algebra 1. lesson 1-3 warm-up algebra 1 lesson 1-3 warm-up

ALGEBRA 1

ALGEBRA 1

Lesson 1-3 Warm-Up

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)

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 NumbersLESSON 1-3

Additional Examples

ALGEBRA 1


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.

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


Additional Examples

ALGEBRA 1


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)

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.

23


Additional Examples

ALGEBRA 1

Write – , – , and – , in order from least to greatest.

–0.75 < –0.625 < –0.583 Order the decimals from least to greatest.

7 12

34

58

– = –0.7534

– = –0.583 712

– = –0.62558

From least to greatest, the fractions are – , – , and – .34

58

712


Additional Examples

Write each fraction as a decimal by dividing the numerator by the denominator.

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


Additional Examples

ALGEBRA 1

Name the set(s) of numbers to which each given number belongs.

1. –2.7 2. 11 3. 16

Use <, =, or > to compare.

4. 5.

6. Find |– |

34

58

rational numbers irrational numbers natural numbers, whole numbersintegers, rational numbers

– –

7 12

> <

7 12

34

58


Lesson Quiz

algebra 1. lesson 1-3 warm-up algebra 1 lesson 1-3 warm-up

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