SAT Math: Ratios, Proportions and Percentages Flashcards

Question 1

Define Part-to-Part Ratio.

Accepted Answer

A ratio that compares one portion of a group with another portion of the same group, without involving the total, such as boys to girls in a class.

Question 2

Define Ratio to Fraction of the Total.

Accepted Answer

To turn a part-to-part ratio a:b into a fraction of the whole, add the parts for the denominator, so the first share is a/(a + b).

Question 3

Define Total Parts Method.

Accepted Answer

A way to split a quantity in a given ratio: add the ratio numbers to get the total parts, find the size of one part, then multiply.

Question 4

Define Three-Term Ratio.

Accepted Answer

A ratio such as a:b:c comparing three quantities at once; two ratios sharing a middle term combine into one by scaling the shared term to match.

Question 5

What is Rate?

Accepted Answer

A ratio between two quantities measured in different units, such as miles and hours or dollars and pounds, showing how one changes per amount of the other.

Question 6

Define Unit Price.

Accepted Answer

The cost of a single unit of an item, found by dividing total price by the number of units; comparing unit prices shows the better deal.

Question 7

Define Conversion Factor.

Accepted Answer

A fraction equal to 1 whose top and bottom are the same amount in different units, used to change units without changing the size of a quantity.

Question 8

Define Dimensional Analysis.

Accepted Answer

Chaining conversion factors so that unwanted units cancel between numerator and denominator, leaving only the units the answer needs.

Question 9

Define Converting Square Units.

Accepted Answer

When converting areas, square the linear conversion factor, because area has two dimensions; for cubic units, cube it.

Question 10

What is Density?

Accepted Answer

The mass of a substance per unit of volume, written as mass divided by volume, so it links the two quantities as a rate.

Question 11

Define Population Density.

Accepted Answer

The number of people (or other individuals) living per unit of area, calculated as population divided by land area.

Question 12

Define Proportional Relationship.

Accepted Answer

A relationship where one quantity is always the same multiple of another, written y = kx, whose graph is a straight line through the origin.

Question 13

Define Inverse Variation.

Accepted Answer

A relationship in which the product of two quantities stays fixed, written xy = k or y = k/x, so doubling one halves the other.

Question 14

Define Setting Up a Proportion.

Accepted Answer

Writing two equal ratios with matching units in the same positions, such as feet over seconds on both sides, before solving for the unknown.

Question 15

Define Area Scale Factor.

Accepted Answer

When every length of a shape is multiplied by k, its area is multiplied by k squared, because area depends on two lengths.

Question 16

Define Volume Scale Factor.

Accepted Answer

When every length of a solid is multiplied by k, its volume is multiplied by k cubed, since volume depends on three lengths.

Question 17

Define Percent Equation.

Accepted Answer

The relationship part = percent × whole, with the percent written as a decimal, which solves any question asking for a part, a whole, or a rate.

Question 18

Define Decimal Multiplier.

Accepted Answer

The decimal you multiply by to apply a percentage in one step: 100% plus an increase, or 100% minus a decrease, written as a decimal.

Question 19

Define Percent Change Formula.

Accepted Answer

Percent change equals (new value minus original value) divided by the original value, times 100; a negative result means a decrease.

Question 20

Define Successive Percent Changes.

Accepted Answer

Two or more percentage changes applied one after another, combined by multiplying their decimal multipliers rather than adding the percentages.

Question 21

Define Reverse Percentage.

Accepted Answer

Finding the original value before a percentage change by dividing the new value by the decimal multiplier instead of subtracting the percent.

Question 22

Define Percentage Points.

Accepted Answer

The plain arithmetic difference between two percentages; it differs from percent change, which measures that difference relative to the starting percentage.

Question 23

Define Percent of a Percent.

Accepted Answer

Taking a percentage of something that is itself a percentage of a whole; multiply the two decimals to find the share of the whole.

Question 24

What is Markup?

Accepted Answer

The amount a seller adds to the cost price to set the selling price, usually given as a percentage of the cost.

Question 25

Define Sale Price.

Accepted Answer

The price paid after a percentage discount, found in one step by multiplying the original price by 1 minus the discount rate.

Question 26

Define Sales Tax.

Accepted Answer

A percentage of a purchase price added on at the till; the total paid is the price times 1 plus the tax rate.

Question 27

Define Simple Interest.

Accepted Answer

Interest earned only on the original principal, calculated as I = Prt, where P is principal, r the annual rate as a decimal and t the years.

Question 28

Define Compound Percent Growth.

Accepted Answer

Repeated growth by the same percentage each period, modelled as P(1 + r)^t, so each increase is calculated on the latest value rather than the original.

Question 29

Define Exponential Decay Factor.

Accepted Answer

The base 1 minus r in a model P(1 - r)^t, describing a quantity that loses the same percentage of its current value every period.

Question 30

Define Relative Frequency.

Accepted Answer

The number of times a category occurs divided by the total number of observations, giving a fraction or percentage of the whole data set.

Question 31

Define Weighted Average.

Accepted Answer

An average in which each value counts in proportion to its weight or group size, found by summing value times weight and dividing by total weight.

Question 32

Define Speed, Distance and Time.

Accepted Answer

Speed is the rate of distance covered per unit of time, so distance = speed × time and time = distance ÷ speed when speed is constant.