Jonathan's multiplying integers

The Sign Rule

When you multiply integers with the same value (+ or -) the product  will always be positive. ex. (-5)x(-4)=+20 or 7x9=49

When the value of the integers are different (+,-) the product will be negative. ex. (+2)x(-8)=-16

Here are 3 more examples so you can understand the sign rule a little bit better-

(-4)x(+2)= -8                          since these integers have opposite signs, the answer will be a negative

remove 4 groups of 2

Now we need to make zero pairs because you can't remove -4 groups of 2.

 <(++++) (++++)>  you need to circle the groups and make arrows so you know if they are coming/going

      - - - - - - - -

Now you are left with -8 which is the answer.

+4x+8= +32                                the numbers have the same sign which means the answer will be positive

4 groups of 8

So all we need to do is make 4 groups of 8

(++++++++) (++++++++) (++++++++) (++++++++)

        ^                     ^                     ^                ^      

Your answer is 32           

(-3)x(-3)= +6                              3x3=6. You need 6 zero pairs

remove 3 groups of -3

       + + + + + +

 < ( - -  -)( -  -  -)>

Sign Rule Continue

When you have an even amount of (-) signs the product is positive. ex. (-5)x(+5)x(-5)=+125

When there are odd number of (-) signs the product is negative. ex. (+5)x(-5)x(+5)=-125

Let's do 2 more examples so you know this concept more well-

4x(-2)x(-2)=

4 groups of -2 groups of -2. This looks difficult so lets do this into parts.

4 groups of -2    (--) (--) (--) (--) this is -8  Now lets rephrase the question ( you don't have to do this step)

                           ^     ^    ^     ^

 It's now -8x-2= +16                8x2=16=16 zero pairs                      + + + + + + + + + + + + + + + +           remove 8 groups of -2                                            <  ( -  -) ( -  -) (-  -)  (- -)  (-  -)  (-  -)  (- -)  (-  -)>

(-3)x4x1=

remove 3 groups of 4 groups of 1

remove 3 groups of 4                               <( +++)(+++)(+++)(+++)>        = -12

                                                                     - - - - - - - - - - - -

-12x1=-12

remove 12 groups of 1                        < (+) (+) (+) (+) (+) (+) (+) (+) (+) (+) (+) (+)>

 -12 is the answer                                    -     -    -    -     -   -    -     -    -    -    -    -

Thanks for looking at my scribe post. Be sure to comment on my work and give me any suggestions if I made a mistake. Here's a video about the sign rule that will make you a genius. 

Jonathan's integer scribe post

We are going to learn how to deal with integers with ''-'' symbol. That symbol means ''remove''.

first problem: 5-(-2)=
First we have to write it in words for this problem
                                                                         5-(-2)=
                                                            have 5 remove owe 2
Then we look at the last integer which is -2. All integer number always start off with positive and negative signs that are the same amount as the integer number. so -2 is actually>++
                                                                                                           - -
After that you take away the sign that the integer has->  -2  ++
                                                                                         (--)>this leaves
Now you are left with ++ which means you basically turned -2 into a +2.
The ''remove'' sign turns into an ''and'' sign after you change the the last integer into the opposite of what it is.
The last thing you do is to combine it all together which gives you +7      

To see if there is a remove sign all you have to do is look if to signs are right next to each other between two of the numbers and have the same sign (also counts with brackets).  ex. 6--2=                         6-(-2) =


Here are ten questions with answers to see that you know how to do removing integers:
1. (-7)-(-5)= -2                                            - - - - - - ->     combine    < +++++      
owe 7 remove owe 5                                                                          (- - - - -)>this leaves
2. 8-(-5)= 13                                                ++++++++>   combine    <+++++
have 8 remove owe 5                                                                       ( - - - - -)>this leaves
3. 5-(-2)=7                                              +++++>          combine     <++
have 5 remove owe 7                                                                         (- -)>this leaves
4. 1-(-2)= 3                                                     +>          combine     <++
have one remove owe 2                                                                      (- -)>this leaves
5. (-5)-(-4)= -1                                       - - - - ->        combine     <++++
owe 5 remove owe 4                                                                       (- - - -)>this leaves

Now lets switch the strategy up and do negative integers another way. All we have to do is change the last number into the opposite sign and make the remove sign into a combine sign. ex. 5-(-2)=5+2=7
Now lets do them on the last 5 questions.
6. (-6)-(-8)= -6+8= -2
owe 6 remove owe 8
7. (-7)-(-2)= -7+2= -5
owe 7 remove owe 2
8. (-4)-(-9)= -4+9= 5
owe 4 remove owe 9
9. (-2)-(-6)= -2+6= 4
owe 2 remove owe 6
10. (-1)-(-2)= -1+2= 1
 owe 1 remove owe 2

Here is a video that will help you understand removing integers better.

