Mathematical Reflection #2

1a. In this Investigation you have used ratios, percents, fractions, and found differences to make comparison statements. How have you found these ideas helpful?
I found these ideas very helpful because you can use them in real life situations when you are trying to convert ratios to fractions to percents.
Example: I want to know how much money I save when buying a sale item, but the information was given to me in ratios.

Sale Price: 2:3 of original price     Original Price: $21
2:3 = 2/5 = 40%
40% of $21 is $8.40
$21 - $8.40 = $12.60



1b. Give examples to explain how part-to-part rations are different from, but related to, part-to-whole ratios.
The difference between part-to-part ratios and part-to-whole ratios is; a part-to-part ratio shows the parts of the whole, but not the whole, and a part-to-whole ratio shows how one part compares to the total, but doesn't give the other parts. Part-to-part and Part-to-whole ratios are still related though, because both are ratios that represent the relationship between each of the numbers in a problem.

2a. How can you use scaling or equivalent ratios to solve a proportion? Give an example.
You can use scaling or equivalent ratios to solve a proportion by doubling each side of the smaller ratio until it gets to the larger one.
Example: Which drink is the most lemony?
Mix 1:  4 cups of concentrate: 9 cups of water
Mix 2: 1 cups of concentrate: 3 cups of water

1:3 ? 4:9
1:3 = 2:6 = 3:9
1:3 or 3:9 < 4:9

2b. How can you use scaling or equivalent ratios to make a decision? Give an example.
You can use scaling ratios to make a decision by converting them to fractions, decimals or percents and comparing them.
Example:
Mix 1: 1 cup of concentrate: 2 cups total      = 33.3% concentrate
Mix 2: 2 cups of concentrate: 3 cups total    = 66.6% concentrate
Mix 3: 4 cups of concentrate: 9 cups total    = 44.4% concentrate
Mix 4: 5 cups of concentrate: 12 cups total  = 41.6% concentrate