Reading Assignment: Integers Add & Subtract*

negative

A plus sign or a positive sign has no effect on the

number.  The number stays positive.  A negative sign

or a subtraction sign will reverse a number to

negative.  A negative sign and a subtraction sign on

the same number will reverse a number to negative

and then back to positive.  This is because the first 

sign (the subtraction sign) reverses it to negative and

 the second sign (the negative sign) reverses the

reverse.  This makes the number a positive.  

 

 

Therefore - -7 is ...

positive

5

On the last question - -7 is acting positive because

 of a double reverse (a subtraction sign and a negative

 sign on the same number). 

 

Signs always belong to the next number.  For example

 in the problem 5 - 7, the subtraction sign belongs

to the 7.  Therefore the 7 will act like a negative.

  The 5 has no sign and is understood to be positive.  

 

 

Because of this in the problem 5 + -7, both the 

plus sign and the negative sign belong to...

 

7

a negative number

On the last problem 5 + -7, both signs belonged

to the 7

 

 

 

 

 

 

 Because the + sign has no effect and the negative

reverses the number, 7 will act like ...

a positive number

8

Because the + sign has no effect and the negative

reverses the number, 7 will act like a negative. 

 

When the numbers are acting the same (both negative

or both positive) we add and keep the sign (same

signs; sum them up and keep the sign). 

 

 

 

 

 Therefore, in the problem -3 + -5 the answer is...

 

-8

-2

2

10

In the problem -3 + -5 the answer is -8 because both 

numbers were acting negative. 

 

When the signs are the same, add and keep the sign.  

 

 

 

 

 

  In the problem -3 -7 the answer is...

 

4

-4

-10

9

In the problem -3 - 7 the answer is -10 because both

numbers are acting negative.  -3 is clearly negative

and the subtraction sign belonging to 7 make it act

like a negative. 

 

 

 

 

 

 

 

 

In the problem 3 - -6 the answer is...

 

3

-9

-3

7

In the problem 3 - -6 the answer is 9.  Both the

subtraction sign and the negative sign belong to the

six.  Both signs cause a double reverse making the

6 act like a positive.  Therefore, both numbers are

acting positive, add and keep the sign. 

 

 

 

 

In the problem 3 + 4 the answer is ...

 

-7

-1

1

-1

 In the problem 3 + 4 the answer is 7.  Come on. What

else could it be?  Both numbers as positive, add and

keep the sign.

 

Now for the fun! Absolute value is how far from zero. 

It ignores the signs.  When numbers are acting with

different signs, the largest absolute value (the 

greatest distance  from zero ignoring the direction)

rules the sign. 

 

Which has the largest absolute value?

 

6

-7

1

10

Which has the largest absolute value... -1, 6, -7, or 1?

 -7 does because it has the greatest distance from

zero.  Therefore in a problem with different signs,

it would rule. 

 

 

 

Let's try again.  How about the largest absolute value

for these...

 

-15

-10

18

the same; therefore, add and keep the sign.

different; therefore, subtract and take the sign of the

larger absolute value.

The largest absolute value for 10, -15, -10, and 18

has to be 18 because it has the greatest distance 

from zero. 

  

Now let's see if the signs are acting the same or

different. 

 

In the problem -3 + 7 the signs are ...

 

different; therefore, subtract and take the sign of the

larger absolute value.

the same; therefore, add and keep the sign.

 In the problem -3 + 7 the signs are different;

therefore, subtract and take the sign of the larger

absolute value.  The answer would be 4

 

 

 

In the problem -6 - -3, the signs are

 

different; therefore, subtract and take the sign of the

larger absolute value.

the same; therefore, add and keep the sign.

 In the problem -6 - -3, the signs are different

(because the subtraction sign and the negative

sign on three create a double reverse and make it

act positive); therefore, subtract and take the sign

of the larger absolute value.  The answer is -3

 

 

In the problem -6 -7, the signs are...

 

the same; therefore, add and keep the sign.

different; therefore, subtract and take the sign of the

larger absolute value.

 In the problem -6 -7, the signs are the same (the

subtraction sign on 7 makes it act like a negative);

therefore, add and keep the sign. 

The answer is -13

 

 

 

In the problem 5 - -3, the signs are...

 

the same; therefore, add and keep the sign.

differently; therefore, subtract and take the sign of

 the larger absolute value.

In the problem 5 - -3, the signs are the same (double

 reverses on 3 make it act positive); therefore, add

 and keep the sign.  The answer is 8

 

In the problem -5 - -3, the numbers are both acting...

 

differently; therefore, subtract and take the sign of

the larger absolute value.

the same; therefore, add and keep the sign.

In the problem -5 - -3, the numbers are both acting

differently (the double reverse on 3 makes it act

positively); therefore, subtract and take the sign of

the larger absolute value.  The answer is -2

 

And now one last problem of this type before we

move on.

 

In the problem -5 + -5, the signs are...

 

-12

In the problem -5 + -5, the signs are the same.  Add

and keep the sign.  The answer is -10

 

 

 

 

-4 - 8 =

 

Now ask yourself are the numbers acting the same

(add) or differently (subtract). 

 

12

-4

4

-12

On the previous problem:

 -4 - 8 (same signs; add and keep the sign) = -12

   

 

 

 

 

 

-4 + 8 =

 

 

 

12

-4

4

-12

On the previous problem:

-4 + 8 =  (different signs find a difference; largest

absolute value rules) 4.

 

 

 

 

 

4 - 8 =

 

12

-4

4

-17

On the previous problem:

4 - 8 =  (different signs find a difference - larger

absolute value rules the sign)  -4

   

 

 

  

 

10 - -7 =

17

-3

3

13

On the previous problem:

10 - -7 = (double reverse on 7 make it act positive -

same signs sum them up) 17.

 

 

 

 

 

 

 

5 - 8 =

-13

-3

3

-13

On the previous problem:

5 - 8 = (different signs - find a difference - larger

absolute value rules) -3.

 

 

 

 

 

 

-5 - 8 = 

13

-3

3

-13

On the previous problem: 

-5 - 8 =  (Same signs, sum them up and keep the

sign) -13.

 

 

 

 

 

 

 

-5 + 8 =

13

-3

3

-13

On the previous problem:

-5 + 8 = (different signs; find a difference -

larger absolute value rules the sign)  3

 

  

 

 

 

 

5 - 8 =

13

-3

3

-13

On the previous problem:

5 - 8 = (different signs; find a difference - larger

absolute value rules)  -3

 

 

 

 

 

 

 

5 + 8 =

13

-3

3

-13

On the previous problem: 

5 + 8 (same signs; sum them up - keep the sign.  13

 

 

 

 

    

 

10 - - 3 =

13

-7

7

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