## Sunday, October 21, 2012

### 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
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.