An in Depth Look at Ratios and Proportions and Their Applications

Ratios Equal Ratios Proportions Special Ratios Constant Ratios

are the comparison of two or more numbers.

Which ratio shows the ratio of 2 fish to 3 bear? A B C D E

Which ratio shows the ratio of 1 soccer ball to 3 basketball? A B C D E

Which ratio shows the ratio of 3 butterflies to 1 apple? A B C D E

Three Ways to Write a Ratio The ratio of 3 boys to 5 girls can be written as: a) 3 to 5 b) 3: 5 c)

Equal ratios are like equivalent fractions. They name the same quantity.

Examples of Equal Ratios :

Two equal ratios form a proportion.

In a proportion the product of the means is equal to product of the extremes.

3 : 5 = 6 : 10 Extremes Means

Extremes 6 x 5 = 3 x = 30

Determine if the following are proportions. 1) 2)

3 x 60 = 5 x = 180 Yes, it is a proportion. 4 x 15 = 8 x No, it is not a proportion.

Corresponding sides of Similar Triangles have the same ratio. Corresponding Angles of Similar Triangles have congruent angles

A is similar to D Triangle A Triangle D

A B C D E F <A  <D<C  <F <B  <E

C A B D FE 4 3 x 6 y Use a proportion to find x and y. 5

Another type of special ratio is a constant ratio or rate. Distance = rate x time is an example of a constant ratio.

Time1234 Distance