Eula's Proportion Post

Proportion Post :)

 Part 1:

Definitions:

Ratio-

Is a comparison of 2 or more numbers. It measures their sizes compared to one another.
           Example: A ratio with 5 boys and 6 girls is 5:6, 5 to 6, or 5/6. And a word ratio would be just the word, in this case it's just boys:girls.
           There are 2 different kinds of Ratios though, The first one is Part-to-Part Ratio which is comparing different parts of one group to each other.
          And the other type is Part-to-Whole Ratio which is comparing one part of the group to the whole (total) group.

 

That photo shows a simple ratio between one teacher and five students.
The word ratio for this would be: Teacher:Students
The Part-to-Part ratio for this would be: 1:5
And a Part-to-Whole ratio for this would be: (Teacher to Total) 1:6

 Rate-

 A ratio that compares 2 quantities with different units.
Example: Money per Hour, Cost per Litre, Km per Hour, etc.

 The photo above shows 3 different rates with the same units. The first one is $1.69 for 414mL of Orange juice, the second one portrays $2.99 for 946mL and the last one shows $5.49 for 1.89 L. They are all rates. But if you are lazy, which most of us are you could just put $2.99/946mL, don't forget the units!
There is a type of rate called unit rate. Unit rate is rate but the second quantity is always 1. It's kinda hard to explain cause i'm really bad at explaining but this picture will kind of show you:

 

 It shows how much Bush's Best White kidney beans for one can.

Proportion-

It means 2 ratios or rates put into an equation to see if they're equal.
Example: 50/100=1/2
Pretty straightforward. But if you are still a little unsure of how to solve a proportion question this photo will show you how, (more information in the next question)

Part 2:

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

To solve this problem you just need to know how to unit rate and the easiest way, that I know of, is to make a t-chart. After you've made the 'T' put the unit of measurements in there (in this case, hours and km) and write down what you know. So far we know that it takes us 5 hours, so put that in the hours section, to travel 360 km, put '360' in the km section.
Now we need to get the number to one, in this case, the hours to an hour, which is one. We have 5 hours, and how do you get 5 to become 1? Divide by 5 (Divide the number by itself). And what you do to one side you do to the other so you need to divide 360 by 5 and the answer is 72.
So, 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?

.60-.28=.32
.38x75=28.50
The answer is 28.50

Part 3:

"What are the three ways you can prove that equivalent ratio statements are true?"
Example: 3/4 = 12/16
1st way:
In which you figure out how you get to the next number horizontal from it but multiplying or diving.

2nd way:
In which, you multiply the 2 numbers diagonal from each other and if they equal the same thing, it is equivalent. If not, its not equivalent.

 

3rd way:

In which you divide the 2 numbers vertical from each other, if they equal the same thing they are equivalent. If not, it's not equivalent.

 

Part 4: Video time!



Thi video will teach you about ratios and proportions & how to solve problems with them.

Though Mr. Harbeck teaches it differently (and way better) this is another way to look at it but it's still the same things. She uses terms like "y" and "x" those are just the missing numbers in a proportion question.

 

 

Part 5: http://www.concurringopinions.com/wp-content/uploads/2011/10/CrimeInAmerica2.jpg

Does this seem fair?

No absolutely, utterly, completely, immensly, 100%-ly not. Just because both men stole something does not mean they get similar sentences.

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

No, not at all because the first man stole 30-flippin-billion dollars and got sentenced to 40 years. Meanwhile the other man stole only a hundred dollars and got sentenced 15 years which is a little less than half of 40 years but 100 dollars is not even close to getting half with 30, not thousand, not million, but billion dollars. And plus, he gave it back so it's like getting charged for nothing.

Why have you made this choice?

I used proportional thinking of course. 15 years+15 years =30 years, which is, as I said a little bit less than 40. And what they stole has an immense difference, I would calculate to see how many 100s there are in 30 billion but if I wasn't so lazy.

What would you have done if you were the judge?

Sentenced the first man 70 years. And sentenced the 2nd man a year since he gave the 100 dollars back. I'm such a sympatethic judge.

Part 5: Bonus!

I chose this photo.


And my question for it is, How many peaches can fit in this box thing?
And this is my answer, well according to this photo, guessing that the peach photos imprinted on the box are life-sized, the peaches are 0.6 cm.
And according to the picture, this box is 9.5cm in length and 5.8 in width.
And to figure out the area of a rectangle you need to times width by height. (I think.) And in this case the question is, 5.8cm x 9.5cm. And the answer is 55.1cm.
So 55.1cm x 0.6cm and the answer to my question is: 33.06 peached in the box.
I don't know if i'm right or wrong it literally is what i'm thinking at the top of my head.

Fin.