Alec's Great Big Book of Integers

Chapter One - Grade 7 Integer Review

-3-(-7)= 4

I used seven zero pairs because I did not have negative 7. I then took away the -7 and I found 3 more zero pairs. It left me with positive 4

-3-7= -10

I drew 3 negative chips then I drew 7 more.

3-7= -4

I drew -7 then drew +3. I found 3 zero pairs to find that I was left with -4.

3+7= 10

I drew 3 then i drew seven. My final answer was 10.

-3+7= 4

I drew seven then -3. I found 3 zero pairs which led me to an answer of 4.

Chapter 2 - Multiplying Integers

(+2)x(+3)= 6

+++ +++

2 groups of (+3)

(+2)x(-3)= -6

- - - - - -

2 groups of (-3)

(-2)x(+3)= -6

++ ++ ++ ----->

- - - - - -

Remove 2 groups of (+3)

(-2)x(-3)= 6

+++ +++

- - - - - - ------->

Remove 2 groups of (-3)

The Sign Rule for Multiplication (Negative Signs)

Whenever you there is an even number of negative factors, the product will be positive.

Whenever you there is an odd number of negative factors, the product will also be negative.

Chapter 3 - Dividing Integers

Partitive Division - When you use a number line to divide integers.

Example :

6÷2=3

-6÷ (-2)=3

Quotative Division - "Share" a number between a specific amount of groups

Example:

(-6)÷2= (-3)

Multiplicative Inverse - Rewriting a division question to a multiplication question. It helps you when you cant find a way to use quotative division or partitive division to solve an answer

Example :

6÷(-2)=(-3) Since I can not share 6 with (-2) groups, I use the Multiplicative Inverse

(-2)x(-3)=6

(-3)x(-2)=6

The Sign Rule for Division (Negative Signs)

The sign rule for division is pretty much the same as the one for multiplication, if there is an even amount of negative signs (-), your quotient will be positive. If there is an odd number amount of negative signs(-), your quotient will be negative.

Step-by-Step Examples:

6÷2= 3

1) I looked at both numbers and divided them (got 3)

2) No negative signs (0 = even number), this meant that it would be a positive number

3) My final answer was 3

-6÷ (-2)= +3

1) I looked at both numbers (not looking at signs) and divided them (got 3)

2) Two negative signs (2 = even number), this meant that it would be a positive number

3) My final answer was +3

(-6)÷2=(-3)

1) I looked at both numbers (not looking at signs) and divided them (got 3)

2) One negative sign (1 = odd number), this meant that it would be a negative number

3) My final answer was -3

6÷(-2)=(-3)

1) I looked at both numbers (not looking at signs) and divided them (got 3)

2) One negative sign (1 = odd number), this meant that it would be a negative number

3) My final answer was -3

Chapter 4 - Order of Operations With Integers

As we come to the end of this book, we talk about the Order of Operations with Integers. It's pretty simple to do, all you have to remember is one word:

B - Brackets

E - Exponents

D - Division

M - Multiplication

A - Addition

S - Subtraction

Division and multiplication, and addition and subtraction can be interchangeable since they are closely related.

Here is a step-by-step example:

(+5) x (-3) + (-6) ÷ (+3)=

1)We look if there are any brackets containing math statements.There are none.

2)We look for any exponents. There are none.

(-15) + (-6) ÷ (+3)=

3) We look for any multiplication/division statements. As you may see, there are two. We solve the first one we see because we read left to right.

(-15) + (-2) =

4) Solve the other division statement.

(-17)

5) We are left with adding. Add the two digits and voila! You get your answer.