Ainsley's Multiplying Integers Scribe

This is my post on how to multiply integers with different signs or the same signs.

The Sign Rule:

• When multiplying integers with the same value (+ or -), or for example (-2) x (-2) = the product will always end up being positive
• When the value of the integers are different (+,-) or for example (+2) x (-3)= the product will always end up being negative.

Another way:

1) When you have an even amount of (-) signs, the product will end up being positive.

(-4) x (-2) x (-1) = -8

|_______|

     +8       x (-1) = -8 

2) When there is an odd number of (-) signs, the product is negative.

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

remove 2 groups of 4 = -8                                 - - - -       - - - - 

Now, these are a few questions that I've solved using the sign rule : Math Links 8.2

17. Question: Without evaluating the products, identify the least product. Explain your reasoning.
 (+99) x (+82)
  (-99) x (-82)
 (+99) x (-82)
To answer this question, I chose (+99) x (-82) because if you recognize the sign rule, you know that when you multiply two integers with different signs, you get a negative. In this case, I didn't have to calculate it because I just saw the signs and I already know it's going to be a negative.

9. Question: Determine each product.
a) (-6) x (-6) = +36
I know that because if you multiply 6 x 6, you get 36. Also, they have the same signs and that means they are positive.
b) (+9) x (+6) = +45

c) (-12) x (+2) = -24
I know this because if you multiply 12 x 2, you get 24. Also, they have different integers and based on the "sign law/rule", when there are two different signs they are going to end up being negative.
d) (+11) x 0 = 0

Ainsley's Integer Scribe Post

This part of the post will show you how I understand how to subtract integers with brackets.

Step One: You write out the question: 7-(-9) = 

Step Two: You have to rewrite it using words such as owe, have, remove, & and.

Note: Owe means it's a negative number and have means it's a positive number.

Answer:  have 7 remove owe 9

Step Three: You model it in integer tiles to help show that you understand or to help you get the answer.

7- (-9) =  + + + + + + +    - - - - - - - - - 

After that, you have to make zero pairs so first you match the negatives (owes) with positives.

7- (-9)=  + + + + + + +     - - - - - - - - - 

                                        + + + + + + + + +       (pretend they're the same size)

Then, you removes those owes/negatives and you add what's left (positives) to your first amount of positives which is 7.

7- (-9)= + + + + + + +      - - - - - - - - - 

                                         + + + + + + + + +    (The highlighted part means that it is leaving.)

After that, you now add it together so : + + + + + + +    + + + + + + + + + = 16 positives or just 16.

Lastly, you add in your answers to the question.

7- (-9) = 16

have 7 remove owe 9 = have 16

Now, you'll see how I did the other questions. 

   

Ainsley's Pay It Forward

Part 1:
Pay it Forward is when you share an act of kindness. In the movie, Pay It  Forward, it shows that it's supposed to have a ripple effect. It starts off and it goes by threes but in our case, it doesn't really matter. It doesn't mean you just think about it and share an idea, you actually do it. The things you do would be kind, helpful, or maybe even generous but afterall, you do it for no reason but to feel good. You don't get paid but you get rewarded with most likely - a smile.

Part 2:
My Pay it Forward act of kindness is was handing out cards and candy canes! The cards had friendly holiday greetings in them. Amanda and I chose this activity because we figured it would be such a simple and easy task yet so thoughtful and kind. It's not everyday where you find an unexpected but super friendly card in your mailbox! Even though it was nice of us to do that, we didn't really "help" anybody. The purpose of this was to make people smile and pass along good vibes. We handed out the cards and candy canes on the 30th of December and on January 3.






Part 3:
Our act of kindness went pretty well. It was really easy putting them in peoples' mailboxes and it was actually pretty fun, which you could tell by the videos. Amanda and I were super cold but we made the best of it! While doing this project, I felt super kind yet cold at the same time. Not cold as in mean and negative but cold as in temperature wise. It was about -30 on that day but having Amanda with me just made it better. I felt kind because we were just volunteering to do all of this. Even though it was for a project, we didn't get paid and we didn't expect to! On that day, I was really happy because I felt so generous and after all, if you know Amanda and I, there's never a dull moment. Anyway, we didn't see how they people reacted because we just left the cards and candy canes in their mailboxes so hopefully they see them. But, in the cards, we did mention to pay it forward so hopefully that gives them an idea.

