Ratio

Definition- A ratio is a quotient of two numbers.

Proportion

Definition- A proportion is an equation stating that two or more ratios are equal.

The Product and Ratio Theorems

• The first and the fourth terms are called the extremes
• The second and the third terms are called the means

Theorem- In a proportion, the product of the means equals the product of the extremes.

Theorem- If the product of a pair of nonzero numbers is equal to the product of another pair of nonzero numbers, then either pair of numbers may be made the extremes, and the other pair the means, of a proportion.

If pq=rs then
p/r=s/q
p/s=r/q
r/p=q/s
All of the above yield the same equation.

The Geometric Mean

Definition- If the means in a proportion are equal, either mean is called a geometric mean, or a mean proportional, between the extremes.

1/4=4/16
a/x=x/r