Ratios
What is the ratio of 3 apples to 4 oranges?
3:4
3 to 4
3/4
What is a rate? Give an example
A rate is a comparison of two different quantities. Example: 60 miles per hour; 12 inches per foot, 2 apples per dollar, etc.
What is a unit rate?
A unit rate is a rate in which the second quantity is 1
What are equivalent ratios?
Ratios that express the same relationship between two quantities
A recipe requires 4 cups of flour for every 2 cups of sugar. What is the ratio of flour to sugar?
4:2 simplifies to 2:1 when we divide both sides by 2
Write the ratio of 5 dogs to 2 cats in three different forms.
5:2
5/2
5 to 2
If you can type 40 words in 1 minute, what is your typing rate?
40 wpm (words per minute)
or 40:1
If 3 notebooks cost $6, what is the unit rate per notebook?
2 notebooks
6 / 3 = 2
Are the ratios 1:2 and 2:4 equivalent? Explain.
Yes, both simplify to be 1:2
If Lisa can read 5 books in 2 weeks, how many books can she read in 6 weeks?
15 books.
5:2 multiply both sides by 3 to get from 2 to 6 - do the same to the other side. 5 x 3 = 15
If there are 8 boys and 12 girls in a class, what is the ratio of boys to girls in simplest form?
2:3
2 to 3
2/3
If a car travels 150 miles in 3 hours, what is the rate of speed?
150 / 3 = 50 mph (miles per hour)
A car uses 12 gallons of gas to travel 300 miles. What is the unit rate of miles per gallon?
300 / 12 = 25 mpg (miles per gallon)
Write an equivalent ratio for 3:4.
Answers will vary.
x2 = 6:8
x3 = 9:12
x5 = 15:20
x10 = 30:40
A car travels 120 miles on 3 gallons of gas. What is the rate of miles per gallon?
120 / 3 = 40 miles per gallon
Create a visual model to represent the ratio 2:5 using squares and circles.
2 squares to 5 circles
A recipe requires 2 liters of water for every 5 liters of juice. What is the rate of water to juice?
2 to 5
2/5
If a package of 8 cookies costs $4, what is the unit rate for one cookie?
4 / 8 = 0.5 or $0.50 or 50 cents per cookie
The ratio of 5:10 is equivalent to what other ratio?
1:2
10:20
15:30
If a school has 120 students and the ratio of boys to girls is 3:5, how many girls are there?
75 girls.
Make a table
G | Students
5 (x 15) | 8 (x 15)
75 girls | 120 students
If a recipe calls for a ratio of 1 cup of sugar to 3 cups of flour, how many cups of flour do you need for 2 cups of sugar?
6 cups of flour
Explain:
S | F
1 | 3
2 | 6
We multiplied both sides by 2
A train travels 300 kilometers in 4 hours. What is its rate in kilometers per hour?
300 / 4 = 75 kph (kilometers per hour)
A recipe calls for 3 cups of flour to make 12 cookies. What is the unit rate of flour per cookie?
3 / 12 = 0.25 or 1/4 cup of flour per cookie
Find two equivalent ratios for 7:3.
x2 = 14:6
x3 = 21:9
x5 = 35:15
x10 = 70:30
A gardener uses a 2:3 ratio of yellow to red flowers. If he has 18 yellow flowers, how many red flowers does he need?
27 red flowers
Make a table
R | Y
2 | 3 (multiply each side by 9)
18 | 27