ALGEBRA 1 2 1 Integers Rational Numbers Vocabulary

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

Vocabulary 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

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

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

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

GUIDED PRACTICE 3. Graph -6 and -1 on a number line. Then tell which number is greater. – 1 – 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.

EXAMPLE 2 Classify numbers Tell whether each of the following numbers is a whole number, an integer, or a rational number: 5, 0. 6, -2 and -24. Number 5 0. 6 2 – 2 3 – 24 Whole Integer? Rational number? Yes Yes No No Yes

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

GUIDED PRACTICE 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. 3 4. 5, – 2. 1, 0. 5 4 Number Whole Integer? Rational number? 4. 5 No No Yes – 3 No No Yes – 2. 1 No No Yes 0. 5 No No Yes 4 3 – 2. 1, – 4 , 0. 5 , – 2. 1. (Order the numbers from least to greatest).

GUIDED PRACTICE 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 Number 3. 6 Whole Integer? Rational number? No No Yes – 1. 5 No No Yes – 0. 31 No No Yes – 2. 8, – 1. 5, – 0. 31, 3. 6 (Ordered the numbers from least to greatest).

GUIDED PRACTICE 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. Number 1/6 1. 75 -2/3 0 Whole Number? No No No Yes Integer? No No No Yes Rational Number? Yes Yes 2 1 – 3 , 0 , 6 , 1. 75. (Order the numbers from least to greatest).

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. Star Color index Rigel – 0. 03 Arneb 0. 21 Denebola 0. 09 Shaula – 0. 22 SOLUTION Begin by graphing the numbers on a number line.

EXAMPLE 3 Order rational numbers 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.

EXAMPLE 4 Find opposites of numbers a. If a = – 2. 5, then – a = 2. 5. b. 3 If a = 4 , then – a = – 3. 4

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

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