INTERESTING INTEGERS What You Will Learn Some definitions

INTERESTING INTEGERS!

What You Will Learn: • Some definitions related to integers. • Rules for adding and subtracting integers. • A method for proving that a rule is true. Are you ready? ?

Definition v. Integers – Integers are all the whole numbers and all of their opposites on the negative number line, including zero. 7 -7

Definition v. Positive number – a number greater than zero. 0 1 2 3 4 5 6

Definition v. Negative number – a number less than zero. -5 -4 -3 -2 -1 0 1 2 3 4 5

Definition v. Opposite Numbers – numbers that are the same distance from zero in the opposite direction -5 -4 -3 -2 -1 0 1 2 3 4 5

Definition v. Magnitude– is the distance of a number from 0. -5 -4 -3 -2 -1 0 1 2 3 4 5

Definition v. Absolute Value – The size of a number with or without the negative sign. The absolute value of 9 or of – 9 is 9.

Negative Numbers Are Used to Measure Temperature

Negative Numbers Are Used to Measure Under Sea Level

Negative Numbers Are Used to Show Debt Let’s say your parents bought a car but had to get a loan from the bank for $5, 000. When counting all their money they add in -$5. 000 to show they still owe the bank.

Hint v. If you don’t see a negative or positive sign in front of a number it is positive. +9

Modeling with Positive and Negative Integers Solve the following 3 word problems below. Please show all of your work AND draw a picture representing each situation. 1. Mt. Kilimanjaro, the highest elevation in Asia, is 19, 341 ft above sea level. The Dead Sea, the lowest elevation, is 1, 312 ft below sea level. What is the difference between these two elevations? 2. The hottest recorded day in San Diego was 111 degrees. The coldest recorded day in California was -45 degrees. What is the difference between these two temperatures? 3. Greek civilization started around 750 BC and ended around 600 AD. How long did this civilization last?

Adding/Subtracting Integers Song: (To the tune of Row Row your Boat) Same sign, add and keep, Different sign subtract! Take the sign of the highest number Then you’ll be exact!

One Way to Add and Subtract Integers Is With a Number Line • When the number is positive, count to the right. • When the number is negative, count to the left. - + -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

One Way to Add and Subtract Integers Is With a Number Line This sign tells us our direction. This number shows our starting point. +3 - 5 = -2 This number tells us how far we will move. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -

One Way to Add and Subtract Integers Is With a Number Line This sign tells us our direction. -2 + -4 = -6 This number shows our starting point. Make a U-Turn! This number tells us how far we will move. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -

One Way to Add and Subtract Integers Is With a Number Line This sign tells us our direction. This number shows our starting point. 6 +-7 = -1 Make a U-Turn! This number tells us how far we will move. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -

“Same Sign, add and Keep!” If the signs are the same, pretend the signs aren‘t there. Add the numbers and then keep the sign of the addends in front of your answer. 9 + 5 = 14 -9 + -5 = -14

Practice “Same Sign, Add and Keep”: 1. -3 - 4 = 4. -1 + -8 = 2. -6 + -2 = 5. 15 + 6 = 3. -5 – 9 = 6. -7 – 10 =

“Different sign subtract! Take the sign of the highest number, then you’ll be exact!” If the signs are different, subtract the numbers. Then take the sign of the highest number and add it to your answer. 6– 7= 7– 6=1 Answer = -1 -8 + 3 = 8– 3=5 Answer = -5

Practice “Different Sign Subtract!” -10 – (+19)= 17 – 21= -38 – 25= -40 – (+16)= 12 – 51= -11 – 18= -33 – (+14)=

Integer Subtraction Rule • When subtracting a negative number ALWAYS ADD! 4 - -2= 4 + 2 = 6 -4 - -2 = -4 + 2= -2

How do we know that “Subtracting a negative number is the same as adding a positive” is true? We can use the same method we use to check our answers when we subtract.

Suppose you subtract a – b and it equals c: a–b=c 5– 2=3 To check if your answer is correct, add b and c: a=b+c 5=2+3

Here are some examples: a–b=c 9– 5=4 a=b+c 9=5+4 a–b=c 20 – 3 = 17 a=b+c 20 = 3 + 17

If the method for checking subtraction works, it should also work for subtracting negative numbers.

If a – b = c, and…. 2 – (-5) is the same as 2 + (+5), which equals 7, Then let’s check with the negative numbers to see if it’s true…

a–b=c 2 – (-5) = 7 a=b+c 2 = -5 + 7 It works! a–b=c -11 – (-3) = -8 YES! a=b+c -11 = -3 + -8