Rates & Ratios

A ratio is a comparison of two numbers. A ratio can be written using a colon, 3 : 5 , or as a fraction 3 5 .

A rate , by contrast, is a comparison of two quantities which can have different units. For example 5 miles per 3 hours is a rate, as is 34 dollars per square foot.

Example 1:

A punch recipe calls for 6 ounces of lime juice, 21 ounces of apricot juice, and 21 ounces of pineapple juice. What is the ratio of lime juice to apricot juice?

Writing the ratio using a colon, we get 6 : 21 .

Note that this can be reduced, like a fraction, by dividing both numbers by a common factor -- in this case, 3 . In simplest form, the ratio is 2 : 7 .

Example 2:

In the recipe above, what is the ratio of apricot juice to the total amount of punch?

To find the total amount of punch, add 6 + 21 + 21 = 48 .

The ratio of apricot juice to the total amount of punch is 21 : 48 . But this ratio is probably more clearly written as a fraction, since the apricot juice makes up a fraction of the whole.

21 48

To reduce the fraction, divide both the numerator and the denominator by 3 .

7 16

Note that this can be reduced, like a fraction, by dividing both numbers by a common factor -- in this case, 3 . In simplest form, the ratio is 2 : 7 .

Example 3:

An adult scolopendromorph centipede has 46 legs and 8 eyes. In a group of 100 centipedes of the same species, what is the ratio of legs to eyes?

Note that it doesn't matter if there are 100 or 10,000 centipedes; the ratio of legs to eyes will remain the same.

Writing the ratio using a colon, we get 46 : 8 .

Divide both numbers by 2 . In simplest form, the ratio of legs to eyes is 23 : 4 .

Example 4:

A bat beats its wings 170 times in 10 seconds. Write the rate as a fraction in lowest terms.

Write the rate as a fraction.

170 wingbeats 10 seconds

Divide both the numerator and the denominator by ten.

= 17 wingbeats 1 second

So, the rate is 17 beats per second.

Example 5:

A mountain climber is 3200 meters from the peak. He climbs 50 meters per hour for 8 hours per day. How many days will it be before he reaches the peak?

The first job is to figure out the rate per day.

50 meters 1 hour 8 hours 1 day = 50 ( 8 ) meters day

= 400 meters day

He is climbing at a rate of 400 meters per day.

Now divide 3200 by the daily rate to find the number of days it will take him to reach the top.

3200 meters 400 meters day = 8 days

d:T2038,

Rates & Ratios

A ratio is a comparison of two numbers. A ratio can be written using a colon, 3 : 5 , or as a fraction 3 5 .

A rate , by contrast, is a comparison of two quantities which can have different units. For example 5 miles per 3 hours is a rate, as is 34 dollars per square foot.

Example 1:

A punch recipe calls for 6 ounces of lime juice, 21 ounces of apricot juice, and 21 ounces of pineapple juice. What is the ratio of lime juice to apricot juice?

Writing the ratio using a colon, we get 6 : 21 .

Note that this can be reduced, like a fraction, by dividing both numbers by a common factor -- in this case, 3 . In simplest form, the ratio is 2 : 7 .

Example 2:

In the recipe above, what is the ratio of apricot juice to the total amount of punch?

To find the total amount of punch, add 6 + 21 + 21 = 48 .

The ratio of apricot juice to the total amount of punch is 21 : 48 . But this ratio is probably more clearly written as a fraction, since the apricot juice makes up a fraction of the whole.

21 48

To reduce the fraction, divide both the numerator and the denominator by 3 .

7 16

Note that this can be reduced, like a fraction, by dividing both numbers by a common factor -- in this case, 3 . In simplest form, the ratio is 2 : 7 .

Example 3:

An adult scolopendromorph centipede has 46 legs and 8 eyes. In a group of 100 centipedes of the same species, what is the ratio of legs to eyes?

Note that it doesn't matter if there are 100 or 10,000 centipedes; the ratio of legs to eyes will remain the same.

Writing the ratio using a colon, we get 46 : 8 .

Divide both numbers by 2 . In simplest form, the ratio of legs to eyes is 23 : 4 .

Example 4:

A bat beats its wings 170 times in 10 seconds. Write the rate as a fraction in lowest terms.

Write the rate as a fraction.

170 wingbeats 10 seconds

Divide both the numerator and the denominator by ten.

= 17 wingbeats 1 second

So, the rate is 17 beats per second.

Example 5:

A mountain climber is 3200 meters from the peak. He climbs 50 meters per hour for 8 hours per day. How many days will it be before he reaches the peak?

The first job is to figure out the rate per day.

50 meters 1 hour 8 hours 1 day = 50 ( 8 ) meters day

= 400 meters day

He is climbing at a rate of 400 meters per day.

Now divide 3200 by the daily rate to find the number of days it will take him to reach the top.

3200 meters 400 meters day = 8 days

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