Olivia's Great Big Book Of Integers

Chapter 1

Grade 7 Integer Review

A zero pair is two numbers, one positive and one negative, that have the same value and equal zero when you add them. Eg. -2, (+)2 = 0. A saying that helps you subtract integers is, "When subtracting something that isn't there, use a zero pair."

When subtracting or adding integers, you can use a number line or integer chips to help you. When you use chips, generally red symbolizes positive and blue symbolizes negative.

1) -3 - (-7) = +4

2) -3 - 7 = -10

3) 3 - 7= -4

4) 3+7 = +10

5) -3 + 7 = +4

Chapter 2

Multiplying Integers

1. (+2) x (+3)

2. (+2) x (-3)

3. (-2) x (+3)

- need 2 groups of (+3) zero pairs, then remove 2 groups of (+3)

- factors (-2), (+3) tell you how many zero pairs you need

4. (-2) x (-3)

The Sign Rule (regarding negative signs)

Chapter 3

Dividing Integers

Partitive Division is when you know how many groups there are and you want to find how many items are in each group; making parts.

Eg.

6 ÷ 2 = 3

-6 ÷ (-2) = -3

Quotative Division is when you know how many items are in each group and you are trying to find the number of groups; sharing you total with groups.

Eg.

(-6) ÷ 2 = -3

Multiplicative inverse to solve 6 ÷ (-2) = :

6 ÷ (-2) = (-6) ÷ 2 = -3

The sign rule for division is the same as the sign rule for multiplication, addition, and subtraction.

Eg.

6 ÷ 2 = 3 There are no negative signs in the question, therefore the answer it positive.

-6 ÷ (-2) = 3 There is an even number of negative signs in the question, so the answer is positive.

(-6) ÷ 2 = -3 There is an odd number (one) of negative signs in the question, therefore the answer is negative.

6 ÷ (-2) = -3 There is one negative sign in the question, therefore the answer is negative.

Chapter 4

Order of Operations with Integers

Use BEDMAS to solve equations, don't use 'E'.

Steps to solve (+5) x (-3) + (-6) ÷ (+3)=

1. Put square brackets around the operation that has to be done first (multiplication, division, addition or subtraction in order from left to right) and solve.

2. Put square brackets around the operation that has to be done next and solve.

3. If necessary, continue steps.

Here are all the steps together: