An in Depth Look at Ratios and Proportions and Their Applications

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

A unit rate identifies how much one item or quantity is worth. If Gatorade is on sale 2 for $3.00, How much does 1 cost?

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

Time1234 Distance