Ivorys Big book of Integers

Chapter 1: Grade 7 Integer Review:

Integers are are -negative- and +positive+ numbers. They can be represented as integer chips or on a number line. You get a zero pair when you have a negative and positive of the same number, example: -1 and +1 make 0.

Adding and subtracting integers:

-3-(-7)
you owe 3 and you pay back 7
=4

-3-7
you owe 3 and you owe 7
=-10

3-7
you have 3 and you owe 7
=-4

3+7
you have 3 and you have 7
=10

-3+7
you owe 3 and you have 7
=4

Chapter 2: Multiplying integers:

Sign rule: when you have an even number of negative integers the product will be positive, odd will be negative.
When you know that, multiply the numbers

- = negative integer chip
+ = positive integer chip

(+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
+++ +++ = remove
--- ---


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

Chapter 3: Dividing Integers:

Partitive division is when you find out how many groups of a number is in another number. It can be shown on a number line:

6 divided by 2=3
__>__>__>
_|_|_|_|_|_|_|_
0 1 2 3 4 5 6

-6 divided by (-2)=3
<____ <____ < ___
_|__|__|__|__|__|__|__
-6 -5 -4 -3 -2 -1 0

Quotative division is sharing groups.

(-6) divided by 2=-3
------
/ \
--- ---

When both integers are the same you can use partitive or quotitive to get the answer.

Chapter 4: Order of operation with integers:

You can solve more complicated questions using order of operations. We use B.E.D.M.A.S. which stands for:
Brackets
Equations
Division
Multiplication
Adding
Subtracting
Square brackets are always done first. Using this order you can solve questions like this:

(+5)x(-3)+(-6) divided by (+3)=
[(+5)x(-3)]+[(-6) divided by (+3)]=
(-15)+(-2)=-17

Sandra's great big book of integers

Chapter 1

Grade 7 integer review
In grade 7, we learned about integers as being only represented as whole numbers that could be either posative or negative. We learned how to represent them by using integer chips and number lines. You can also make zero pairs with an even amount of posative integers and negative integers.

Find zero pairs for the following integers:

Integers in Grade 7
+4 is like saying you have 4 and -4 is like saying you owe 4.

In grade 7 we wrote integers using brackets ex. (+4) + (-4), these are just "training wheels", the actual standard form is written like this: +4-4 and the pure standard form is written like this: 4-4.

10-(-4) you are removing the negative part of the zero pair.

-3-2 is not subtracting, rather you have to add the negative integer.

Here are some questions:

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

2.-3-7=-10




3. 3-7=-4

4.3+7=10

Chapter 2: Multiplying Integers

Here is how I multiplied these integers:




1.2x3=6























2. 2x(-3)=-6






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


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


Chapter 3: Dividing Integers

There are two different types of division: Partative and quotative. Partative division is when you know the number of groups but what you are trying to find is the number of items in that particular group.
Ex.



1. 6/2=3






2. -6/-2=+3


Quotative Division is the oposite of partative divisiong, you have to try and find the number of groups.


Ex.





-6/2=(-3)

There are some sign rules you may need to keep in mind for multiplying and dividing integers: When you are dividing two integers that are the same, the answer will be posative. However, if you are dividing two integers that are different, the answer will be a negative integer.


Chapter 4: Order of operations with integers

(+5) x (-3) + (-6) ÷ (+3)=

When solving this problem we will have to apply the BEDMAS rules.

(+5)x(-3)+(-6)/(+3)=
(-15)+-6/(+3)=
-15+-2=-13







Sorry, I can't leave a video, my internet won't let me :(

Suzie's Great Big Book Of Integers

Chapter 1: Grade 7 Integer Review

*Zero pairs are the same number in positive and negative form. Example: +2 and -2. +18 and -18. They cancel each other out and make 0.



Integer questions from math:
1) -6-(-4)= -2

2) -10+6= -4

3) 6-7+2= 1

4) 14-(-3)= 11

5)* -3-(-7) = 4

6) -3-7= -10


since the -3 is negative and you're taking away positive, the subtracted positive adds on to the negative.

7) 3-7= -4


you don't have enough to take away the 7, so it goes into the negatives.

8) 3+7=10


just like adding.

9) -3+7=4


The negative 3 and the positive 3 make a zero pair and leave positive 4.

Here's a video about integers. I don't know if anyone else posted this video, but it's catchy and really helpful.



Here is a site to help you with integers. Hope you enjoy!

Chapter 2: Multiplying Integers


1)


2)



3)




4)




Stuff you should also know:


Even: If you have an even number of negative factors the product is positive.
Odd: If you have an odd number of negative factors the product is negative.

(+6) x (+4) (+9) x (+3)
-When 2 brackets touch they "kiss" and then they multiply. This includes when a number and bracket are touching.

Chapter 3: Dividing Integers

Partitive division is when you divide the integers into parts. Get it? "Part"itive division. Think, "how many groups of the same amount can I make?"








Quotative division is when you share equally with groups.



Multiplicative inverse can help you if you switch the numbers around so you can check your answer. For example: 6 ÷ (-2) = -3. 6 ÷ (-3) = (-2)


The Sign Rule:
If there is an odd number of negative signs, the product is negative. If there is an even number of negative signs the product is positive. For example:


6÷2= 3. No negative numbers, so it's positive.
-6÷ (-2)= 3. Even number of negative signs, so it's positive.
(-6)÷2= -3. Odd number of negative signs, it is negative.
6÷(-2)= -3. Odd number of negative signs, so negative again.


Chapter 4: Order of Operations with Integers


Let's solve this question!:

(+5) x (-3) + (-6) ÷ (+3)=

Use BEDMAS. (Brackets, exponents, division, multiplication, adding, subtracting).
See any brackets? Yes, a lot, so that doesn't matter. See any exponents? No. See any division? Yes! So we do that first.

(-6) ÷ (+3)= -2. So we put that in.

(+5) x (-3) + (-2)=

Then we just to the multiplication.

(+5) x (-3)= -15.

Put it together: (-15) + (-2)= (-17)

There you go!

Raelynn's Great Big Book Of Integers

Chapter 1 Grade 7 Integer Review:

Integers are natural numbers (positive or negative) or zero.


















Brackets are like training wheels.
For example; (-2) + 5 + (-7)

A zero pair are any of the same number that has a positive and a negative that will equal to zero. For example: -2+2 = 0

Examples of Standard forms:
4-5+6=5
-5-6=
4-5-7=

Questions and Answers:
-3-(-7)=4











-3-7=-10











3-7=-4










3+7=10










-3+7=4

The great Big Book of Integers Chapter 2:
(+2)x(+3)= +6

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












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












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












Chapter 3; Dividing Integers

Partitive Division is to divide something into parts. An example for it is;

Sign Rule:

• The quotient of two integers with the same sign is: positive when even amount of "-" signs.
• The quotient of two integers with different signs is: add number of "-" means negative.

Quotative Division involves taking a set of size a and forming groups. (Sharing with groups)
eg.

Multiplicative Inverse to solve 6 ÷(-2)=;

Chapter 4; Order of Operations with Integers
We solve this using B.E.D.M.A.S. (brackets, exponents, division, multiplication, addition, and subtraction)

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