1. ALGEBRA 1

2. Lesson 1-3 Warm-Up

3. ALGEBRA 1 Lesson 1-3 Warm-Up

4. ALGEBRA 1 “Exploring Real Numbers” (1-3) What are “natural numbers”, “whole numbers”, and “integers”? What are “rational” and “irrational” numbers? natural numbers: the positive numbers from 1 to infinity (1, 2,3,…….) whole numbers: the positive numbers from 0 to infinity (0,1,2,3…….) Integers: all of the positive and negative numbers (…-2, -1, 0, 1, 2,…) rational numbers: any number that can be expressed as a fraction or whose decimal form either terminates or repeats (examples: 6, or 6.0, terminates, or ends, and 8.242424… repeats) irrational numbers: any number that cannot be expressed as a fraction or whose decimal form doesn’t terminates or repeats (examples: 0.101001000…, , and  3 do not terminate or repeat)

5. ALGEBRA 1 Name the set(s) of numbers to which each number belongs. a. –13 b. 3.28 integers, rational numbers rational numbers d. 42 natural numbers, whole numbers, integers, rational numbers rational numbers 13 25 c. Exploring Real Numbers LESSON 1-3 Additional Examples

6. ALGEBRA 1 “Exploring Real Numbers” (1-3) What is a “counterexample”? counterexample - an example that proves a statement false Example: A friend says all integers are whole numbers. You prove that this is false by stating -3 is an integer but not a whole number. You only need one counterexample to prove a statement false.

7. ALGEBRA 1 Which set of numbers is most reasonable for each situation? a. outdoor temperatures b. the number of beans in a bag integers whole numbers Exploring Real Numbers LESSON 1-3 Additional Examples

8. ALGEBRA 1 “Exploring Real Numbers” (1-3) What is a “inequality? How can you compare the order of numbers? What are “opposites”? What is “absolute value”? Inequality: a mathematical sentence that compares the values of two expressions using inequality symbols such as , , ≥, or ≤. (as opposed to an equality which uses the = sign  is read as “greater than”  is read as “less than” ≥ is read as “greater than or equal to” ≤.is read as “less than or equal to” To compare numbers, put them on a number line. Numbers on the right are always bigger than numbers on the left. You can also write them all in decimal form and compare the place values from largest to smallest. Example: Opposites: Two numbers that are the same distance from zero on a number line or in “opposite” directions from zero Example: absolute value: a numbers distance from zero shown by surrounding the number with these absolute value brackets | | Example: |-3| and |3| both have an absolute value of 3 (both are opposites that are 3 away from 0); |-24| and |24| both have an absolute value of 24 (both are 24 away from 0)

9. ALGEBRA 1 Determine whether the statement is true or false. If it is false, give a counterexample. All negative numbers are integers. False. A negative number can be a fraction, such as. A fraction is not an integer. 2323 Exploring Real Numbers LESSON 1-3 Additional Examples

10. ALGEBRA 1 Write –, –, and –, in order from least to greatest. –0.75 < –0.625 < –0.583Order the decimals from least to greatest. 7 12 3434 5858 – = –0.75 3434 – = –0.583 7 12 – = –0.625 5858 From least to greatest, the fractions are –, –, and –. 3434 5858 7 12 Exploring Real Numbers LESSON 1-3 Additional Examples Write each fraction as a decimal by dividing the numerator by the denominator.

11. ALGEBRA 1 Find each absolute value. a. |–2.5| b. |7| –2.5 is 2.5 units from 0 on a number line. |–2.5| =2.5 7 is 7 units from 0 on a number line. |7| = 7 Exploring Real Numbers LESSON 1-3 Additional Examples

12. ALGEBRA 1 Name the set(s) of numbers to which each given number belongs. 1. –2.72. 113. 16 Use to compare. 4.5. 6. Find |– | 3434 5858 rational numbersirrational numbersnatural numbers, whole numbers integers, rational numbers –– 7 12 > < 7 12 3434 5858 Exploring Real Numbers LESSON 1-3 Lesson Quiz