Module 15: Ratios

Question 1

Ratios can be expressed in three ways:

Answer 1

1) fractions
2) A : B
3) “A to B”

“There are 5 men and 10 women in a room.”

5/10 (or 5/15 if representing the whole # of ppl)
5 : 10
5 to 10

Question 2

Ratio Multiplier definition & how to find it (2 ways)

Answer 2

If the ratio of A:B is a to b, and x is the ratio multiplier, then ax represents the actual quantity of A, and bx for B.

** The ratio multiplier will not always be an integer. Keep the unit in mind to determine if it’s possible to have half of one.

1) If given the true quantity of one item in the ratio: Divide the true quantity by the ratio quantity
2) If given the total: Add up the value of all numbers in the ratio, divide the total by that number

Question 3

Is 4r / r + 50 a usable ratio? Why or why not?

Answer 3

NO - variables that are added/subtracted won’t be proportionate as the variable shifts. (Multiplication/division is OK)

Question 4

Adding or Subtracting to Achieve The Desired Ratio: 2 steps (and a note)

Answer 4

1) Determine how many of each item is actually present.
2) Let the number necessary to add to the desired ratio represent a variable, add or subtract it to the relevant piece of the ratio, and set that equal to the desired ratio. Then solve for the variable.

Note: be careful… remember to distinguish between part-to-part ratios (variable in numerator ONLY) and part-to-whole (variable in denominator definitely, in numerator if the same part in the question is the one being added).

Question 5

Express this proportion: “3 is to 7 as 18 is to ____.”

Answer 5

3/7 : 18/x

7/3 = ~2.4

18 * 2.4 = 42

3/7 : 18/42

Question 6

Positive Constant - Direct variation in ratios

Answer 6

When the ratio between two variables is direct:

y = kx, where K is a positive constant.

Question 7

Positive Constant - Inverse variation in ratios

Answer 7

When the ratio between two variables is inverse:

y = k/x, where K is constant.

Question 8

Express: “X is jointy proportional to y and z.”

Answer 8

x = k * yz

Question 9

Express: “X is inversely jointly proportional to y and z.”

Answer 9

x = k / yz

Question 10

Express: “X is inversely proportional to the cube of Y and directly proportional to the square root of Z.”

Answer 10

x = k * [ sqrt(z) / y^3 ]