Mikaela's Proportion Post.

Part 1

A ratio is a comparison of two different quantities that have the same unit of measure. 

-There are two types of ratios including:

A part-to-part ratio compares different parts of a group to each other (i.e. 8:12 is the part-to-part ratio of white chocolate bars to dark chocolate bars).

A part-to-whole ratio compares one part of the group to the whole group (i.e. 2:24 is the part-to-whole ratio of milk chocolate bars to total number of chocolate bars)

-You can also compare the quantities as:

Three term ratios; which compare three quantities measured in the same units (i.e. 1:5:9 is the ratio of blue to green to pink flowers). 

Two term ratios; clarifies two quantities measured in the same units (i.e. 5:15 is the ratio of green to total flowers). 

-A ratio can be written as a fraction, decimal or percent.

A rate compares two quantities measured in different units (i.e. 100 beats per second or 100 beats/second is a heart rate).
-There are two types of rates including:

A unit rate is a rate in which the second term is one (i.e. 77 kilometers per hour or 77 km/hr).

A unit price is similar to both a rate and unit rate in which it could be used to purchase bulk foods (i.e. $2.29 per 100 g or $2.29/100 g).

A proportion is a relationship that says that two ratios or two rates are equal. Can be written in fraction form. 

Example:

Part 2

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

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?

Emma saved 21 dollars last week for every 28 cents she saved when she earned a dollar.

Part 3

You can prove that this equivalent ratio statement is true by using cross multiplication/products (shown in pink), multiplying (in this case) horizontally (shown in green) and using a ratio table (shown in purple).

Part 4

Task 5

I don't think this is just or fair at all. The ex-mortgage CEO was sentenced to a little over 3 years (40 months) in prison for participating in a $3 billion scheme. While the homeless man was sentenced to 15 years (approximately 180 months) for stealing $100 from a bank. All the homeless man was trying to do was probably get some food for himself pay the detox center so he could have some shelter for himself. He also only took one 100 dollar bill and returned the rest of the money to the bank teller. I really feel that the ex-mortgage CEO should have something close to a life sentence because it really seems silly for a man that stole $100 dollars to go to jail for 15 years whilst another man involved in a $3 billion scheme goes to jail for only 3 years.*

4. If I were the judge I would have sentenced the ex-mortgage CEO to a life sentence (as I said in my first paragraph) because 3 000 000 000 (dollars) divided by 12 (months, or a year) is 250 000 000. 250 years in jail is way over an average human's life span and would then be considered as a life sentence. On the other hand, I would have sentenced the homeless man 8 months in jail plus community service because 100 (dollars) divided by 12 (months, or a year) is a little over 8. As 8 years would seem much too extreme for a criminal offense such as this one I brought it down to months. I added the sentence of community service because stealing is stealing and by law it has to be punished in some way. 

*I have meshed questions 1 through 3 together as one paragraph

BONUS

What is the height difference between the boy and the tallest tree in the background?

I'm estimating the age of the boy is 12. I've searched up on Google that the average 12 year old boy's height is 4 foot 9 (4'9 ft.) or 121.92 cm. I used my ruler and measured that on screen, full size the boy's height is 6.4 cm. I will consider the tree to the boy's right to be the tallest tree in the picture. I measured said tree to be 18.4 cm. 6.4 cm (boy's on screen height) divided into 18.4 cm (tallest tree's on screen height) is 2.875 cm, I'll round to the nearest tenth making it into 2.9 cm. I will now multiply the 121.92 cm (average 12 year old boy's height) with 2.9 cm (how many times the on screen boy's height was divided into the tallest tree's on screen height), which equals 353.568 cm. I will round that to the nearest tenth and get 353.6 cm. I converted that into feet and got 11.60105 ft. (11'6 ft. rounded to the nearest tenth). I will now take the estimated tree's height and subtract the average 12 year old boy's height and get 6'7 ft. My final answer is there is a 6'7 ft. difference between the boy and the tallest tree.