Jonathan Lu and Raymond Bautista Pay it Forward

Our Pay it Forward act of kindness was to brighten people's day with kind messages. We chose this activity because we wanted to make people think positively and to encourage them to do something nice to other people in the future. For our act of kindness, we are going to help random strangers in one street. We placed sticky notes that have positive sayings onto people's mailboxes. We did this random act of kindness on December 12 and December 16.

Our endeavor went well because we made a few people happy and it also made us delighted. We stuck notes on peoples mailboxes and made some people very happy. I felt really joyful inside because I know that the people are happy and some even gave us positive feedback. One of the strangers was really happy about what we did and it made his day. Probably some other people felt the same way. We did tell him to ''pay it forward'' and gave a little explanation on what ''pay it forward" is about. The person agreed to take part of ''pay it forward'' sometime in the New Year.

I think the idea of ''pay it forward'' is important because people need to help others to make a difference in the world in a positive way. Without ''pay it forward'', everything would be the same and nothing would get better. We need the world to be a better place for everyone. Our act of kindness made a difference because people were happy and they will do the same to others. If that kept on going the whole world will be a positive, happy, safe place to live in.

Jonathan's Percent Post

A percent is an equivalent fraction out of one hundred.

100 percents mean a whole or everything.
To find 100 percent you divide the number by one.

50 percent means half or 50/100.
To find 50 percent you divide the number by two.

10 percent means 10/100 or 1/10.
To find 10 percent you divide the number by ten.

25 percent means 25/100 or 1/4.
To find 25 percent you divide the number by four.

1 percent means 1/100.
To find 1 percent you divide the number by one hundred.

Representing Percents

a) 180% means 180 out of 100 or 180/100 or 1.80/1.8

180%

b) 0.6% means 0.6 out of 100 or 0.6/100 or 0.006

0.6%

c) 12 3/8% means 12 3/8 out of 100 or 12 3/8 /100 or 0.12375









12 3/8%

Converting a fraction to a decimal and a percent
3/40 also means 4 divided by 40. 3/40=0.075/1(decimal).
0.075/1 x 100=7.5% out of 100. But that is a ratio, not a fraction.

Converting a decimal to a percent and a fraction
0.0064 x 100=0.64%
0.64/100 x 100=64/10000 divided by 8=8/1250 divided by 2=4/625

Convert a percent to a decimal and a fraction
0.3/100=0.003
0.3/100 x 10=3/1000

convert from Decimals to Percents to Fractions:
 26%/100=0.26x100=26% out of 100. 26/100 divided by 2=13/50 which is the fraction.
7/10=0.7x100=70%. 70/100 divided by 10=7/10.
0.024x100=2.4%. 2.4/100 divided by 2=1.2/50 divided by 2=0.6/25

20% of 60                              percent/ number                                   20% of 60 is 12.
                                                100   /     60
                       divided by 5       20    /     12         divided by 5
20/100= /60
20x60=1200
1200/100=12

0.1% of 40                             percent/number
                                               100    /     40
               divided by 1000         0.1   /    0.04                divided by 1000
0.1/100= /40
40x0.1=4
4/100=0.04

250% of 400                       percents/number
                                              100   /     400
               multiply by 2.5         250   /    1000       multiply by 2.5
250/100= /400
400x250=100000
100000/100=1000











50% of or 25% off of an already reduced price of 25%:
50% off:                                                           25% off:              25% off of an already reduced price 25%:
50/100= /200                                                   25/100= /200      25/100= /150
200x50=10000                                                200x25=5000     150x25=3750
10000/100=100                                               5000/100=50      3750/100=37.50
200-100=$100-answer                                    200-50=$150      150-37.50=$112.5-answer


50% of is better than 25% off of an already reduced price of 25% because 50% of goes straight to the half of the price. But 25% off of an already reduced price of 25% is more expensive because it cuts the half price in half which makes the price a different 100%.

http://www.youtube.com/watch?v=ZBOBfZT562c