Unit Rate
Imagine a new theater has opened across town. You call to see how much
their tickets cost, anticipating that their matinée (afternoon entertainment)
tickets will be in the $4.00 - $5.00 range and the evening shows will cost
anywhere from $6.00 to $9.00. When you ask how much their tickets cost,
their answer surprises you. "Our price for the evening movies are $2,452.50
for 327 tickets." Well ... that's annoying.
Now imagine you are driving a car (about five years from now). You look
down to check your speed and the speedometer indicates you that you are
travelling 469 mpsaoth (miles per seven-and-one-third hours). Irrrrritating.
You may not have thought about this before, but people like a "denominator of one." That is, we want to know the price for one ticket, or one gallon of milk, or one pair of jeans. And we want to know how fast we are going in miles per one hour. This is called the unit price or unit rate. Unit means one person or thing.
rate: a ratio comparing two quantities with different kinds of units
unit rate: a rate that is simplified so that it has a denominator of 1
unit price: the cost per unit
When we compare the number of red m&m's to green m&m's in a bowl, it might seem like they are different items, but they are both the same hard-shelled candies, each containing about the same number of calories.
We compare their quantities by using ratios, such as 5 to 7. It may also seem like we are comparing something different when we compare apples to oranges, cats to dogs, or boys to girls. But we aren't. These comparisons are between fruits, pets and genders. As stated above, a rate compares different kinds of units, such as miles to hours, pounds to inches, or dollars to movie tickets.
When we work with fractions, we are used to simplifying them by finding a common factor. 15/20 becomes 3/4 because we divide the numerator (top) and denominator (bottom) by the common factor 5. With unit rate, we always divide by the number in the denominator. For example, if a snail crawls 15 inches in 20 minutes, we can represent this as a fraction:
15 inches
20 mins
Now divide the numerator and the denominator by the number in the denominator (20). This gives us a unit rate of .75 inches per minute, the speed of snail.
Every bit as important as the numbers are the units, or labels. A carefully arrived at answer of 2.54 will also result in partial or full credit be subtracted, because the number itself tells the reader nothing. Include the units to show that there are 2.54 cm/inch. The slash ( / ) means "per" or it can be read as "for every." For example, the snail crawls .75 inches for every minute, or there are 2.54 centimeters for every inch.
It is very important to pay attention to the setup of a rate problem. For example, "Tastee Burgers uses 20 pounds of fresh hamburger meat to make a batch of 32 sandwiches. How many sandwiches can they make with one pound of hamburger?" Don't be too quick to reach for the calculator and type 20 ÷ 32 = .625. It does, but that wasn't the question.
Rewrite the question: How many sandwiches per 1 lb of hamburger?
Set up a fraction using the given information. 32 sandwiches
20 pounds
Divide the top and bottom by the number in the denominator (20).
This gives us 1.6 sandwiches per lb. of hamburger.
So what does .625 represent? That is the answer to the question,
"how many pounds of hamburger are there in one sandwich?"
their tickets cost, anticipating that their matinée (afternoon entertainment)
tickets will be in the $4.00 - $5.00 range and the evening shows will cost
anywhere from $6.00 to $9.00. When you ask how much their tickets cost,
their answer surprises you. "Our price for the evening movies are $2,452.50
for 327 tickets." Well ... that's annoying.
Now imagine you are driving a car (about five years from now). You look
down to check your speed and the speedometer indicates you that you are
travelling 469 mpsaoth (miles per seven-and-one-third hours). Irrrrritating.
You may not have thought about this before, but people like a "denominator of one." That is, we want to know the price for one ticket, or one gallon of milk, or one pair of jeans. And we want to know how fast we are going in miles per one hour. This is called the unit price or unit rate. Unit means one person or thing.
rate: a ratio comparing two quantities with different kinds of units
unit rate: a rate that is simplified so that it has a denominator of 1
unit price: the cost per unit
When we compare the number of red m&m's to green m&m's in a bowl, it might seem like they are different items, but they are both the same hard-shelled candies, each containing about the same number of calories.
We compare their quantities by using ratios, such as 5 to 7. It may also seem like we are comparing something different when we compare apples to oranges, cats to dogs, or boys to girls. But we aren't. These comparisons are between fruits, pets and genders. As stated above, a rate compares different kinds of units, such as miles to hours, pounds to inches, or dollars to movie tickets.
When we work with fractions, we are used to simplifying them by finding a common factor. 15/20 becomes 3/4 because we divide the numerator (top) and denominator (bottom) by the common factor 5. With unit rate, we always divide by the number in the denominator. For example, if a snail crawls 15 inches in 20 minutes, we can represent this as a fraction:
15 inches
20 mins
Now divide the numerator and the denominator by the number in the denominator (20). This gives us a unit rate of .75 inches per minute, the speed of snail.
Every bit as important as the numbers are the units, or labels. A carefully arrived at answer of 2.54 will also result in partial or full credit be subtracted, because the number itself tells the reader nothing. Include the units to show that there are 2.54 cm/inch. The slash ( / ) means "per" or it can be read as "for every." For example, the snail crawls .75 inches for every minute, or there are 2.54 centimeters for every inch.
It is very important to pay attention to the setup of a rate problem. For example, "Tastee Burgers uses 20 pounds of fresh hamburger meat to make a batch of 32 sandwiches. How many sandwiches can they make with one pound of hamburger?" Don't be too quick to reach for the calculator and type 20 ÷ 32 = .625. It does, but that wasn't the question.
Rewrite the question: How many sandwiches per 1 lb of hamburger?
Set up a fraction using the given information. 32 sandwiches
20 pounds
Divide the top and bottom by the number in the denominator (20).
This gives us 1.6 sandwiches per lb. of hamburger.
So what does .625 represent? That is the answer to the question,
"how many pounds of hamburger are there in one sandwich?"
Now You Try
Unit Rate Story | |
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