Allison Concepcion's Scribe Post: How to divide integers

There are many ways to divide integers some ways will work some cannot. Dividing integers is a bit more complex than multiplying integers but the same sign rule applies. A positive and a positive equals a positive. A negative and a positive equals a negative, and a negative and a negative equals a positive.

What does ÷ mean? This symbols means you are sharing _?_ into _?_ equal groups in this case lets just say you are sharing (+8) into 2 equal groups. When you are dividing integers the numerator is what you have ( you have 8) and the denominator represents how many groups there are (you have 2 groups) e.g.

8- What you have
2- How many groups you have

First off, if you are dividing two positives, there are two possible ways to show your work.

(+8)÷(+2)= 4

Step 1: Have (+8) and have 2 groups.
Share (+8) into 2 equal groups.

Step 2: Now you share (+8) into two equal groups
Your answer will be 4

Now that you've figured out how to show your work in one way, here's another way of how to show your work.

You are asking yourself, how many groups of (+2) are in (+8)?

Step 1: have your (+8)

Step 2: Now, ask yourself how many groups of (+2) are in (+8)
There are 4 groups of (+2) in (+8)
Your answer is 4

If you are dividing a negative and a positive integers, try to use the same method as before.

(-8)÷(+4)= -2

Step 1: Share (-8) into 4 equal groups

Step 2: You share (-8) groups into 4 equal groups
Your answer is -2

Method 2: How many groups of (+4) are in (-8)?
You cannot do this method because there are no groups of positive 4 in negative 8.

X

This time you are dividing a negative by a negative and also see if one of the two methods work.

Method 1: Share (-8) into (-4) groups.
It is not going to work because there is no such thing as (-4) equal groups.

X

Method 2: How many groups of (-4) are in (-8)?

Step 1: Have your (-8)

Step 2: Now ask yourself, how many groups of (-4) are in (-8)

↓ ↓

1 group + 1 group = 2 groups

Your answer is 2.

Now, you are dividing a positive by a negative, same rules apply try the same two methods to see if one of the two methods work.

(+8)÷(-4)= -2

Step 1: Share (+8) into (-4) equal groups

X

You cannot do this method because there is no such thing as sharing positive 8 into negative 4 equal groups.

Method 2: How many groups of (-4) are in (+8)?

X

Once again you cannot do this method because there are no groups of (-4) in (+8)

Since none of these methods work there is another different method that we can use which is called Multiplicative Inverse. Multiplicative inverse is basically the opposite of dividing so instead od dividing to figure out the answer you have to multiply to get the answer.

Step 1: Ask your self (-4) multiplied by what will equal (+8)?

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

Step 2: If you figure out what the missing number is that will be your answer.

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

-2 will be your answer.

You cannot show this method by using a model you can only show this method by using multiplicative inverse.

multiplying integers when the integers have different value, ( - or + ) the product is negative.

when the integers have same value, ( -,+ )the product is positive. when multiplying integers, count the negative signs odd number = negative even number = positive

8.2 textbook

10. Estimate and then calculate 1) (+17) * (-24) = 408 est: (+20) * (-24) = -480 I changed 17 to 20 because 17 is close to 20, also i can calculate 20 * 24 in my head fast. Then i used the sign rule to solve this question, when the integers have different value, the product is negative. 2) (+37) * (+22) = 814 est: (+40) * (+22) =880 I changed 37 to 40 because 37 is close to 40, also i can calculate 40 * 22 in my head fast. Then i used the sign rule to solve this question, when the integers have same value, the product is positive. 3) (-72) * (+15) = -1080 est: (-70) * (+15) = 1050

I changed 72 to 70 because 72 is close to 70, also i can calculate 70 * 15 in my head fast. Then i used the sign rule to solve this question, when the integers have different value, the product is negative. 4) (-28) * (-47) = 1316 est: (-30) * (-45) = 1350

I changed 28 to 30, 47 to 45 because 28 is close to 30,and 47 is close to 45 also i can calculate 30 * 45 in my head fast. Then i used the sign rule to solve this question, when the integers have same value, the product is positive.

