Ysabelle's Great Big Book of Integers

Grade 7 Integer Review

Integers

An integer is a number that is not a fraction. An integer is any of the natural numbers (positive or negative) or zero.

positive-red

negative-blue

Brackets are training wheels.

Examples:

-4-(-8)

-4+8 ---> standard form

4-(+9)

4-9 ---> standard form

-7+(-8)

-7-8 ---> standard form

A zero pair is a pair of number with a positive and negative sign whose sum is zero. (+,-)

Examples:

-6 and +6

-4 and +4

-10 and +10

When subtracting something that isn't there, use a zero pair.

Here are the * questions:

-3-(-7)=4

-3-7=-10

3-7=-4

3+7=10

-3+7=4

Chapter 2
Sign Rule:
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.

(+2) x (+3)= 6
2 groups of positive 3

(+2) x (-3)= -6
2 groups of negative 3

(-2) x (+3)= -6
remove 2 groups of positive 3

(-2) x (-3)= 6
remove 2 groups of negative 3

Chapter 3
Dividing Integers

Partitive Division
You are trying to find out how many times a number contains another number.

Examples:
6÷2=3


-6÷(-2)=3


Quotative Division
Sharing equally with groups.

Example:
-6÷2=-3




Multiplicative Inverse can help you solve 6÷(-2)= by checking your answer. When you found out what the quotient is, switch its place with the divisor's place.

6÷(-2)=-3 ---> 6÷(-3)=-2

Sign Rule
When you divide two integers with the same signs, the quotient would be positive.
When you divide two integers with different signs, the quotient would be negative.

6÷2=3 - positive because they have same signs
-6÷(-2)=3 - positive because they have same signs
(-6)÷2=-3 - negative because they have different signs
6÷(-2)=-3 - negative because they have different signs



Chapter 4 Order of Operations with Integers

(+5) x (-3) + (-6) ÷ (+3)=
You could solve this problem by using BEDMAS-brackets, exponents, division, multiplication, addition, subtraction.
- Perform division and multiplication as they occur from left to right.
- Perform addition and subtraction as they from left to right.

(+5) x (-3) + (-6) ÷ (+3)= -15+(-2)
(+5) x (-3) + (-6) ÷ (+3)=-15-2
(+5) x (-3) + (-6) ÷ (+3)=-17