4/9|a| = |-4/9| = 4/9

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