Rates, Ratios, and Percentages

Question 1

1. what is ratio
2. how are ratios expressed? (usually!!)
3. what is something important that matters for ratios?
4. when is this thing unimportant, exceptionally?

Answer 1

1.
ratio is how much of something you have per unit of something else, expressed in smallest integers (so that neither number is a decimal!) = how much you have for (every time you have) y units of something else.
2.
- x:y
- x/y
- x to y
3.
order of numbers is important, because ratio of something given a number of y must be expressed as something:y !!! (not the opposite way around, otherwise for every given unit of y you get a different (smaller than one instead of larger than one or viceversa) decimal number)!!!
4.
order of fraction is unimportant when x and y have same ABSOLUTE value (might have different signs), because ratio will always = 1 or -1.

Question 2

what is a proportion and how can you solve?

Answer 2

• proportion is an equality of ratios (two things have different magnitude (they are not expressed as x:1 (number given one unit of y) or as number given a specific units of y), but different units of y, so that units of x will also differ, but differ in the same proportion. A proportion is saying that two ratios are the same but just elongated / shrunk
• you can solve by cross multiplying!!

Question 3

what is a fraction?

Answer 3

n/d with n numerator and d denominator

Question 4

special kinds of fraction and what they are (3+3)

Answer 4

• equivalent fractions = fractions that are the same. <=> they are = when reduced to their lowest term (through greatest common divisor = gcd)
• reciprocal fractions = reciprocal of n/d = d/n
• mixed numbers = numbers represent partly by a number and partly by a fraction (8 1/5 = 8 + 1/5 (fraction unrelated to integer, but to convert whole number into fraction turn integer into fraction using 5 (fraction’s denominator) as denominator!!!))

Question 5

1. what is a percent?
2. how is percent usually written?
3. how does a percentage differ from a ratio?
4. how do you convert percentage to fraction?

Answer 5

1. units expressed as units given that you have 100y
2. • percent
   • per hundred
   • n number out of 100

3.
percentage can be a decimal, since 10 is given you don’t always have a relation btw integers!!!

4.
percentage can be turned into a ratio by:
- if percentage smaller than 1 then multiply the decimal by a number that gives you the lowest possible integer both in numerator and in denominator (multiply n and d by same number!!!)
- if percentage greater than 1 then divide by number (even decimal number) that gives you the lowest term fraction (so smallest ratio with integers). If not possible to divide by a decimal, multiply the decimal number greater than one and 100 by the same number, and try simplifying through largest factor method (reduced fraction to lowest terms).