Unit Rates

Unit rates are a ratio comparing one unit of one item to a quantity of another.  The most common unit rate is miles per hour.  The interstate speed limit is 70 miles per hour which literally means (barring any changes of speed due to accidents, getting off the interstate, bad traffic etc) that you would travel 70 miles in 1 hour.  This is usually represented as a ratio:

70 miles to 1 hour

70 miles : 1 hour

70 miles
1 hour

In class, we have been going over unit rates in terms of chewy gummy worms.  Let's say we have a giant gummy worm that is multi-colored.  Each color represents a segment.  Let's say we have a 4 segment chewy gummy worm and it looks like this:

If we divide this worm for 4 people, each person would get 1 segment, so the unit rate would be 1 segment per person.  If we only had two people, each person would get 2 segments, so the unit rate would be 2 segments per person.  But what if we have 8 people?

Here, we have to cut each segment in half, meaning each person would get 1/2 segment.  The unit rate now would be 1/2 segment per person.  This can be done a different way, but the ultimate goal would be to reach the 1/2 segment per person ratio (unit rate).

You can do this without drawing a picture.  Just divide the amount of segments by the number of people.  Below are two examples.

If we have an 8 segment worm divided among 6 people, you can set it up like a fraction (see picture).  We have 1 6 inside of 8, so we pull it out.  That leaves us with 2/6 left, which reduces to 1/3.  So the unit rate would be 1 1/3 segments per person.  What if the you have more people than segments?

Take 8 segments and divide it by 12 people.  Basically, simplify the fraction 8/12 by dividing both the numerator and the denominator by the GCF (4).  This give you 2/3.  The unit rate would be 2/3 of a segment per person.

The key when doing unit rates by fractions is to make what you want to be the 1 on the bottom (in this case we wanted PER PERSON).  Then simplify the fraction or divide.