Summary
Highlights
A ratio is a comparison between two numbers or quantities with the same units. It can be expressed in four ways: colon form (e.g., 2:3), division form, phrase form (e.g., 'two is to three'), and fraction form (e.g., 2/3).
To simplify a ratio, divide both parts by their greatest common factor (GCF). Examples include converting units (hours to minutes, weeks to days) to ensure consistency before simplification, and understanding how to extract information to form the correct ratio from a word problem.
A proportion is an equation that shows two ratios are equal. It can be written as 'a is to b as c is to d' or a/b = c/d. For a proportion to be valid, the denominators (b and d) cannot be zero.
Two ratios form a proportion if the product of their means (inner terms) equals the product of their extremes (outer terms) (a*d = b*c). Alternatively, if two ratios can be simplified to the same lowest term, then they are equal and form a proportion.
The video introduces several properties: cross-multiplication (a*d = b*c), alternation (a/c = b/d), inverse (b/a = d/c), addition ( (a+b)/b = (c+d)/d ), subtraction ( (a-b)/b = (c-d)/d ), and sum property ( (a+c)/(b+d) = a/b ).
Examples demonstrate how to apply the different properties of proportion to complete statements or find equivalent forms of a given proportion.
The cross-multiplication property is used to solve for missing values in a proportion. This involves setting up the cross products and solving the resulting linear equation. Examples include solving for 'x' or 'b' in various proportion formats, including those with fractions and polynomials.