Adding and subtracting rational numbers

Adding and subtracting rational numbers

by Felicia Taylor

​Adding two positive numbers...

​When you add two positive numbers, it is just like you did in elementary school.

​

​5 + 6 = 11

​

​2/5 + 1/5 = 3/5

​

​

​12.34 + 56.78 = 69.12

​Subtracting a smaller number from a bigger number, is just like you did in elementary also...

​

​

​

​9 - 3 = 6

​

​4/5 - 1/5 = 3/5

​

​

​56.78 - 12.34 = 44.44

​So what happens when I try to subtract a number bigger than the first number....

​

​

​

3 - 6 = ???

​

​First step is to always rewrite the subtraction equation as addition.

​

​3 + -6 = ????

​

​Now we can see that we have two numbers with different signs, now what?

​When adding two numbers with different signs, always SUBTRACT the two numbers and keep the sign of the BIGGEST number.

​

​3 + -6 = ???

​

​We know that 6 minus 3 is 3.

​

​We know that 6 is bigger than 3. Since the 6 is negative, the answer will be negative!!!!

​

​3 + -6 = -3

Multiple Choice

2 - 7 =

What is the first step in finding the answer?

• Rewrite the subtraction equation as an addition equation.

  2 + -7

• Just solve and get the answer.

• Do nothing.

• Change the order of the numbers.

  7 - 2

Multiple Select

How do you rewrite the equation

2 - 7  =

as an addition equation?

• 2 + -7 = 

• 2 + (-7) =

• -7 + 2 =

  we haven't learned this yet but it is TRUE.

• 7 - 2

Multiple Choice

What is the answer to

2 - 7 =

• 2 + -7 = -5

• 2 + -7 = 5

• 2 + -7 = 9

• 2 + -7 = -9

​What do you do when you need to add a positive number to a negative number?

​

​

​

​-1 + 4

​

​Step 1: Since the numbers are opposite/ different signs (the 1 is negative and the 4 is positive), you SUBTRACT!!!!

​Step 2: 4 - 1 = 3

​Step 3: The answer will have the same sign as the BIGGEST number.

​Step 4: Since the 4 is BIGGEST and POSITIVE, the answer is positive.

​What if the negative number is larger when adding a positive and negative number?

​

​

​

​-9 + 7

​

​Step 1: Since the numbers are opposite/ different signs (the 9 is negative and the 7 is positive), you SUBTRACT.

​Step 2: 9 - 7 = 2

​Step 3: The answer will have the same sign as the BIGGEST number.

​Step 4: Since the 9 is the BIGGEST and NEGATIVE, the answer is negative.

​Step 5: -9 + 7 = -2

Multiple Choice

-2 + 4 = ??

• 6

• -2

• -6

• 2

Multiple Choice

-8 + 5 =

• 13

• -3

• -13

• 3

​What happens when I need to subtract a negative number from a negative number?

​

​

​-4 - 7 = ???

​

​Step 1: Rewrite the subtraction equation as an addition equation.

​Step 2: -4 + -7 =

​Step 3: Remember that when the numbers are the same/ like signs (the 4 is negative and the 7 is negative), you ADD the numbers.

​Step 4: -4 + -7 = 11

​Step 5: Keep the signs of numbers that are the same/ like when added together. -4 + =7 = -11

Multiple Choice

First step in doing this problem

-5 - 8 = ???

• Do nothing.  Just subtract.

• Rewrite the subtraction as addition

  -5 + -8

• Rewrite the subtraction as addition

  -5 + 8

• Rewrite the subtraction as addition

  5 + 8

Multiple Choice

What is the answer is

-5 - 8 = -5 + -8 = ????

• 13

• 3

• -3

• -13

​So remember...

​1 + 2 = 3

​1 - 2 = -1

​1 + -2 = -1

​-2 + 1 = -1

​-1 + 2 = 1

​-1 - 2 = -3

​1 - -2 = 3

​-1 - -2 = 1

Poll

So how do you feel about adding and subtracting positive and negative integers?

• I still have no idea what to do.

• I kind of understand.

• I understand everything except subtracting negatives.

• I got this!

Multiple Choice

5 + 4 =

• 1

• -1

• 9

• -9

Multiple Choice

9 - 1

• 10

• -10

• 8

• -8

Multiple Choice

7 + -1 =

• 8

• -8

• 6

• -6

Multiple Choice

-8 + 4 = ???

• -4

• 4

• 12

• -12

Multiple Choice

-6 - 7 = ???

• 1

• -1

• -13

• 13

Multiple Choice

-5 + -9 = ???

• 14

• -14

• 4

• -4

Multiple Choice

8 - -7 = ??

• 1

• -1

• -15

• 15

Multiple Choice

-3 - -6 = ???

• 3

• -3

• 9

• -9

Poll

Now how do you feel about adding and subtracting positive and negative numbers?

• ???

  I still am clueless

• I understand a little bit.

• I think that I can do it.

• I already understand all of this.