Ch 5 Ratios & Proportion Vocabulary

Ratio

A comparison of two quantities using division; ratios can be expressed in 3 different ways (to, colon or as a fraction); ratios must ALWAYS be in simplest form

Rate

A comparison of two quantities with different units and uses the term per

complex fraction

A fraction has at least one fraction in the numerator, denominator, or both. You may need to simplify complex fractions when finding ratios and rates.

Equation

A number sentence containing an equal sign. ex. x+7=9

Unit Rate

A rate with a denominator of 1; money should always be in the numerator when finding unit rate

Ratio Table

A table with columns filled with pairs of numbers that have the same ratio.

Proportion

An equation stating that two ratios are equivalent.

Testing for Direct Variation

Since all Direct Variation equations MUST pass through the origin (0,0), we will use (0,0) as our test coordinates on all equations EXCEPT division. x and y SHOW direct variation when you substitute (0,0) into the equation and you get a true statement (for ex. 2=2) x and y DO NOT SHOW direct variation when you substitute (0,0) into the equation and you DO NOT GET A TRUE STATEMENT (for ex. 3= -5)

Greatest Common Factor (GCF)

The largest of the common factors of two or more numbers

simplest form

The lowest form of a fraction.

Equalivalent Ratios

Two equal ratios that are multiplied or divided by the same number

Proportional

Two ratios that form an equivalent proportion; these ratios simplify to the same ratio

direct variation

an equation of the form y=kx when a line passes through the origin; k (slope) is called the constant of proportionality.

negative slope

falls from left to right

cross products

from the proportion, the products of numbers on the diagonal

zero slope

horizontal line

Graph of Direct Variation

must go through the origin (0,0) AND must be a line

positive slope

rises from left to right

constant of proportionality

slope; k = y/x

Pay rate

the amount of money ($) workers are paid per hour, week etc.

slope

the rate of change between any 2 two points on a line. It is a measure of the steepness of a line. To find the slope of a line, find the ratio of the change in y (vertical change) to the change in x (horizontal change). slope = change in y/change in x slope = rise/run

undefined slope

vertical line

Cross Product Method

when the cross products of a proportion are equal, the ratios are proportional