Ratio: A comparison between two or more values measured in the same units. (ex: 5 apples compared to 3 apples. They are both measured in APPLES).
Rate: A comparison between two values measured in different units. (ex: 100km in 1 hour, one is measured in kilometers, the other in hours).
These are the differences between a ratio and a rate: A ratio can compare more than 2 values, but a rate can only compare 2. A ratio can only compare the same units, a rate can compare different units.
Page 60, question 4:
Determine the unit rate in each.
a) An Orca swims 110km in 2 hours. In order to figure this out, I use a ratio table. But since i can't draw one on here, I will just explain the steps. First, you find the rate. The rate in this case is 110km/2h. In order to get a unit rate you have to change the last value to 1. In this case, you would divide 2h by 2 to get 1h. BUT REMEMBER... WHAT YOU DO TO ONE SIDE, YOU DO TO THE OTHER! So, now we have to divide 110km by 2, to get 55km. This means that our unit rate is 55km/h.
I think that pretty much explains how to do unit rates, so lets move on to a question on page 62.
Page 62, question 14.
Conversion rates among currencies vary from day to day. The numbers in the table give the value in foreign currency of one Canadian dollar, on one particular day.
$1.00 Canadian= $0.8857 US= $1.1527 Australian= 0.694 European Union Euros.
What is the value of $600 Canadian in euros?
In order to figure this out, we need to figure out the unit rate. In this case, it would be
This is our question: ? euros/ $600 Canadian
So far, we have multiplied the Canadian dollars by 600. Now, we have to multiply the euros by 600 because, as I said before... WHAT YOU DO TO ONE SIDE, YOU MUST DO TO THE OTHER! 0.694 X 600= 416.4 This means that the answer is 416.4 euros/$600 Canadian.
Here is a question from the COIN MATH that can be answered as a rate:
How many coins are there per 1 cm of the jar?
1/2 pound ground beef
1 med. onion diced
1 celery finely sliced
1 clove of garlic
14 oz can of tomatoes chopped
1/2 can of tomatoe paste
1 tsp. Parsley
1 1/2 tsp. Basil
1 tsp. Oregano
1 tsp. Sugar
1/2 tsp. Worchestershire Sauce
1/2 tsp. Seasoning Salt
1 bay leaf
This recipe serves 4 people. (It is spaghetti sauce).
1) What would the recipe look like if you had to serve 10 people?
Alright, first how do you get to 10 from 4? Well, you can multiply it by 2.5! That means that you have to multiply all of the ingredients by 2.5.
0.5 x 2.5= 1.25lb ground beef
1 x 2.5= 2.5 med. onion diced
1 x 2,5= 2.5 celery finely sliced
1 x 2.5= 2.5 clove garlic
14 x 2.5= 35 oz can tomatoes chopped
0.5 x 2.5= 1.25 can of tomato paste
1 x 2.5= 2.5 tsp. Parsley
1.5 x 2.5= 3.75 tsp. Basil
1 x 2.5= 2.5 tsp. Oregano
1 x 2.5= 2.5 tsp. Sugar
0.5 x 2.5= 1.25 tsp. Worchestershire Sauce
0.5 x 2.5= 1.25 tsp. Seasoning Salt
1 x 2.5= 2.5 Bay leafs
2) What would the recipe look like if you only had to serve one person?
To get from 4 to 1, you have to divide by 4. So, now we have to divide everything by 4.
0.5/4= 0.125lb ground beef
1/4= 0.25 med. onion diced
1/4= 0.25 celery finely sliced
1/4= 0.25 clove garlic
14/4= 3.5 oz can of tomatoes chopped
0.5/4= 0.125 can of tomato paste
1/4= 0.25 tsp. Parsley
1.5/4= 0.372 tsp. Basil
1/4= 0.25 tsp. Oregano
1/4= 0.25 tsp. Sugar
0.5/4= 0.125 tsp. Worchestershire Sauce
0.5/4= 0.125 tsp. Seasoning Salt
1/4= 0.25 bay leaf
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