Ratio and Proportion

A ratio is the quotient of two numbers of like quantities and is of the form

A ratio can be expressed as:

Example: If the Red Sox win 96 games of the 162 games played. What is the ratio of

wins to games played?

A rate is the ratio of unlike quantities

Example: A person earns $140 for 8 hours of work. What is the person’s hourly rate?

Problems

(1) Write each ratio in simplest form:

(a) $1500 to $250

(b) 300 miles to 750 miles

(c) 12 hours to 8 hours

(d) In a town election, 850 people voted for a tax increase, 1250 people voted against the tax increase. What is the ratio of those who voted against the tax increase to those who voted for a tax increase?

(2) Write each rate in simplest form:

(a) 400 miles to 16 gallons of gas

(b) 48 hits to 150 times at bat

(c) 8 cups of milk to 2 cups of flour

(d) 25 carbohydrates to 10 ounces of food

Answers

(1)

(a)

(b)

(c)

(d)

(2)

(a)

(b)

(c)

(d)

Proportion

A proportion is a statement of equality between two ratios and is of the form:

Rule of proportions:

Examples:

(a)

(b) A scale on a map is inch to 50 miles. What is the distance between 2

cities that are 8 inches apart on the map?

Problems

(1) 12 gallons of gasoline are used to travel 264 miles. How many gallons would be used

to travel 462 miles?

(2) 30 deer are tagged in a wildlife preserve. Later, 50 deer are captured and 3 are

tagged. Estimate the number of deer in the preserve.

(3) A recipe requires 3 cups of flour for 5 cups of milk. How many cups of flour are

required for 3 cups of milk?

Answers

(1) 21 = n

(2) n = 500

(3)