Ratios and Rates:

A simple way to compare things

VocabularyRatio: a comparison of 2 quantities

using divisionExample: A band instructor may use a ratio comparing how many students are in the brass and stringed sections of the band. From this ratio, he may plan out how to fairly divide the time in a band concert.

There are sixteen band students who play brass instruments and twelve

students who play stringed instruments. The ratio is 16:12; 16 to 12; 16/12

What is the ratio in its simplest form?

Another example of how ratios are used in everyday life:

Researchers determine how much daily exercise is needed to increase an average person’s lifespan.

Their research may show that 30 minutes per day will increase the likelihood of living an additional ten (10) years. But, 60 minutes a day may add only 10 and ½

years. With this information, health experts make recommendations based on maximum benefit compared

to effort required.

People may use ratios in planning an exercise program. They may compare the length of their workouts when they first begin working out to their ultimate goal of time spent at the gym.

30 minutes to 60 minutes; 30:60; or 30/60

Equivalent Ratios

Equivalent ratios are ratios that name the same comparison. You can find an equivalent ratio by multiplying or dividing both terms of a ratio by

the same number.

Example: 3:6 is the same as 6:12. (You multiplied the top term and bottom term by 2.)

45:60 is the same as 3:4. (You divided the top term and bottom term by 15.)

What is a Rate?A rate is a way of comparing two (2) quantities that

have different units of measure. Example: A large package that contains twelve (12)

small bags of chips sells for $3.96. When the comparison is to one unit, the rate is called

a unit rate. In this example, you would divide the $3.96 by 12 and get a unit rate of $0.33/bag.

A smaller package contains six (6) equal sized bags of chips and sells for $2.40.

Which is the better value?

Unit Rate Word Problems

If Jonathan earns $18.00 for every 3 hour shift he works at the car wash, how much extra

will he earn if he works a 4 hour shift? How much will he earn

altogether for that day’s shift?

How do Teachers Determine my Grade?Equivalent Ratios

If Tyson got 16 out of 20 problems correct on his math quiz, his grade would be 16/20,

which = ?/100. What would Tyson’s grade be? Hint: You may simplify first, if you like.

Now, what if you scored 9 out of 20 correctly. What would be your grade?

Jogging Your Memory:

• What’s an easy way to remember 7x8?• What are two (2) other ways we can write the

ratio 5 to 7?• Which ratio is equivalent to 1/20?

a. 9:180 b. 180 to 9 c. 4:100 d. 100/4

Rate Word ProblemA dozen (12) eggs cost $1.25 at one grocery store. If you purchase (buy) the 18-count carton, the cost is $2.00. Which is the better buy?

$1.25/12 compared to $2.00/18

A Final Ratio Problem: Keeping Track of Gasoline Needed for a Trip

If Selena’s dad knows that Selena’s Honda allows her to drive 300 miles on 10 gallons of gas, how

many gallons of gas will Selena need to drive 450 miles to go visit her cousin at college?

Now, it’s your turn. Create a ratio or rate problem about something that

interests you. (You will share with the class.)