COMBINING INTEGERS:Adding & Subtracting Negative & Positive

Whole Numbers

by S. Bradley

Definition

•Positive number – a number greater than zero.

0 1 2 3 4 5 6

Definition

•Negative number – a number less than zero.

0-1-2-3-4-5-6

Definition• Opposite Numbers – numbers

that are the same distance from zero in the opposite direction on a number line.

0 1 2 3 4 5 6-1-2-3-4-5-6

Definition

•Integers – Integers are all the whole numbers and their opposites.

7 opposite -7

Negative Numbers Are Used to Measure Temperature

Negative Numbers Are Used to Measure Below Sea Level

0102030

-10-20-30-40-50

Negative Numbers Are Used to Show Debt

Let’s say your parents bought a car buthad 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.

Positive & Negative Numbers

Working with positive and negative numbers is like driving in traffic. You have to watch the traffic signs and follow the driving rules.

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

9 = 9+

Integer Addition Rules•Rule #1 – If the signs are the

same, pretend the signs aren’t there. Add the numbers and then put the sign of the addends in front of your answer.

9 + 5 = 14(-9) + (-5) = -14

Solve the Problems

•(-3) + (-5) = a•4 + 7 = b•(-6) + (-7) = c •5 + 9 = d•(-9) + (-9) = f

Solutions:

• a = -8• b = 11• c = -13• d = 14 • f = -18

Monday’s Problems:

•13 + 3 = a

•(-12) + (-5) = b

•(-2) + (-3) = c

Solutions to Monday’s Problems:

•16

•-17

•-5

Integer Addition Rules•Rule #2 – If the signs are

different pretend the signs aren’t there. Subtract the smaller from the larger one and put the sign of the larger one in front of your answer.

-9 + 5 =9 - 5 = 4Larger number

Answer = - 4

Solve These Problems

•3 + (-5) =•7 + (-4) =•3 + (-4) =•(-6) + 7 = •-9 + 5 =•(-9) + 9 =

-25 – 3 = 2

0

-41-1

3

9 – 9 = 0

9 – 5 = 47 – 6 = 14 – 3 = 1

7 – 4 = 3

How do I remember the addition rules? Simple! Let’s apply the rules to a song we all know – “Row, Row, Row Your Boat”

•Same sign – add & keep!•Different signs – subtract,

take the sign of the highest number, your answer will be exact!

Practice:

•(-4) + 5 = x

•(-13) + 3 = y

•-18 + 5 = z

Solutions to Practice:

•1

•-10

•-13

Tuesday’s Problems:

•-5 + (-2) = k

•10 + (-4) = j

•-23 + 7 = n

Solutions to Tuesday’s Problems:

•-7

•6

•-16

One way to add integers is using a number line…

0 1 2 3 4 5 6-1-2-3-4-5-6

When the number is positive, countto the right.

When the number is negative, countto the left.

+-

Here’s an example:

0 1 2 3 4 5 6-1-2-3-4-5-6+

-

3 + (-5) = -2

Using Integer Addition Rules or a Number Line – You choose!

•-150 + (-5) = g

•43 + (-20) = f

•24 + (-30) = v

Solutions to Practice:

•-155

•23

•-6

Wednesday’s Problem:

• The Georgia Bulldogs were playing the Auburn Tigers in a playoff game. Auburn’s offense received a penalty which resulted in a loss of 10 yards. If they were at the 25 yard line, what yard line would they be moved to after the penalty? (Write an equation, then solve.)

Wednesday’s Solution:

•-10 + 25 = h

•h = 15 yard line

Subtracting Integers

• Use the additive inverse. This simply means to change the problem to addition & follow the addition rules. How? Leave the first number “as is”; change subtraction to addition; lastly, change the SECOND number to its opposite…

Example:

• -18 – 5 = n*-18 remains “as is”*subtraction becomes +*change +5 to -5-18 + (-5) = n *Now, simply

follow the addition rules…n = -23

Example Problems for Subtraction:• -17 – 11 = d

-17 + (-11) = -28

• 25 – 32 = u25 + (-32) = -7

• 13 – (-5) = r13 + 5 = 18

You try it!

• 10 – (-6) = h

• -19 – 7 = w

• 9 – 11 = k

Solutions to Practice

• 10 – (-6) = h10 + 6 = 16

• -19 – 7 = w-19 + (-7) = -26

• 9 – 11 = k9 + (-11) = -2

Thursday’s Problems:

• 16 – (-5) = t

• -3 – 8 = p

• -14 – (-10) = q

Thursday’s Solutions:

• 16 – (-5) = t16 + 5 = 21

• -3 – 8 = p-3 + (-8) = -11

• -14 – (-10) = q-14 + 10 = -4

Practice for Friday:(Pay attention to the operation given…)

•-4 + 5 = a•-17 – 8 = b•-13 – (-7) = c•-12 + (-8) = d

Solutions for Friday’s Practice:

•a = 1•b = -25•c = -6•d = -20

Monday’s Problems:

• -11 + (-6) = m

• -16 – (-57) = c

• 8 + (-5) = h

Monday’s Solutions:

• m = -17

• c = 41

• h = 3

Tuesday’s Problem:

• A submarine is 33 feet below sea level. It rises 15 feet. What integer best represents the submarine’s location after its rise? (Write an equation, then solve.)

Tuesday’s Solution:

•-33 + 15 = ff = -18 feet

Wednesday’s Problem:

• You went to the bank and borrowed $200. One week later, you went back to the same bank and borrowed $250 more. How much are you in debt? (Write an equation, then solve.)

Wednesday’s Solution:

•-200 – 250 = d-200 + (-250) = d

d = -$450

Thursday’s Problems:

• -3 + (-19) = k

• 15 – (-7) = j

• 17 + (-10) = a

• -8 – 12 = f

Thursday’s Solutions:

• k = -22

• j = 22

• a = 7

• f = -20

GOOD LUCK ON FRIDAY’S ASSESSMENT!