Summer's Great Big Book Of Intergers

Chapter one: Grade 7 integers review

Integers
- number line
- integer chips
- zero pair



























- negative and positive numbers

Integers










































- Number line


Song:
"When subtracting something that isn't there use a zero pair"



Find the zero pairs for the following integers

-6 +10 -16 63
+6 -10 +16 -63


-11 +11

+ 14 -14

19 -19


integers Ala grade 7

have 4 owe 4
(+4) + (-4) = O

Brackets are training wheels.
Standard form:

+4 + -4
+4 -4

pure standard form:
4 -4

























3 -2 = Subtraction = adding a negative integer.











Questions:

-3 - (-7) = -10

-3 - 7 = 10

3 - 7 = -4

3 + 7 = 10

-3 + 7 = 4


Chapter 2 multiplying integers:

multiplying integers:

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

(2) x (3) = 6

(2) (3) = 6 2 (3) = 6
standard form





(=2) x (+3) = 6

or

2 groups of ( +3) = 6










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

or

2 groups of (-3) = -6











(-2) x (+3)

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

remove 2 groups of (+3)
(use zero pairs)









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















(-3) x (-4) = + 12











(+2) x (+4) = +8

(+5) x (-2) = -10

(+4) x (+2) = -8 - 4 x 2 for zero pairs remove (+) left with (-)

(-6) x (-1) = -6




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:

Partitive division using a number line:

6 / 2 =

















-6 / (-2) =


















Quatative Division:

(-6) / 2 = -3


Multiplicative Inverse:

6 / (-2) = 4

Sign Rule for Division: using

6 / 2 = 3

-6 / (-2) = -4

(-6) + 2 = -4

6 / (-2) = 4



Chapter 4 order of operations with integers:

explain how to solve this:

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

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

-8 + -17 = -25

first add extra brackets then do the problems that are inside the extra brackets then add the two numbers that came from the extra brackets together and you have your answer.

Christian's Big Book of Integers

Chapter 1 Grade7 Integer Review

When something isn't there, make a zero pair.

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

I made 7 zero pairs because I didn't have -7. So then I took away -7 and had 3 zero pairs.

Answer: +4

2.) -3 - 7 = -10

I made 7 zero pairs and took away 7.
Answer: -10

3.) 3 - 7 = -4

I drew -7 and +3. I had 3 zero pairs.
Answer: -4

4.) 3 + 7 = 10

I drew 3 then 7 more.
Answer: 10

5.) -3 + 7


I drew -3 and 7. I had 3 zero pairs.
Answer: 4

Chapter 2 Multiplying Integers

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

+++ +++ two groups of three.

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

--- --- two groups of negative three

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

+++ +++ -----> - - - - - - remove two groups of positive three

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

+++ +++ --- --- remove two groups of negative three


The Sign Rule for Multiplication

When theres an even amout of negative signs, the product will be positive.

When theres an odd amout of negative signs, the product will be negative.

Chapter 3 Dividing Integers

There are different ways to divide integers.

Partitive Division - When you use a numberline to divide integers.
Quotative Division - Share a number between an amout of groups.

Multiplication Inverse - When you rewrite a division question to a multiplication question. It helps when you can't find a way to use partitive or quotative division.

The Sign Rule for Division

The sign rule for division is almost the same as multiplication. The amout of negative sign rules is the same.

Chapter 4

(+6) x (-2) + (-6) / (+2) = ?

Do the multiplication first. Ex. [ +6 x (-2) = -12 ]

Then division -6 / (+2) = -3

Answer: -15

Maya's Great Book of Integers

Chapter 1 - Grade 7 Integer Review

Integers
- Number lines
- Integer chips
- Zero pair

- Positive and negatives ( + and - )
- "When subtracting something that isn't there, use a zero pair."

-6 - (-4) = -2
-10 + 6 = -4
14 - (-3) = 17
-3 - (-7) = 4
-3 - 7 = 10
3 -7 = 4
3 +7 = 10
-3 +7 = 4

Chapter 2 - Multiplying Integers

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

Chapter 3 - Dividing Integers
When you have an off number of negativ e signs in a division question, the quotient is negative.
If you have no negative or even number of negative signs in a division question, the quotient is positive.

Here is an example from our notes:

6 / 2 = 3
-6 / (-2) = 3

Quotative Division or sharing your total with groups.

