Ian's Dividing Integers Post

The Sign Rule makes integers easier. The Sign Rule is: If the question is a + and a + or a - and a - then the answer is postive. If they are have + and a - or - and a + then the answer is Negative.
++ = Positive
-- = Positive
+- = Negative
-+ = Negative

Question 1:
(+8) / (+4) =
There are 2 ways to answer this question.
1. "Share (+8) into (+4) equal groups."
2. "How many equal groups of (+4) are in (+8)?"

So, first way is to Share 8 into 4 equal groups.

The answer is +2

We are simply sharing 8 into 4 equal groups.





The second way, "How many equal groups of 4 are in 8?"

The answer is +2 also.
Since there is 2 groups of 4 in 8.




Question 2:
(-8) / (-4) =

First way: "Share (-8) into (-4) equal groups" You can't do the first way because we can't share -8 into -4 equal groups. So we have to do the second way.
Second way: "How many equal groups of (-4) are in (-8)?"
The answer is +2
It is a positive because of the Sign Rule. - and - make +.

Question 3:
(-8) / (+4) =
First way: "Share (-8) into (+4) equal groups"
Second way: "How many equal groups of (+4) are in (-8)?" We can't do the second way because there isn't an equal group of +4 in -8.

 The answer is -2.





Question 4:
(+8) / (-4) =
First way: "Share (+8) into (-4) equal groups"
Second way: "How many equal groups of (-4) are in (+8)?"
Both of them are wrong. So there is this thing called "Multiplicative Inverse"
Which is:
(-2) x (-4) = +8


Here is a video about Dividing Integers

Ian's Integer Scribe Post

Integers Subtraction and Addition :

Question 1.

9-1=

For this question, we need to write it in words. Owe = Negative (-), Have = Positive (+)

Have 9 and Owe 1 =

Also you don't need to put the And, It just makes it easier.

Second Step.

You need to do it using Chips.

+ + + + + + + + +

- 

Then you can see that there is 3 Zero Pairs. + and - make a Zero Pair.

So we have to take those out. Just pretend the red ones are removed.

+ + + + + + + + +

-

Now all there is left is Positive 8. So the answer for Have 9 and Owe 1 is Have 8 or 9-1 = +8

You also don't need to put the + sign for the answer since if there is no sign it means it is positive.

If you decide to do a number line for this question this is what you do.

                                                        +9

                                              --------->

<----------------------------0------------------------------->

                                                     +8 <-

                                                          -1              

And as Mr. Harbeck told us, Positive on the Number Line go on the top and Negative on the Number Line go on the bottom.

Question 2.

6 + (-7) = 

Now you know the concept. Let's do this question.

Write it in words.

Have 6 and Owe 7 =

Second Step, Chips.

+ + + + + +

-  -  -  -  -  -  - 

Zero Pairs.

+ + + + + +

-  -  -  -  -  -  -

Left is Negative 1. So the answer for Have 6 and Owe 7 is Owe 1 or 6 + (-7) = -1

This time you need to put a negative sign for the answer because if you don't the answer will be Positive 1 which is wrong.

Number Line.

                                                    +6

                                               ------>

<-----------------------------0-------------------------------->

                                     -1   <--------

                                                      -7

Question 3.

8 - (-2) =

Now this question is different. This time we are REMOVING. If you see a question with  # - ( - #) it means we are removing. The # means numbers.

First we write it in words.

Have 8 Remove Owe 2 =

Second Step, Chips

+ + + + + + + +       - -

We have to turn the Negative into a Positive so we have to do a Zero Pair

+ + + + + + + +      - -

                              + +

Then we remove the Negatives. Like I said I'm using Red Font for removing.

Then we add it together.

+ + + + + + + +

                    + +

The answer for Have 8 Remove Owe 2 = Have 10 or 8 - (-2) = +10

Number Line.

     

            +8         +2

         --------> --> +10

<----0----------------------------------->

Question 4.

10 + (-2) = 

Words.

Have 10 and Owe 2 =

Chips.

+ + + + + + + + + +

-  -

Zero Pairs.

+ + + + + + + + + +

-  -

We have +8 left.

Answer : 10 + (-2) = +8 or Have 10 and Owe 2 = Have 8

Number Line

                      +10

               ---------->

<--------0--------------------------------->

                     +8  <--

                              -2

Question 5.

10 - 4 = 

Words.

Have 10 and Owe 4 = 

Chips

+ + + + + + + + + +

-  -  -  -

Zero Pairs.

+ + + + + + + + + +

-  -  -  -

We have +6 left.

Answer : 10 - 4 = +6 or Have 10 and Owe 4 = Have 6

Question 6.

