Nils' Great Big Book Of Integers

Chapter 1
Grade 7 Integer Review

We need to know what a zero pair is to know how to do the homework questions.

A zero pair is a pair of numbers with a positive and a negative sign which adds up to zero
Eg. (4, -4) are integers. (10, -10), ( 100, -100), ( 3, -3) are all examples

Zero pairs can be used to solve math problems with both positive and negative numbers in them.
Zero pairs can be represented by using different coloured chips. Commonly blue represents negative and red represents positive. Let's use zero pairs to solve the first starred homework question.

1) -3 - (-7) = 4
In this question you need to use Isfeld's rhyme " When subtracting something that isn't there use a zero pair." You make the zero pair for -7 and you remove -7 so all you have left is +7. You then just make zero pairs using the 3 blue chips and you have 4 positive chips left.


2) -3 - 7 = -10
For this one you have to make a zero pair so you can take away +7. You then combine negative 3 and negative 7 to get -10.


3) 3 - 7 = -4
You should use zero pairs for this because it makes it easier to understand. Make a zero pair for 7. Remove the positive part. Now make zero pairs with the three positve chips. You should have -4 remaining.

4) 3 + 7 = 10
This one is kind of obvious but let's use chips to figure it out. You should get 10.

5) -3 + 7 = 4
This one is pretty straight forward. Make zero pairs out of the 3 negative chips and you should have 4 left over.

Chapter 2
Multiplying Integers

To find out how to multiply integers we will use examples from today's class.

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

To find out the (obvious) answer we will use chips. The statement in standard form is (2)(3) and it means "two groups of positive three". So this is what it looks like.

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

To find the solution to this one we need to know that it means " two groups of negative three." This is what it should look like.

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

This one is a little more complex. You need to know that the minus sign means "remove." So it means "remove two groups of positive three." To remove those groups you need to make zero pairs. You will have negative six left.

4) (-2) x (-3) = +9

This question is similar to question 3 because they both use zero pairs. This question means "remove two groups of negative three." In order to do this you need to make zero pairs to remove negative six.



Sign Rule (negative signs)

Even - When you have an even number of negative factors the product is positive.

Odd - When you have an odd number of negative factors the product is negative.

Chapter 3

Dividing Integers

A) 6/2 = 3

To get the answer you must use partitive division. It means spreading into parts or groups. This question is asking you "how many parts or groups of 2 are in 6?"

B) (-6)/(-2) = +3
How many groups of -2 are in -6?

C) (-6)/2 = -3

This question is asking you "how do you share (-6) with 2 groups?"

In the picture each group has -3.

D) 6/(-2) = -3

For this question you must use multiplicative inverse to get the answer.

The multiplicative inverse of this question is (-2) x _ = 6. The answer to the newly inversed question is positive. That means that both of the factors are negative. That means that the blank is -3 because the answer is positive and one of the factors (-2) is already negative.

Sign Rule

When there is one negative sign or an odd number of negative signs the quotient is negative.

Chapter 4

Order of Operations with Integers

(+5) x (-3) + (-6)/(+3) =

We must use BEDMAS to solve this problem. To help us do that you should put square bracket around multiplication or division parts. The question should look like this.

[ (+5) x (-3) ] + [ (-6)/(+3) ]

(-15) + [ (-6)/(+3) ]

(-15) + (-2)

-17