Part 4: 
The idea of Pay It Forward is important because it's not a negative act, it's a positive act. This shows that no matter how young, old, tall, or short you are, you could do it and it will lead to a positive impact. It could lead to a bunch of smiles and it will also show who you could be and who you truly are. Our act of kindness might have not made a big difference but it might have gave people ideas and maybe even motivated them to pay it forward as well. This might have made them think that something so small can make anyone's day.

Ainsley's Percent Post

A percent is an equivalent fraction of 100. In other words, fractions are turned into decimals and those decimals are turned into percentages!

100 percent means everything 100/100 or 10/10. 
To find 100 percent, you have to divide the denominator by 1. 
For example: If you had 40 apples and you wanted to find 100% of those 40 apples, you just have to divide 40 by 1. That still give you 40 which means 40 is 100%. You do that because 40 is the denominator or in other words, the whole or whole amount. 

50 percent means half, 1/2, or 50/100. 
To find 50 percent, you have to divide the denominator by 2.
You have to divide the denominator by 2 because it is half. For example, if you wanted to find 50% of those 40 apples, you divide 40 by 2. That gives you 20 which means 50% of 40 is 20.

25 percent means 25/100 or 1/4. 
To find this percent, you have to divide the denominator by 4. 
For example: If you had 100 and divided it by 4, that would equally give you 4 x 25. In our case, we have 40 apples. That means you have to divide 40 by 4 instead of 100 by 4. That gives and leaves you with 10.
10 x 4 = 40

10 percent means 10/100 or 1/10.
To find 10 percent, you have to divide the denominator by 10.
You have to do that because for example, the whole percent is 100. If you wanted to find 10% of 100, you would just have to divide it by 10. In this case, you have 40 apples and that means your "whole amount" is 40. Now if you divide 40 by 10, you get 4. To check if it's right, you can do the opposite operation which is multiply. (4 x 10=40)

1 percent means 1/100. 
To find this percent (1 percent), you have to divide by 100.
Example: If we divided 100 by 1, we would get 1. In our case, we have 40 apples instead of 100 so it's different. We would have to divide 40 by 100. Once we do that, we get 0.4 or 0.40 (same thing). Now to show that that makes sense, we can multiply by 100 (opposite) and get 40 as our answer. 

Representing Percents: 

180: 

 12 3/4 %

 0.6%

 OR

Converting Percents, Fractions, and Decimals.

Converting fractions to decimals and percents: 

3/40: To do this you have to divide the numerator by the denominator. Then, you have to multiply that decimal by 100 to get your percent. 3 divided by 40= 0.075. 0.075 x 100= 7.5%

Converting decimals to percents and fractions: 

5.98: To do this, you have to multiply by 100. To find the fraction, you may count the amount of digits or 0's which in this case is 3 but you replace the first digit or the ones with a 1. 5.98 x 100= 598%. 5 98/100.

Converting percents to decimals and fractions:

750%: To do this, you have to divide the percent by 100. That is because a percent is always equivalent to 100 so you have to do the opposite operation. 750 divided by 100 = 7.5. In this case, it would be 7 1/2 since 50 is half of 100. 

Show How You Know: 
20% of 60:
20 ÷ 100= 0.20
0.20 x 60= 12
20% of 60 = 12

0.1% of 40:
0.1 ÷ 100= 0.001
0.001 x 40= 0.04
0.1% of 40= 0.04

250% of 400:
250 ÷ 100= 2.5
2.5 x 400= 1000
250% of 400= 1000


5- Combining Percents
Question 3 - Page 148. Example #- 200

15 ÷ 100 = 0.15
0.15 x 200 = 30
200 + 30= 230

10 ÷ 100= 0.10
0.10 x 230 = 23
230 + 23 = 253

25 ÷ 100 = 0.25
0.25 x 200 = 50
200 + 50 = 250

Kyle is not correct because 253 > 250.

Show You Know - Page 148
Example # - 200
Store A- 50% off one day only.
Store B- 25% one day + 25% off the reduced price the second day. 

50 ÷ 100 = 0.50
0.50 x 200 = 100
200 - 100 = 100

25 ÷ 100 = 0.25
0.25 x 200 = 50
200 - 50 = 150

25 ÷ 100 = 0.25
0.25 x 150 = 37.50
150 - 37.50 = $112.50

Store A has the better buy or price because at the end, the sale price would be $100. At Store B, you would have to pay $12.50 more than Store A.