(-8) + (-3) =

Words

Owe 8 and Owe 3 =

Chips

- - - - - - - -

- - -

No Zero Pairs.

We have -11.

Answer : (-8) + (-3) = -11 or Owe 8 and Owe 3 = Owe 11

Number Line

<--------------------------0---->

               -11 <--- <-------- 

                          -3        -8          

Question 7.

0 - 5 =

Zeros are neither Positive or Negatives they are the Middle.

Words

0 and Owe 5 =

Chips

- - - - -

No Zero Pairs.

We have -5.

Answer : 0 - 5 = - 5 or 0 and Owe 5 = Owe 5

Number Line

            -5

   -5 <-----

<---------0------->

Question 8.

8 - 4 =

Words.

Have 8 and Owe 4 =

Chips

+ + + + + + + +

-  -  -  -

Zero Pairs

+ + + + + + + +

-  -  -  -

We are left with +4.

Answer : 8 - 4 = +4 or Have 8 and Owe 4 = Have 4 

Number Line

                               8+

                           -------->

<----------------0---------------->

                            +4 <----

                                    -4

Question 9

9 - (-4) =

Words

Have 9 Remove Owe 4 =

Chips

+ + + + + + + + +      - - - -

Make Zero Pairs

+ + + + + + + + +      - - - -

                                 + + + +

Remove Negatives.

+ + + + + + + + +      - - - -

                + + + +

We are left with +13.

Answer : 9 - (-4) = +13 or Have 9 Remove Owe 4 = Have 13

Number Line

       +9              +4

      ---------> ----> +13

<--0-------------------------------->

Question 10

(-5) + (-3) = 

Words

Owe 5 and Owe 3 =

Chips

- - - - -

- - -

No Zero Pairs.

We have -8.

Answer : (-5) + (-3) = -8 or Owe 5 and Owe 3 = Owe 8

Number Line

<--------------------------0--->

                    -8   <--- <-----

                             -3      -5

Here's a video about Adding and Subtracting Integers

Ian's Pay It Forward

Part 1

Pay It Forward is a random act of kindness to anyone. You do something good for them and they do good for 3 other people. The chain gets bigger and bigger.

Part 2

For my Pay It Forward, I volunteered at Winnipeg Harvest. I chose this activity because Winnipeg Harvest helps a lot of people so I wanted to help at Winnipeg Harvest. We sorted different kinds of bread that will be distributed to people in need. I did my act of kindness in December 28 2013.

Part 3

It went really well. There was other people volunteering, doing many things. I felt good for volunteering. They felt proud of us because we wanted to help other people in a young age. They are already helping other people because they were working or volunteering there. I did not ask them because they are already doing an act of kindness.

Part 4

The idea of Pay It Forward is important because doing a random act of kindness to a friend, family or someone you don't know is good.  The person that you did an act of kindness may do a random act of kindness to another person too which will keep people happy. I don't know if my act of kindness has made a difference yet.

Ian's Percent Post

A percent is an equivalent fraction out of 100/100

100% means everything or 100/100
To find 100% you need to divide the denominator by 1.

50% means half or 50/100
To find 50% you need to divide the denominator by 2.

25% means 25/100
To find 25% you need to divide the denominator by 4.

10% means 10/100
To find 10% you need to divide the denominator by 10.

1% means 1/100
To find 1% you need to divide the denominator by 100.


Representing Percents
   
     180%

    0.6%

12 3/4%

Converting Percents, Fractions and Decimals.

Converting Fractions to Percents and a Decimal.

3/40

To change 3/40 into a decimal, you need to divide the numerator by the denominator.

3 divided by 40 = 0.075

To make it into a percent, you take the 0.075 and multiply it by 100.

0.075 x 100 = 7.5/100 or 7.5%

Converting Decimals to a Percent and a Fraction.

0.268

To change 0.268 into a percent, you take the 0.268 and multiply it by 100.

0.268 x 100 = 26.8/100 or 26.8%

To make it into a fraction, you need to lay it out like this. 

0.268 The 1 is the place holder.

1 000 After this you need to make it into short term form so:

 268  =  134 =  67

1000     500    250

Converting Percents to a Decimal and a Fraction.

750%

To change 750% into a decimal, you need to divide it by 100.

750% divided by 100 = 7.5

To make it into a fraction, you simply take 7.5 and make it into a fraction.

7.5 = 7 1/2

Combining Percents 

For example if  it's $75
50% OFF of $75 is $37.50
If it's 25% then 25% off the second day of $75
$75 x 25 = 1875/100 = $18.75
$75-18.75=56.25
56.25 x 25 = 1406.25/100= $14.0625 or $14.07
56.25 - 14.07 = $42.18