Everything Harvey knows about Fractions

Ash L.'s Proportion Post

Part 1

The Definitions

   Ratio: A ratio is a comparison between 2 quantities measured in the same unit of measurement (e.x. balls in a bag, 2 people's mark on a test, etc.). There are 2 different types of ratios, listed below.

     Part to Part

 A part to part ratio takes one part of the quantity and compares it to another part (e.x. red balls to blue balls, carrots to broccoli, etc.,).

     Part to Whole

  A part to whole ratio compares part of the whole to the whole (e.x.      green balls to total balls, how many Boston cream donuts in the whole box, etc.,).
    Rate: A rate is a comparison between quantities measured in different units of measurements (e.x. 110 kilometers per 5 minutes, cupcakes to donuts, etc.,).
   Proportion: An proportion is a mathematical statement that shows how 2 ratios are equivalent
    Part 2 
The Statements
  1. If it takes you 5 hours to drive 360 km., what is the unit price?
Well, the way to answer that is by first dividing 5 by 5 to get i hour, because in unit price, we would figure out what one unit of the first measurement is, then you make it even by dividing 360 by 5, and you would get 72. So the proportion is 360 km/5 h = 72 km/ 1 h.

2. If Emma saves 28 cents per dollar she earns, and she earns $75 last week, how much money has she saved? Well, to figure that out, we multiply the 28 cents by the 75 dollars, the product will be the amount of money Emma has saved. First, I will multiply .28 by 10. which will give me 2.8. She saves 2.80 dollars per 10 dollars she makes. 2.8 divided by 2 will make our 5%, and we should get 1.4. Now all we need to do is multiply our 10% by 7, which is 19.6, add our 5%, 19.6 +1.4= 21.0
Emma saves $21 per $75 she works for.
Part 3
Comparing Equivalent Ratio Statements
How to compare ratios to find out if they are equivalent or not
    One way is multiplying across.
 This is how you do it. The fractions of choice are 4/5 and 12/15. Multiply the fraction across by a factor (which in this case would be 3) we would result in 4x3=12. So now we know the numerators are equivalent. But now we ask ourselves if the denominators are equivalent. Since we realized with the magic of math that 5x3=15, we know these are equivalent fractions.
    Second is cross multiplication.
 This is how you do it. Now I will use 3/4 and 12/16. Multiply the numerator of the first fraction (3) with the denominator of the second fraction (16) and keep the answer (48). To make sure these 2 fractions are equivalent, we must even the question, by multiplying the denominator of the first fraction (4) by the numerator of the second fraction (12) and if we get the same answer, we will know that 3/4 is equivalent fractions. 12x4=48, so yes these are equivalent fractions.
     The last way to find out is by vertical division.
 This is how you do it. My last set of fractions are 4/8 and 9/18. You simply divide the denominator (8 in the first one, 18 in the second one) by the numerator (4 and 9) and if you get the same result, you have a set of equivalent fractions. Since both fractions give quotient of 2, we know 4/8 and 9/18 or equivalent to one another.
Part 4
Proportion Video

     
Part 5
Social Justice Questions and Answers
Question 1. Does this seem fair?
No it doesn't. My question is how can anyone think this is fair?
Question 2. With what you know about proportion, look and read what is in the image above. Does it seem just and fair.
 No it doesn't. A poor homeless guy stole only $100, it wasn't an armed robbery, he was only going to use it to eat, and he confessed and turned him self in for mercy, and he gets 15 years!? My only logic for that period of time for that crime is that the judge decided maybe it could be like a shelter and he could get some food and a place to sleep. as for the other guy, he's only getting just over 3 years for 3 BILLION dollars! So this guy is getting about a year per billion dollars he stole, and Roy Brown is getting a year per every 6 or 7 dollars he stole.
Question 3. Why have you made this choice?
Because one guy who only wanted $100 dollars so he could eat, because he was poor and homeless, is getting a year per $6.6666666667 that he stole only to eat, and surrendered, no one asking him to or being cornered, just going up to the police saying " excuse, yesterday, I am a criminal guilty of stealing $100 so I can eat, so please punish me," and he gets 15 years, for wanting to eat, and the other guy steals 3 billion dollars and he only gets 40 months. That's 3 years and 4 months. That's a month per 75 million he stole, no confessions, wasn't any much poor, just a criminal.
Question 4. What would you have done if you were the judge?
I'd switch the times in jail around, no, maybe not. Probably a month or so for Roy and 20 years for the guy who stole 3 billion. I think that sounds a bit more fair. Or a lot more fair.

Jandro's Proportion Test

Part 1.

Ratio- shows the size of 2 or more values

Rate- compares two numbers measured in different units

Proportion- comprares the relation between things

Part 2:

5 hours to travel 360 kilometers is about _72_km/h.

