7th Grade Math Number System

Day 1 Number System, Opposites & Absolute Value

Number System Real Rational 1/3 Integer 5/2 Whole 0.22 Irrational Natural 1,2,3... Whole Integer ...-4, -3, -2, -1 Rational 1/5 5/2 8.3 -2.756 -3/4 1/3 -1/11 Real Irrational

X Define Integer Definition of Integer: The set of whole numbers, their opposites and zero. X Examples of Integer: {...-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7...}

X Define Rational Definition of Rational: A number that can be written as a simple fraction (Set of integers and decimals that repeat or terminate) X Examples of rational numbers: 9 , ½ 0, -5, 8, 0.44, -0.23,

X Define Irrational Definition of Irrational: A real number that cannot be written as a simple fraction X Examples of irrational numbers:

Rational and Irrational Perfect Squares: Rational Imperfect Squares: Irrational Terminating Decimals (3.89) and Repeating Decimals ( ) are rational.

Rational & Irrational Numbers is rational because the radicand (number under the radical) is a perfect square If a radicand is not a perfect square, the root is said to be irrational. Ex:

Perfect Square – a number multiplied by itself. Ex: 82, 102, 132 Square Root – also called radical. a number that is multiplied by itself to form a product called a square. Imperfect Square Root – a radical whose square root is not a whole number. Ex:

Changing a Repeating Decimal to a Fraction to a fraction n = Multiply both sides by 100. 100n = (100) 100n = 45. Subtract n from both sides. -n - _________________ 99n = 45 Divide both sides by 99. __________________ n = 45/99 n = 5/11

Natural Numbers: Whole Numbers: Additive Inverse:

Classify each number as specific as possible: Integer, Rational or Irrational ¾ 3.2 -6 -21 1 5 ½ π 9 5 3¾ -65 -6.32 2.34437 x 103 integer rational irrational

Rational Numbers on a Number Line Negative Numbers Positive Numbers Zero -5 -4 -3 -2 -1 1 2 3 4 5 Numbers to the left of zero are less than zero Zero is neither positive or negative Numbers to the right of zero are greater than zero

Which of the following are examples of integers? 2 Which of the following are examples of integers? A -5 B C -3.2 D 12 1 2 E Answer: A, B, D

Which of the following are examples of rational numbers? 3 Which of the following are examples of rational numbers? 1 3 A B -3 C 10 D 0.25 E 75% Answer: A, B, C, D, E

Numbers In Our World

Numbers can represent everyday situations You might hear "And the quarterback is sacked for a loss of 5 yards." This can be represented as an integer: -5 Or, "The total snow fall this year has been 6 inches more than normal." This can be represented as an integer: +6 or 6

Write a number to represent each situation: Spending $6.75 Gain of 11 pounds Depositing $700 10 degrees below zero 8 strokes under par (par = 0) feet above sea level

Which of the following numbers best represents the following scenario: 4 Which of the following numbers best represents the following scenario: The effect on your wallet when you spend $10.25. A -10.25 B 10.25 C D +/- 10.25 Answer: A

Earning $50 shoveling snow. Which of the following integers best represents the following scenario: Earning $50 shoveling snow. A -50 B 50 C D +/- 50 Answer: B

Which of the following numbers best represents the following scenario: 6 Which of the following numbers best represents the following scenario: You dive feet to explore a sunken ship. A B C Answer: A D

Opposites The numbers -4 and 4 are shown on the number line. 1 2 3 4 5 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 Both numbers are 4 units from 0, but 4 is to the right of 0 and -4 is to the left of zero. The numbers -4 and 4 are opposites. Opposites are two numbers which are the same distance from zero.

7 What is the opposite of -7? Answer: 7

8 What is the opposite of 18.2? Answer: -18.2

What happens when you add two opposites? Try it and see... Click to Reveal A number and its opposite have a sum of zero. Numbers and their opposites are called additive inverses.

X To Review An integer is a whole number, zero or its opposite. A rational number is a number that can be written as a simple fraction. An irrational number is a number that cannot be written as a simple fraction. Number lines have negative numbers to the left of zero and then positive numbers to the right. Zero is neither positive nor negative. Numbers can represent real life situations.

Absolute Value of Numbers The absolute value is the distance a number is from zero on the number line, regardless of direction. Distance and absolute value are always non-negative (positive or zero). 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 What is the distance from 0 to 5? 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 What is the distance from 0 to -5?

Absolute value is symbolized by two vertical bars |4| This is read, "the absolute value of 4" 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 What is the | 4 | ?

Use the number line to find absolute value. Move to check |9.6| = 9.6 Move to check |-9| = 9 Move to check |-4| = 4 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10

14 Find Answer: 56

15 Find |-8| Answer: 8

Treat Absolute Value Symbols as parenthesis. Examples: a) b) c) Answer: 7.3

17 What is ? Answer: 22 3/5

18 Find Answer: 3.55555…

Which numbers have 15 as their absolute value? 20 Which numbers have 15 as their absolute value? A -30 B -15 C D 15 E 30 Answer: B, D

Which numbers have 100 as their absolute value? 21 Which numbers have 100 as their absolute value? A -100 B -50 C D 50 E 100 Answer: A, E