Wednesday, October 12, 2011

Jackie's Proportion Post

1) What is the definition of ratio, rate and proportion?

Ratio: A ratio is a
comparison of two quantities that have the same unit of measure.
Rate: A rate is a comparison of quantities measured in different units.
Proportion: A proportion is an equation which states that two ratios are equal. *A proportion has 2 equivalent fractions. ( ratios)*

Here is an example of all these.

Rate And Proportion:The red shows how they are equivalent which proves how this is a proportion statement.
The words on the side show the word ratio.
The blue is the rate of how much shirts I would get for 2 dollars. The whole statement is the proportion statement.

Ratio: This shows 3 starfishes to 4 pearls.
There are many ways to show this.
Like part to part ratios. 3:4, 4:3, or in words starfishes:pearls, pearls:starfishes.
Another one is part to whole or whole to part ratios.
3:7, 4:7. 7:3, 7:4.
Part to whole and whole to part ratios are when you compare the whole to a piece.

2)5 hours to travel 360 miles is about _____mph or miles per hour.

Sentence: 5 hours to travel 360 miles is about 72 mph.

72miles/h

In order to get this answer, First I found the word ratios which were hours and miles. Secondly I put down the math information that fits into the problem into the right spaces, which were 5 hours so it goes beside hours and 360 miles beside miles. The 1 is what we are trying to find, which is how many miles per hour. Next I tried to find any relationships with the numbers and what i saw was 5 to 1, so 5 divided by 5 gets to one. So what you do to the top you do to the bottom. 360 divided by 5 = 72 miles which get your answer!

Question 2 B) As a playgroup worker, if I increase the amount of apple juice I am serving at the playgroup from 25 ml to 100 ml, how much should I increase the the orange juice to, to keep the quantities in the same proportion? The orange juice is 50 ml to start with.

Sentence: He should increase the orange juice to 250 ml.

The way I got my answer to this question is actually the same concept of what I did in the first question just with different numbers and on my first explanation in the picture above. It is pretty much the same thing just that I saw an easier relationship between 20 and 100 rather than 20 and 50. It isn't wrong if you do it the other way it just takes longer to find the relationship between harder numbers.

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

3/4=12/16 or 4/9=16/32

Three ways I can prove that equivalent ratios statements are true is by using diagonal by multiplying the number diagonal of them and both of the answers are the same.Another way is using horizontal multiplying. If the relationships horizontally on the bottom and top are the same and can get to the number placed there its equvalent. Lastly using the verticle way. The verticale way is the same concept just that you have to see the relationship at an up and down angle.

Just for note the 1.3 is repeated. Since the 1.3 repeated times the 3 does not equal 4, it is because 4 divided by 3 ends up with a repeating decimal but if you multiply it by three it ends up to be very close to 4. It is because the relationship between 3 and 4 is very hard to work with in relationships. Like having to work with 2 and 4 it is very easy because you get to use whole numbers and no repeats.

So this ratio statement is true.

This is a picture of the second ratio statement.
As you can see in all three ways they had to multiply by something else to get the the number that I needed to get to, to prove if the statement is true. But in this one it isn't because the results have to be multiplied by the same number for which ever way you chose just like the first statement above.

So this ratio statement is false.

Answer: So my answer is that the first ratio statement is the equivalent and true statement.

Here are some videos on proportions and ratios.

1) Does this seem fair?
I don't think this is fair at any circumstance.

2)With what you know about proportion look and read what is the image above. Does it seem just fair? Why have you made this choice.

This is my answer because 10 is a number that can fit into both 180 and 40. You might be wondering where I got 180 from. I got 180 months because there is 12 months in a year, and Roy was put in jail for 15 years so I multiplied 12 by 15 and got 180.
My proportion statement shows that if Roy stole \$12.50 dollars he would go to jail for 10 months?!?!?! That's just plain CRAZY! Especially if Paul stole \$750,000,000 dollars he would go to jail for 10 months. Plus Paul stole money even though he had a great job, while he didn't think of what he already had, so right now he just turned his life around. Unlike Roy he stole for a particular reason, it was to survive, and to pay to stay where he lives, and facing the fact he turned himself in from feeling guilty. This is clearly not a fair statement that happened.

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

What i would of done if I were the judge is that I would put Paul in for jail for the 15 years while Roy would be in jail for about a month, or month in a half.