Adding and Subtracting

Introduction

This is a seventh grade webquest about addition and subtraction.

Introduction

In this webquest, you will become addition and subtraction experts! In class, we have been talking about addition and subtraction of integers.

Now we want to expand your minds and help you to figure out why these basic addition and subtraction facts work and I also want you to be able to use them throughout your lives. You will see that addition and subtraction are

very important and you will use it everyday outside of the classroom.

Task

Use the number line for adding and subtracting integers:

Add a positive integer by moving to the right on the number line
Add a negative integer by moving to the left on the number line
Subtract an integer by adding its opposite

Process

Numbers Can be Positive or Negative:


"−" is the negative sign.	"+" is the positive sign

No Sign Means Positive

If a number has no sign it usually means that it is a positive number.

Example: 5 is really +5

Adding Positive Numbers

Adding positive numbers is just simple addition.

Example: 2 + 3 = 5

is really saying

"Positive 2 plus Positive 3 equals Positive 5"

You could write it as (+2) + (+3) = (+5)

Subtracting Positive Numbers

Subtracting positive numbers is just simple subtraction.

Example: 6 − 3 = 3

is really saying

"Positive 6 minus Positive 3 equals Positive 3"

You could write it as (+6) − (+3) = (+3)

Balloons and Weights

This basket has balloons and weights tied to it:

The balloons pull up (positive)
And the weights drag down (negative)

Here is what adding and subtracting positive numbers looks like:

You can add balloons (you are adding positive value)

the basket gets pulled upwards (positive)

You can take away balloons (you are subtracting positive value)

the basket gets pulled downwards (negative)

Now let's see what adding and subtracting negative numbers looks like:

You can add weights (you are adding negative values)

the basket gets pulled downwards (negative)

And you can take away weights (you are subtracting negative values)

the basket gets pulled upwards (positive)

That last one was interesting ... subtracting a negative made the basket go up

Subtracting a Negative is the same as Adding

Example: What is 6 − (−3) ?

6−(−3) = 6 + 3 = 9

Example: What is 14 − (−4) ?

14−(−4) = 14 + 4 = 18

We also found that taking away balloons (subtracting positives) or adding weights (adding negatives) both made the basket go down.

And Positive and Negative Together ...

Subtracting a Positive
or
Adding a Negative
is
Subtraction

Example: What is 6 − (+3) ?

6−(+3) = 6 − 3 = 3

Example: What is 5 + (−7) ?

5+(−7) = 5 − 7 = −2

The Rules:

It can all be put into two rules:

	Rule		Example
	Two like signs become a positive sign	+(+)	3+(+2) = 3 + 2 = 5
−(−)	6−(−3) = 6 + 3 = 9

	Two unlike signs become a negative sign	+(−)	7+(−2) = 7 − 2 = 5
−(+)	8−(+2) = 8 − 2 = 6

They are "like signs" when they are like each other (in other words: the same).

Now Play With It!

Try playing Casey Runner, you need to know the rules of positive and negative to succeed!

Another Example You Might Like

Ally's Points

Ally can be naughty or nice. So Ally's parents have said

"If you are nice we will add 3 points (+3).
If you are naughty, we take away 3 points (−3).
When you reach 30 Points you get a toy."

Ally starts the day with 9 Points:

Ally's Mom discovers spilt milk:	9−3 = 6

Then Dad confesses he spilt the milk and writes "undo". Mom calculates:	6−(−3) = 6+3 = 9

So if you subtract a negative, you gain points
(i.e. the same as adding points).

So Subtracting a Negative is the same as Adding

A few days later. Ally has 12 points.

Mom adds 3 points because Ally's room is clean.	12+3 = 15

Dad says "I cleaned that room" and writes "undo" on the chart. Mom calculates:	15 − (+3) = 12

Dad sees Ally brushing the dog. Writes "+3" on the chart. Mom calculates:	12 + (+3) = 15

Ally throws a stone against the window. Dad writes "−3" on the chart. Mom calculates:	15 + (−3) = 12

See: both "15 − (+3)" and "15 + (−3)" result in 12.

Evaluation

Add according to the rules for adding terms.

a)	6 + 2 =	b) −6 + (−2) =

c)	−6 − 2 =	d) −4 − 1 =

e)	−6 + 2 =	f) 6 + (−2) =

g)	2 + (−6) =	h) −2 + 6 =

Add these terms.

a)	8 + (−3) = 5	b)	−8 + 3 = −5	c)	−8 + (−3) = −11

d)	−8 − 3 = −11	e)	2 + (− 5) = −3	f)	−2 + (− 5) = −7

g)	−2 − 5 = −7	h)	8 + (− 11) = −3	i)	−7 + (− 6) = −13

j)	9 + (− 2) = 7	k)	−9 − 2 = −11	l)	−9 + (− 2) = −11

m)	6 + (− 10) = −4	n)	−6 − 10 = −16	o)	−6 + 10 = 4

p)	−9 + 9 = 0	q)	−9 − 9 = −18	r)	9 + 9 = 18

Rewrite without parentheses and calculate.

a)	7 − (− 4) = 7 + 4 =	b)	1 − (− 9) = 1 + 9 =

c)	8 − (− 5) = 8 + 5 =	d)	−8 − (− 5) = −8 + 5 =

e)	−5 − (− 7) = −5 + 7 =	f)	2 − (− 10) = 2 + 10 =

g)	−9 − (− 8) = −9 + 8 =	h)	−20 − (− 1) = −20 + 1 =

i)	4 − (−4) = 4 + 4 =	j)	−4 − (−4) = −4 + 4 =