Emma saves 28 cents of every dollar that she earns. Emma earned $75 last week. How much money did Emma save last week?
28 cents x 75=$21

Part 3

What are 3 ways you can prove equivalent fractions are true

cross mulitplication, 1 horizantal, 2 vertical
Part 4:
http://www.youtube.com/watch?v=qP6UZY623pk&feature=relmfu
Part 5:
http://www.concurringopinions.com/wp-content/uploads/2011/10/CrimeInAmerica2.jpg

When I read this report I was surprised by the fact that a homeless and hungry man who confessed of being guilty of robbing $100 from a bank was sent to jail for 15 years. While a man who was involved in one of the biggest corprate frauds which in total was $3 billion stolen, was sent to jail for ONLY 3 YEARS. First I am outraged by the fact that a homeless man who stole $100 and gave it back feeling guilt and confessing his wrong doing got 15 years in prison for being honest and truthful while a sick corprate criminal would get 3 years after stealing $3 billion. When i thought of justice, I thought that if you are guilty and ADMIT your wrong doing your sentence in jail will be lessened. But in this case the judge didnt look at the mans good heart for the judge just looked at the wrong doing he has done and since he thought he was homeless he would think that it wouldnt be important. Just simple compare the stats, $100: $3 billion and with that goes a 15 year sentence:3 year sentence. Also look at the age 55:54 add then 3 to the 55 and 15 to the 54 then the age when they get out of jail is 58:69. 3 years in jail for robbing $3 billion and 15 years for just robbing $100? I just doesnt seem right. I made this desicion because even thought both have down wrong things in life the one that confesses his guilt should be rewarded but yet must still face his penalty but for the one that is guilty but does not confess and try to get out of it must face the major consequence. But the fact of 15 year for $100 and 3-4 years for $3 billion is just not right in this world. If I were the judge i would have given the man 1 year just for his confession of his wrong doing of stealing $100 and give the other man 15-20 years for his act of fraud of many americans which totaled a $3billion fraud.

Mac's Proportion Post

Part 1
Definitions
Ratio - A ratio is a comparison of two quantities using a fraction or division.
Rate - A rate is a ratio that compares two quantities expressed in different kinds of units.
Proportion - The proper factors of a number are all its factors except the number itself.
5 hours to travel 360 kilometers is about 72km/h.

Emma saves 28 cents of every dollar that she earns.  Emma earned $75 last week.  How much money did Emma save last week? Emma saved 21 dollars last week.


Part 3
What are the three ways you can prove that equivalent ratio statements are true?
3/4 = 12/16
                x4   

Way 1  3       12            Way 2                   3                 12                                             N       |    D
            --       ---                    divided by 4                               divided by 16   W3  ----------------------------
            4       16                                          0.75            0.75                                            3     |    4
                x4                                                                                                          x4   (          |       )  x4
                                                                                                                                       12     |  16                                                          
                                                                                                                                               
                                                                                                                                              12
                                                                                                                                              ----
                                                                                                                                              19

Part 4

Part 5
http://www.concurringopinions.com/wp-content/uploads/2011/10/CrimeInAmerica2.jpg
Couldn't get the picture to go here, but this is the website.
1. Does this seem fair? Well I'm not sure because on one hand it is the law, and the law is the law, but on the other hand he was homeless and what else could he do, he didn't hurt anyone and it was only 100 dollars, at least in jail he will have food and shelter not very nice food and shelter but food and shelter non the less. So in conclusion the law is the law, what can you do, BUT 15 years? I mean come on he didn't even have a weapon, I don't know I just think that's a bit much.
2. With what you know about proportion look and read what is in the image above.  Does it seem just and fair?   Didn't I just answer that above? 
3. Why have you made this choice?  I have made this choice because that is what I think about that question. 
4. What would you have done if you were the judge?  If I were the judge I would have given him a shorter sentence. 

Special thanks to JMQM Officials for the video, and my Dad for the math.

Jordy's Proportion POst

Part 1:

Definitions

Ratio:Compares two different parts of a group.

It can be written like this:  4:8 or a fraction. 4/8.
You should always simplfy!
4/8 = 1/2
 




Rate:
is a ratio that compares two quantities of different units.
 
An example of Rate:
 
Unit rate is a rate in which the second term is 1.
     
Jordy wrote 20 words in 10minutes.




Proportion:





A proportion is an equation is stating that two ratios are equivalent.

Part 2

1. 5 hours to travel 360 kilometers is about __72_km/h.

2. Emma saves 28 cents of every dollar that she earns. Emma earned $75 last week. How much money did Emma save last week?

Part 4

http://www.youtube.com/embed/VgSl_YzTXlU

Here's a video to help you if your having trouble with proportion!

 

 

Part 5

1.Does this seem fair?

