Ariel's Proportion Post

I.
Definitions.
a)  Ratio:
A comparison of 2 quantities that have the same unit of measure.
e.g. 5 red blocks : 3 green blocks
Pictorial example:

b)  Rate:
A comparison of 2 quantities that have the different unit of measure.
e.g. 35 words per minute
Pictorial E.g.:

c)  Proportion:
A statement that 2 numbers are equivalent
e.g. 4/12 = 24/72
Pictorial E.g.:

II.
a) 5 hours to travel 360 kilometers is about _____km/h.
A: 5 divided by 5 = 1
    360 divided by 5 = 72
    360 km/5 hrs = 72 km/hr
b)  Emma saves 28 cents of every dollar that she earns.  Emma earned $75 last week.  How much money did Emma save last week?
A:  1 x 75 = 75 dollars
     28 x 75 = 2100 or 21 dollars
     28 cents/dollar = 2100 cents/ $ 75.00

III.
3 ways to approve equivalent statements: 3/4 = 12/16 and 4/9 = 16/32
a) Horizontal:
3/4 = 12/16 = ✓
A:   3 x 4 = 12
A:   4 x 4 = 16

4/9 = 16/32 = X
A:  4 x 4 = 16
A:  9 x 4 = 36

b) Vertical:
3/4 = 12/16 = ✓
A:







4/9 = 16/32 = X
A:






c) Diagonal:
3/4 = 12/16

A:

4/9 = 16/32

A:

So, are both statements true?

A: No, only the first one is true because the numerator and denominators have some sort of relationship (vertical, horizontal, diagonal). The second one is wrong because the denominators has no relationship whatsoever. 

IV:


V:



V: a) This is not even close to fair.
    b) This doesn't seem very fair and just.
    c) This isn't fair because the homeless guy is sent to prison for 15 years for stealing only $100, while on the other hand the CEO is sent to prison for only 40 months for a $3 billion fraud.
    d) I would have sent the CEO to jail for 6 years because that was the original term sought by the federal prosecutors. Then I would have sent the poor man to jail for 3 years because the minimum prison sentence for 1st degree robbery in Louisiana is 3 years, but I would lessen it to 2 years because he voluntarily surrendered himself and only stole 100 bucks.







Bonus Question:
How many kids does it take to measure one tree?