Vocabulary
What is a ratio? How are they written?
A ratio is a comparison between two quantities. They are written as fractions (2/5), as text (two red crayons for every 5 blue crayons), or with a colon in between (2:5, which is read as 2-to-5).
A table says the following:
Students with brown hair: 10
Students with blonde hair: 6
Students with red hair: 2
What is the ratio of students with red hair to the total number of students? (Make sure to reduce)
2 to 18 (2:18, 2/18, etc.) which reduced to:
1 to 9 (1:9, 1/9, etc.)
Find the rate, then the unit rate:
Your parents gave you $50 for 10 hours of work around the house.
Rate: $50/10 hours
Unit rate: $5 dollars an hour,
Write this number as a percent:
31 over 50 (the fraction 31/50)
62%
How many centimeters are in 5 inches?
12.7.
There are 2.54 centimeters per inch.
What is an equivalent ratio?
Two ratios that describe the same relationship are equivalent. These are usually shown in tables.
In equivalent ratios, you can add or subtract quantities OR multiply or divide to get to the next quantity.
For instance:
Dogs: 1 2 3
Cats: 3 6 9
For dogs, the number increases by 1 each time. For cats it increases by 3. You will notice, however, that we can reduce each fraction to the same thing (1 dog to 3 cats, then 2:6 reduced to 1:3, then 3:9 can also reduce to 1:3)
Which ratio is not equivalent to the rest? How do you know?
3:4 (read as 3 to 4)
9:12
12:15
12:16
12:15 When reduced, it equals 3:5. The others reduce to 3:4
You get the following table. Give a rate, then a unit rate for the scenario:
Miles 90 150 210
Hours 1.5 2.5 3.5
Rate: 90 miles in 1.5 hours
Unit Rate: 60 miles per hour.
Write this number as a percent:
The mixed number 1 and one-half.
150%
How many meters are in 3 kilometers
3000m
Remember, kilometers are bigger, so there has to be more meters. The number we assigned to kilometers is 3, meaning we move the decimal 3 places. Because we know the end result has to be bigger, we move 3 to the right. Remember 3 is really 3.0. When we move 3 places to the right, we end up with 3000
What is a rate? Take that one step further and explain a unit rate as well.
A rate is a comparison between two quantities with different units. (Think about when we talk about how many miles a car goes on a certain number of gallons of gas)
A unit rate takes this one step further and compares a quantity of one unit to 1 unit of the other item. (Think about when we tell how many miles per a gallon a car goes...how far they can go on one gallon of gas. OR speed limits in miles per hour...how many miles you are allowed to travel in one hour)
You an a friend are selling pies for a school bake sale. You sell 3 pies for every 5 pies your friend sells. When you sell 12 pies, how many has your friend sold?
20. When you sold 12 pies, you've sold 4 sets of 3 pies (12/3=4), so you friend has also sold 4 sets of pies, but they sell 5 for every set. 4 times 5 is 20.
You run 3 kilometers in 18 minutes. At this rate, how long will it take you to finish a 5 kilometer race?
30 minutes
Why? 18 divided by 3, tell us that you run 1 km in 6 minutes, so to figure out how long it will take you to run 5 kilometers, take 5 kilometers times 6 minutes.
Write this percent as a fraction (make sure to reduce):
90%
Why? we put 90 over 100, and then reduce. We can take a 10 out of both, so it reduces to 9/10
How many pints are there in 1.5 gallons of water?
12.
There are 4 quarts per gallon and 2 pints per quart, so we know we have 8 pints in every gallon. 1.5 times 8 equals 12 pints.
What is a percent?
It's a part to whole ratio, but put into terms where the whole is actually 100 (also written as a fraction with a denominator (bottom number) of 100.
48 students are eating in the cafeteria. The ratio of boys to girls is 5:7. How many more girls than boys are eating in the cafeteria right now?
8
Why? We know that it's a 5:7 ratio. 5+7 is 12, so we can group the students into groups of 12. 48 divided by 12 is 4. This means we have 4 groups of students with a 5:7 ratio of boys to girls. If we have 4 groups, and each group has 2 more girls than boys, then we can take the number of groups and multiply it by 2 (how many more girls are in each group) and get a total of 8 more girls than boys.
Are these equivalent? Explain.
126 points in 3 games.
210 points in 5 games.
Yes.
126 points in 3 games gives a unit rate of 42 points per game. Likewise, 210 points in 5 games also gives a unit rate of 42 points per game. Since these are equal, the two are equivalent.
125% of what number is 50
40
Remember to set this up as equivalent ratios.
125 over 100 = 50 (the part) over x. Then cross multiply and solve for x.
I signed up for a race that claims to be 10 kilometers. I'm a little nervous because I don't actually know how far that is. How far will I be running?
6.2
Remember, miles are smaller than kilometers, so our end number has to be smaller. The conversion factor is 1.61 to get from miles to kilometers, so we can take the number of kilometers (10) and divide by the conversion factor (1.61) to get the answer.
What is a conversion factor?
It's a number that tells you how many of one unit is equivalent to another unit. For instance, there are 1.61 kilometers in every mile
Find two numbers that satisfy the following:
A + B = 30, Where A:B is equivalent to 2:3
12 and 18
These number can still reduce to 2:3, which means they are equivalent to it. They also add up to 30.
A school printer can print 28 pages in 8 minutes. How long would it take for the printer to print an additional 21 pages?
6.
Why? if we take 28 divided by 8, we find out that the printer can do 3.5 pages per minute. 21 pages divided by 3.5 pages per minute, will tell us that it takes 6 minutes to print those pages.
What is 3% of 52?
1.56
Why? 3% is 3 out of 100, so we can set the fraction 3 over 100 equal to the fraction x over 52 (part over whole). After we cross multiply, we get 100x = 156. This means that x is 1.56
Germany has a suggested speed limit, on the autobahn, of 130 kilometers per hour. Ms. Keesha decides to go to Germany and is driving 90 miles per hour. Is she sticking to the suggested speed limit?
No. 130 km per hour equals 80.75 miles per hour (130 divided by 1.61). Ms. Keesha is going too fast.