Yes. Although he did the wrong thing , he needed the money to survive, now he must face his punishment.

2.With what you know about proportion look and read what is in the image above. Does it seem just and fair?

Urh, no! The man in the first article took 3B and is only in jail for 3years? Where else the one in the second took 100$ and returned it the next day and is there for 15years?

3. Why have you made this choice?

Because it doesn't seem right. Neither of them did the right thing, but the homeless man was hungry but still went back the next day. The other man was probably planning on spending his 3B on something silly.

4. What would you have done if you were the judge?

Switched it around.
3B= 15years.
100= 3years.

http://www.concurringopinions.com/wp-content/uploads/2011/10/CrimeInAmerica2.jpg

1. Does this seem fair?
2. With what you know about proportion look and read what is in the image above. Does it seem just and fair?
3. Why have you made this choice?
4. What would you have done if you were the judge?

Read more: http://sargentparkmathzone.blogspot.com/search?updated-max=2012-10-03T11:39:00-07:00&max-results=7#ixzz29VX0cARw
Under Creative Commons License: Attribution Share Alike

John's Proportion Post

Part 1 - Define

Ratio

A comparison of two different types of numbers

Ex - 128 students out of 11 teachers = 128:11

Picture Example

Rate

A ratio that is comparing two quantities of different units

Ex - I bring in 38 wooden sticks inside my home and it takes me about 10 minutes

Picture Example

Proportion

Equation showing two ratios that are equal

Ex - I have 10 cows and 20 dolphins = 10/20 or 1/2

Picture Example

Part 2 - Solve

1) 5 hours to travel 360 kilometers is about _____km/h.

5 ÷ 5 = 1 & 360 ÷ 5=72

A = 72km/h

2) Emma saves 28 cents of every dollar that she earns.  Emma earned $75 last week.  How much money did Emma save last week?

1 x 75 = $75 & 28 x 72 = $21.00

A = $21.00

Part 3 - Improvement

3/4 = 12/16 - 1/2 = 6/8

4/9 = 16/32 - 1/2 = 4/8

Part 4 - Video Example

Task 5 - Discussion

1) Does this seem fair?

A) $3 billion = 40 months. $100 = 15 months. Not at all.

2) With what you know about proportion look and read what is in the image above.  Does it seem just and fair?

A) For the CEO, it's $75,000,000 each month. The homeless man, it's around $1.30 each month.

3) Why have you made this choice?

A) It seems pretty obvious that it's not fair at all. Comparing $75 MILLION to $1.30 cents? It's clear that this isn't fair or just.

4) What would you have done if you were the judge?

A) Let him go. He stole a $100, told and probably and obviously was taken from him or he gave it back, so it's all good.

Bonus Question

Q) How tall are the trees?

A) First, I went onto paint, copied and paste the guy, and stacked them together on each other and see how many of them are needed so the guy is high as the trees. My result was I had to copy and paste 2 of them which is making 3 of them, and there was a little space above, i'd say ¼. I guessed that this guy is about 14 years old so then I went to the internet and searched the average height of a 14 year old teen. So what I got was that the average height for a 14 year old teen was 64 inches tall. So I calculated - 64 x 3 = 192 - so i'm guessing the tress are 192 inches tall.

Abhi's proportion post.

PART 1

1)Ratio - A pair of numbers that compares different type of units. 

 








2)Rate - Compares two quantities measured in different units.
 


 3)Proportion - Is the equation that shows two ratios that are equal.





 PART 2

 1) 5 hours to travel 360 kilometers is about _____km/h

 First I divided 5 by 5 to get 1 Then i divided 360 by 5 to get 72.

72km/per hour



2) Emma saves 28 cents of every dollar that she earns.  Emma earned $75 last week.  How much money did Emma save last week?




 

PART 3

 

What are the three ways you can prove that equivalent ratio statements are true?

 3/4 = 12/16  or 4/9 = 16/32
  

1. Using time table

2. Dividing it

3. Multiplying it

Part 4

 

http://www.youtube.com/watch?v=Ss3fp51ghMo

Part 5

1. Does this seem fair?
 No it isn't fair.
2.With what you know about proportion look and read what is in the image above.  Does it seem just and fair? 
100 dollars for 15 years? Too much. It should be about few thousand or tens of thousands to be 15 years. So no, it does not seem just or fair. 

3.Why have you made this choice?  

Because 15 years is way too much for 100 dollars, and that guy was homeless now I feel bad for him. 

4.What would you have done if you were the judge? 

I would let him in jail for a week or so, because he only stole 100 dollars, and he gave it back and admit he stole it.

 

bonus question

 

 How tall are the trees?

I guessed that this guy is about 5.3 then i stacked the guy till i reached the top of the trees which was three stacks.

 5.3x3=15.9. so the trees must be 15.9 ft tall.