Here is an example of what we did in class:



Chapter 4 - Order of Operations with Integers
(+5) x (-3) + (-6)/ (+3)

First, you make a box around (+5) x (-3) so it's 5 groups of negative 3.

That would equal -15.
Then, you put a box around (-6) / (+3)
How many groups of positive 3 would be in negative 6?
Negative 2.
So, -15 + -2 = -17.

Krizna's Great Big Book of Integers

Chapter 1

This is what we did in class.
We learned how to solve different kinds integer problems,
We learned how to solve it in different ways we can use :

Integer Chips
https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-AqrLyhFFC0afJdt3-8jzigjmE4rOiF5r2xpag-R-rrJ1csrgdub_BJkapzY7fXAAtmTUgwASP_aHw20q9JDnQsmdE4NpyLtFHsT6cE85Nqs5rQ8PZX-4zGQnjhiHk8hHIIyEjsDlYZs//Positive%2Band%2Bnegative%2Bchips%2B...%2Bintegers.png

or

Number Line
https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxj3TEwRONXQnWq-RvSCegblYrOslxeSjHKE8ndocd4KgpUsN1HBHqabm-L8m01b8MSxNrVG-H_afiLUFpgPKbbFpywi3LI0dp_8muQffMKs-agDf-bdK7KaC_bBzgHA7tF2E7QZpb12w/s1600/Number+line+...+integers.png

We learned about zero pairs too,
A zero pair is a number with answer of zero
"when subtracting something that isn't there use a zero pair"

Chapter 2 Multiplying Integers

(+4)x(+2) = 8

Make 4 groups of positive 2











Make 4 groups of negative 2

(+4)x(-2) = -8














(-4)x(+2) = -8 Remove 4 groups from positive 2















Chapter 2

Dividing Integers

Even = When you have a even number of negative factors your product is positive.

Odd = When you have a odd number of negative factors your product is negative.

Partitive Division - when you use groups to find your quotient.

6 ÷ 2 = 3













(-6) ÷ (-2) = 3









Quotative Division - Sharing numbers in groups

(-6) ÷ 2 = - 3











Quotative Division - Sharing numbers in groups

(-6) ÷ 2 = - 3

Chapter 4

Order of Operations

(+6) x (-2) + (-6) ÷ (+2)= ?

1) Always do multiplication and division first
2)Put square brackets around (+6) x (-2) ex. [(+6) x (-2)]
3)Put square brackets around (-6) ÷ (+2) ex. [(-6) ÷ (+2)]
4) Solve (-12)+(-3) = + 15

Ryan's Great Big Book Of Integers

Chapter 1 Grade 7 Integer review

Integers can be represented with

-number lines

- integer chips

red = positive

blue = negative

red and blue = zero pair When something isn't there use a zero pair.

example -6+6=0, -8+8=0, -1256+1256=0

(+4)+(-4)=0

standard form 4-4=0

Chapter 2 Multiplying integers

1. (+3)x(+2)

3 groups of positive 2

standard form (3) (2)

2.(+2)x(-3)

2 groups of negative 3

standard form (+2) (-3)

3. (-2)x(+3)

removing 2 groups of 3

standard form (-2) (+3)

4. (-2)x(-3)

removing 2 groups of positive 3

standard form (-2) (-3)

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.

Chapter 3 Dividing Integers

Partitive division is how many groups of a number are in a given value.

Quotative Division is sharing a certain number between a given value.

Chapter 4 Operations with Integers

(+5) x (-3) + (-6) ÷ (+3)=

(-15) +(-6) ÷ (+3)=

(-15) + (-2) = -7

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.

Mark's Great Big Book of Integers

Chapter 1 Grade 7 Integer Review

If something is not their, use a zero pair!

Grade 7 - (+7)-(-3)=

Standard - 7 - (-3)=

Chapter 2

Chapter 3

Dividing Integers

Partitive division is creating groups of numbers.

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

Quotative division is sharing numbers in groups.
(-6)÷2=

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

Chapter 4

Order of Operations with Integers

To solve (+5) x (-3) + (-6) ÷ (+3)= you would have to use BEDMAS

first you would divide the answer using square brackets.

Remember, square brackets are the first thing you do.

From then, you would keep shortening the question until you get an answer

Ex. (+5) x (-3) + (-6) ÷ (+3)=

[(+5) x (-3)] + [(-6) ÷ (+3)]=

(-15)+(-18)=

+33