Positive and Negative Numbers What is a positive

Positive and Negative Numbers

What is…

… a positive number? �A number that is greater than zero

… a negative number? �A number that is less than zero.

…an opposite number? � Numbers that are the same distance from zero in the opposite direction.

…an integer? � All whole numbers and their opposites on a number line 9 opposite -9

This is a number line negative positive

Using positive and negative numbers… Is like driving in traffic. You have to watch for the signs!

This is the positive sign!

This is the negative sign!

Hint: � If you don’t see a sign in front of a number, don’t panic! No sign means it is a positive number!

What do we already know? � Positive integers are on the right side of zero. 4 � Negative integers are on the left side of zero. -4 � This means that they are opposites. Negative Positive -3 + 3 = 0

Comparing Integers Use the number line to compare the following integers with >, <, or =. 1 < < -2 -3 -5 > -4 0 Hint: On a number line, the number to the left is always less than the number to the right.

Comparing Integers Use the number line to compare the following integers with >, <, or =. > -5 -5 > -3 0 0 > -1 Hint: On a number line, the number on the top is always greater than the number on the bottom.

Ordering Integers Use the number line to put the following integers in order from least to greatest. -4, 3, 0, and -5 -5, -4, 0, 3

Now, you’re probably saying, “That’s interesting and everything, BUT where are negative numbers in the real world? ?

Negative Numbers Are Used to Measure Temperature

Negative Numbers Are Used to Measure Under Sea Level 30 20 10 0 -10 -20 -30 -40 -50

Positive and negative numbers are used when keeping track of money. + Positive + $$ you earn - Negative $$ you spend

Write an integer to describe the real world situation: � Gain 3 pounds: � Withdraw � 5 $15: 3 or +3 -15 feet below sea level: � Move ahead 4 spaces: -5 4 or +4

Positive Numbers are Used to Show Earnings or Assets When you get paid (or win the lottery), you add that $$ to your account.

Negative Numbers are Used to Show What You Owe or Debt If your mom loaned you $10 for pizza, Mom, I. O. U. $10 The $10 you owe her is described by the integer -10.

You know how to plot an expression on the number line and find the sum. 5 + -2 = 3 Step 1: Plot the first integer on the number line. Step 2: Plot the second integer on the number line beginning where the last number left off. -2 5

You know how to plot an expression on the number line and find the difference. 5 + -2= 3 Step 1: Plot the first integer on the number line. Step 2: Plot the second integer on the number line beginning where the last number left off. -2 5

You know how to plot an expression on the number line and find each sum. -3 + -1 = Step 1: Plot the first integer on the number line. Step 2: Plot the second integer on the number line beginning where the last number left off. -4 -1 -3

Addition Rule 1 �Rule �(+) + (+) = (+) #1 – If �(-) + (-) = (-) the signs are the SAME, � EXAMPLE: ADD the 5+1=6 numbers and then KEEP the sign of the -2 + -5 = -7 addends.

Addition Rule 2 � Rule #2 – If the signs of the addends are DIFFERENT, SUBTRACT and keep the SIGN of the larger number � EXAMPLE: -5 + 3 = -2

Solve the Problems + -5 = -8 10 � 4 + 6 = �+3 + (+4) =7 �-6 + -7 = -13 14 � 5 + 9 = �-9 + -9 = -18 �-3

Adding Integers Using a Number Line * adding a positive integer * Start 6 t a here ex. (-6) + 5 = -1 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 + then count forward or right 5 spaces

Solve the Problems • 8+6= 14 • (-9) + 5 = -4 • (– 11) + 11 = 0 • (– 8) + 16 = 8

Integer Subtraction Rule Subtracting a negative number is the same as adding a positive. Change the signs and add. CHANGE KEEP ex. -1 – (-2) is the same as -1 + (+2) and -1 + 2 = 1