12. A telephone company offer its customer a $15 discount per month if they also sign up for internet service. how much is the annual discount? (+12) * (-15) = -180 12 groups of (-15) 12 month of $15.00 off I used negative sign for $15 because discount means off (getting 15 dollars off each month) annual means one year, there are 12 months in a year, and we have $15.00 off each year. so we need to calculate how much is the annual discount, we multiply 12 by -15 because we have 12 groups of -15. Then we use the sign rule to solve this question, when the integers have different value, the product is negative. 12 * 15 equals 180, the answer has to be negative so, it is -180. 13. A hot air balloon is descending at 60 m/min. how far does it descend in 25 min? (+25) * (-60) = -1500 25 groups of (-60) 25 min of 60 m/ min I used negative sign for 60 m because descend means going down, the hot air balloon is going down 60 m/ min. The hot air balloon is descending at 60 m/min, and the question ask how far does it descend in 25 min? that means, we have 25 groups of 60 because , 60 m/ min, and there are 25 of them. To solve this question we need to multiply 25 by (-60). we can use the sign rule to solve this question, when the integers have different value, the product is negative. 25 * 60 = 1500, the answer has to be negative so it is

here is a video that can help you with multiplying integers (with the chip model) multiplying integers is not hard, you can do it! hope my scribe can help you!

When multiplying integers, here is the basic lesson.
Here's an example:
(+7) x (+2)=
In words, this would be seven groups of positive 2.
In repeated addition: (+2) + (+2) + (+2) + (+2) + (+2) + (+2) + (+2) =
You could use integer chips as so:

The red symbolizes positive.

You can also represent this equation as a number line, either vertical or horizontal.

And you'll have your answer, which is (+14).

Here's something new:

scribe rule

When the integers have the same value (+ or -), the product is positive.

When the integers have different values (+, - ), the product is negative.

Let's apply this rule.

(+5) x (+4) =

Just multiply and then see whether or not the signs match or not.

5x4= 20

both positive, so the answer is positive.

(+ 5) x (+4) = +20)

(-6) x (+2)=

Multiply, 6x2= 12

They have different signs, meaning it's negative.

(-7) x (-8)=

Find the answer of 7x8, = 56

Then to see whether 56 or the answer is positive or negative, check the signs.

The two signs are the same, meaning the answer is going to be positive.

= (+56)

sign rule part 2

When multiplying integers , count the negative signs. When the number turns out to be an even number, it is going to be a positive product, and an odd number while counting equals to a negative product.

For example: (+4) x (+6) x (-7) x (-1) =

count the negative signs, and there are 2.

2 is an even number, therefor the answer will turn out to be a positive product.

To solve it, just do order of operations.

(+4) x (+6) x (-7) x (--1) =

(+24) x (-7) x (-1) =

(-168) x (-1)=
(+168) = answer. :)
See, it's a positive product.

Let's try this again.
(-4) x (-1) x (-3) x (+2) =
by following the same rule from before, this must be a negative product since there are 3 negative signs, and 3 is odd.

(-4) x (-1) x (-3) x (+2) =
(+4) x (-3) x (+2) =
(-12) x (+2)=
(-24) = answer

Let's try with more factors.
(-4) x (+2) x (-1) x (+1) x (-5) x (+1) =
There are 3 negatives, and 3 is an odd number meaning that the answer is going to be a negative product.

(-4) x (+2) x (-1) x (+1) x (-5) x (+1) =
(-8) x (-1) x (+1) x (-5) x (+1) =
(+8) x (+1) x (-5) x (+1) =
(+8) x (-5) x (+1) =
(-40) x (+1) =
(-40)= answer.
See it wasn't that bad.
If you're having problems with multiplying integers, please refer to the video below,

P
Please feel free to play this game, and apply the sign rules to your answers. :)

If you have to show the work you put 7 positive and 2 negatives.
+ + + + + + +
- -

After you draw you find the zero pairs.

+ + + + + + + - - That is how you get the answer.

Removing

To add or subtract something that's not there you have to do the zero pair. You only use the zero pairs when you happen to see 2 negative sign right beside each other. Example: 6-(-9)= 15 have 6 and remover -9 + + + + + + - - - - - - - - - >>>>>> remove + + + + + + + +
+ + + + + + + + + + + + + + + = 15

~ We have 6 and we owe9 but we can't remover 9 from 6 because 9 is a higher number than 6, so we have to add the zero pairs. We need to add 9 zero pairs and remover 9 zero pairs. Now we have 6 and have 9, we add those two numbers together and we got the answer. :)

6+9= 15

examples.

