Lesson 6 — Activity 1: Understanding Rates

$Speed signs show rates.$

$This ad also shows a rate.$

$On the road to Calgary$

$There are ways to determine the best price for products.$

$Image 3$ SALE:

4 bags of chips for $3.96

Check your answer here:

$Now you will compare items to see which is a better value.$

$22.89 ÷ 3 = $7.63 a pizza

$16.95 ÷ 2 = $8.48 a pizza

Lesson 6 — Activity 1: Understanding Rates

Getting Ready

Sometimes it is necessary to be able to compare two different things in order to find an answer. One way to do this is to figure out a rate.

The following are examples of rates:

A rate is a comparison of two different measurements with different units.

Here are some further examples:

If you tell me you travelled to Calgary at 110 km/h, you have given me a rate, because you are comparing distance and time. You also might have heard of someone running at so many metres per second. This is another rate.

Rates always compare two items in the lowest possible terms.

For example, you never hear someone say, "I travelled 220 km/2hrs." Instead they would say, "I travelled 110 km/h." They have reduced both numbers to the lowest possible limits. This was done because both numbers are divisible by 2.

Sometimes rates will be expressed in a way that is not a number compared to only one of the other numbers. This may sound complicated, but it isn't.

Let's say that you made 6 tiny car models in 40 minutes. What rate did you make the models? Both numbers are even so they both can be divided by 2.

Because 20 and 3 are not evenly divisible by any number, you cannot reduce the fraction any further.

Therefore the answer to the question would be that you can make 3 car models every 20 minutes.

You can also use rates to figure out other information.

For example, if you travel at a rate of 100 km/h, it is easy to figure out how far you will have gone in 6 hours. Simply multiply the rate by the time.

100 km/h x 6 = 600km

You will travel 600 km in 6 hours.

Perhaps the question is how long it will take you to travel 900 km. In that case, you will divide the distance by the rate.

900 ÷ 100 km/h = 9h

It will take you 9 hours to travel 900 km at 100 km/h.

It will take you 9 hours to travel 900 km at 100 km/h.

Comparing Prices

You can use unit rates to compare prices. This will help you determine if a product is a good buy.

Say you noticed a sale on potato chips at your local grocery store.

SALE:

4 bags of chips for $3.96

Is it a good deal? That would depend upon how much each individual bag cost. Unit price information can be used to calculate the cost per item.

$3.96 ÷ 4 bags of chips = $0.99 a bag

That sounds like a pretty good deal!

Try this:

Say you noticed that soup was offered at 6 cans for $3.56. Solve to find out how much each individual can of soup cost.

$3.56 ÷ 6 = $0.59 a can

You can also use unit pricing to find out which size of product is a better value for the money. Calculating unit prices allows comparisons to be made.

You may come across this kind of information when you are considering buying pizza:

3 large pizzas go for $22.89 or 2 large pizzas go for $16.95. Which is the better buy?

You can do this in parts:Part 1: Find the cost of 1 pizza if 3 pizzas were purchased.

$22.89 ÷ 3 = $7.63 a pizza

Part 2: Find the cost of 1 pizza if 2 pizzas were purchased.

$16.95 ÷ 2 = $8.48 a pizza

You can see from this that the better buy is 3 large pizzas for $22.89.

For example, you never hear someone say, "I travelled 220 km/2hrs." Instead they would say, "I travelled 110 km/h."

They have reduced both numbers to the lowest possible limits. This was done because both numbers are divisible by 2.

For example, if you travel at a rate of 100 km/h, it is easy to figure out how far you will have gone in 6 hours.

Simply multiply the rate by the time.

Perhaps the question is how long it will take you to travel 900 km.

In that case, you will divide the distance by the rate.

$Image 3$ SALE:

You can do this in parts:

Part 1: Find the cost of 1 pizza if 3 pizzas were purchased.