Ratios
What is the definition of a ratio? Provide an example
A ratio is a comparison of two quantities by division. Example: 3:4 or 3/4
What is a unit rate? Give an example.
A unit rate compares a quantity to one unit of another quantity. Example: 60 miles per 1 hour (60 mph).
What is a proportion?
A proportion is an equation that states two ratios are equal.
How would you express the part-to-part ratio of 10 brown beads to 8 red beads?
10:8 or 5:4 (simplified)
What is the unit price of an item?
The cost per single unit of the item.
Solve for x:
2/3 = x/6
x = 4
At a bakery, a sugar cookie recipe calls for a 2:3 ratio of flour to sugar. How many cups of flour will you need for 12 cups of sugar?
8 cups of flour
Express the ratio of 90 wins to 72 losses in two different ways.
90:72 and 5:4 (simplified)
Calculate the unit rate if you travel 960 kilometers in 10 and a half hours.*Round to the nearest tenth*
91.4 km/h
If you have the ratios 1:2 and 3:6, are they equivalent? Explain.
Yes, they are equivalent because 1/2 = 3/6.
What is the part-to-whole ratio of 5 blue beads in a total of 23 beads?
5:23
If a 10-pound bag of rice costs $5, what is the unit price per pound?
$0.50 per pound.
Solve for x:
5/8 = x/24
x = 15
A car's fuel efficiency is 25 miles per gallon. If the car's gas tank holds 15 gallons, how far can it travel on a full tank?
375 miles
If there are 2 red marbles, 6 green marbles, and 4 blue marbles, what is the three-term ratio?
2:6:4 or 1:3:2 (simplified).
If you buy 4 kg of potatoes for $3.25, what is the unit price per kg? *Round to the nearest hundredth*
$1.23/kg
Solve for x in the proportion
3/x = 6/12
x = 6
If a class has 12 boys and 8 girls, what is the part-to-part ratio of boys to girls?
12:8 or 3:2 (simplified)
Determine the unit price if 6 cans of soda cost $3.00.
$0.50 per can.
Solve for x:
3/5 = 12/x
x = 20
You are trying to win the town's annual contest for the biggest pumpkin. To improve your chances you are planting 100 pumpkins. In order to plant 5 pumpkins, you require 4 pounds of soil and 1.5 pounds of fertilizer. How many pounds of soil and fertilizer do you need in total?
80lbs of soil and 30lbs of soil
100/5 = 20
4 x 20 = 80
1.5 x 20 = 30
Explain the difference between a part-to-part ratio and a part-to-whole ratio.
A part-to-part ratio compares two parts of a whole, while a part-to-whole ratio compares one part to the total.
How do you determine the unit rate from a ratio of two quantities?
Divide the first quantity by the second to find the amount per 1 unit.
Provide an example of a proportion using real-life quantities.
If 2 cups of flour make 12 cookies, then 4 cups of flour will make 24 cookies. (2:12 = 4:24 or
2/12 = 4/24
Provide an example of a part-to-part ratio in a fruit basket with apples and bananas.
If there are 7 apples and 5 bananas, the part-to-part ratio is 7:5.
How does finding the unit price help consumers make decisions?
It helps consumers compare costs and choose the most economical option.
Solve for x:
7/x = 14/21
x = 10.5
A school's student council has 25 members, and the ratio of the number of boys to the number of girls is 2:3. How many members are girls?
15 girls
25/5 = 5
5 x 2 = 10
5 x 3 = 15
Simplify the ratio 10:8 and express it in lowest terms.
5:4
If you travel 240 kilometers in 4 hours, what is your speed in kilometers per hour?
60 km/h
Explain how to check if two ratios form a proportion.
Cross-multiply the terms. If the products are equal, the ratios form a proportion.
Compare the part-to-part ratio of 15 cats to 10 dogs and simplify it.
15:10 or 3:2 (simplified).
If you buy 3 notebooks for $4.50, what is the unit price per notebook?
$1.50 per notebook.
Solve for x:
(4x)/5 = 16/20
x = 1
A group of 6 friends are going camping and owe $378 for their site. Bill will pay for Sandra and himself, James is going alone and will pay for himself. Lily invited Maria and Matty so she is going to cover their share. Determine the 3-term ratio and how much money Bill, James, and Lily will each owe.
2:1:3, Bill owes $126, James owes $63, and Lily owes $189
378/6 = 63
63 x 2 = 126
63 x 3 = 189