(-3) - 5= -8 ( we don't have to remove because we only remover when we have 2 negative sign together -(-7) )

We start volunteering at Winnipeg Harvest on our 2nd week here in Winnipeg. My parents joined first, then they invited us to volunteer for the next Saturday, so we start to volunteer every other Saturdays. We volunteer sorting breads, creating boxes, cleaning and sorting goods. We work from 9:00 am to 12:00 pm.

Paying it forward is a benefit that involve doing something good for someone in response to a good deed done on your behalf or a gift you receive. When you pay it forward it doesn't have to be something extraordinary or elegant. It is something you are cable of doing it. Also when paying it forward, however, you don't repay it to the person who did something nice to you. Instead you do something nice to someone else, like neighbors, families, friends, etc. The movie pay it forward, a boy named Trevor was given an opportunity to change the world and put it into actions. He decides that if he can do three good deeds to someone. This assignment was given us student a chance to make adifference like Trevor.

PART 2: WHAT WAS YOUR PAY IT FORWARD ACT OF KINDNESS?

My pay it forward act of kindness is only one action: stick a notes with candy canes in front of my neighbor's door.

WHY DID YOU CHOOSE THIS ACTIVITY?

I choose this activity because it's something that I can really do well and something that I'am capable of doing it. By doing this activity I discovered that even though your neighbors don't see what is your doing, you can feel the greatness inside that your actually doing this to them to make them happy.

WHO DID YOU HELP?

I had mostly helped my neighbors. I helped them by making them happy. I stick a notes in front of my neighbors door. I did that because, even though their tired from work they will feel great. WHAT DID YOU DO? On the first day, me and my family went to Super Store to buy candy canes and also groceries, after that I made notes for my neighbors. On the second day I stick every notes and candy canes together and put it in a bag, after that I went out side and just stick the notes to my neighbors door. WHEN DID YOU DO YOUR ACT OF KINDNESS? I started my act of kindness on December 28 and December 29, 2013.

PART 3: HOW DID YOUR ACT OF KINDNESS GO? Of course it wasn't easy because it was cold outside. I thought making a difference was easy to do and I didn't think that I'am going to achieve my assignment. I know I work hard but when you feel the hardness that you go through to make changes in the world you'll forget that hardness. WHAT HAPPENED? I just did it on my own because my parents have work and my sister have her own business, so I need to help my self, if not no one will help me. I just take a photo of one note in my neighbors door. So I was grateful that I actually finish my assignment without help form others. HOW DID YOU FEEL? I feel great because I actually make some changes in the world, even though I just did a little bit of help to make them great. Also happy because I finish this assignment. HOW DID THE PERSON OR PEOPLE REACT? I actually don't know, I would guess they will react unthinkable where the notes came from and also I guess thankful. DID YOU ASK THE PERSON OR PEOPLE TO "PAY IT FORWARD"? Actually no, because the point of this assignment is you are willing to help other people without asking them what you actually need to do to help them or make their day good, just do what is best to make a differnce. IF YOU DID NOT ASK THE PERSON TO "PAY IT FORWARD", HOW COME? My first reason, why I didn't ask the person to pay it forward, it's because I'm shy and sometimes the people were not at their home so I just did it without asking them.

PART 4: WHY IS THE IDEA OF "PAY IT FORWARD" IMPORTANT?

The idea of pay it forward is important because it's something that will inspired people of doing good or nice things to other people. I think pay it forward is important because we can learn something from it like how to help other people without thinking that "Am I going to help them, or not" and also it's important because you are making a difference, inspiring other people and and you are helping to change the world.

HAS YOUR ACT OF KINDNESS MADE A DIFFERENCE?

I think my act of kindness made a difference, even though you only did small thing to them. It doesn't matter though, how big or small you did to make a difference.

-6 -9=-15 when you have double like this -(- you must remove wich
owe 6 owe 9= owe 15 makes the negative go away and make a
------ --------- new mate with the positive

-10+10= 0
owe 10 have 10= 0 ---------- you say bye bye to -----------
++++++++++= 0
and say high too ++++++++++++++++