Ratios and Rates
What is the difference between a ratio and a rate?
A ratio compares two quantities, while a rate compares two quantities with different units.
Fill in the missing value:
Apples: 4, 8, 12, ?
Oranges: 2, 4, 6, 8
16
If 4 notebooks cost $8, what is the cost of one notebook?
$2 per notebook
If a runner completes 5 laps in 10 minutes, how long does it take to complete one lap?
2 minutes per lap
True or False: The rate 50 miles per hour is equivalent to 25 miles per 30 minutes.
True
Write a ration 8 apples to 12 oranges in simplest form.
2:3
From this table, find the unit rate:
Miles: 60, 120, 180
Hours 1, 2, 3
60 miles per hour
A car travels 300 miles on 10 gallons of gas. What is the unit rate of miles per gallon?
30 miles per gallon
A recipe calls for 3 cups of sugar for every 4 cups of flour. If you use 12 cups of flour, how much sugar is needed?
9 cups
Compare the rates: 8 cookies in 4 minutes vs. 15 cookies in 10 minutes. Which is faster?
8 cookies in 4 minutes because it’s 2 cookies/min, compared to 1.5 cookies/min.
What does it mean if two ratios are equivalent?
They represent the same relationship.
Complete the table:
Hours: 1, 2, 3, ?
Distance (miles): 45, 90, 135, 180
4 hours
Which is the better buy: 12 oz of cereal for $4.80 or 16 oz for $6.40?
16 oz for $6.40 because the unit price is $0.40/oz.
A car drives 150 miles in 3 hours. If the car continues at the same speed, how far will it travel in 5 hours
250 miles
Is the ratio 10:5 equivalent to the ratio 20:15? Show your work.
No, because 10:5 simplifies to 2:1, while 20:15 simplifies to 4:3
Simplify the ratio 45:60
3:4
A graph shows a line passing through the points (0, 0) and (2, 8). What is the unit rate?
4, since 8 ÷ 2 = 4
If a machine makes 240 widgets in 6 hours, how many widgets does it make per hour?
40 widgets per hour
A truck uses 18 gallons of fuel to travel 360 miles. How far can it go on 6 gallons?
120 miles
Which is the better deal: 5 apples for $3 or 8 apples for $4.80?
8 apples for $4.80 because the cost per apple is $0.60, compared to $0.75.
Write a ratio for the following situation (in simplest form): A classroom has 15 girls and 10 boys.
3:2
A table shows the following values:
Time (hours): 2, 4, 6, 8
Distance (miles): 50, 100, 150, ?
What is the missing distance value?
200 miles
A store sells 3 loaves of bread for $5.25. What is the price per loaf?
$1.75 per loaf
A recipe uses a ratio of 2 cups of milk to 5 cups of flour. How much flour is needed if you use 6 cups of milk?
15 cups of flour
Compare the rates: 12 miles in 4 minutes vs. 18 miles in 6 minutes. Which is faster?
Both rates are equal because 12 ÷ 4 = 3 miles per minute, and 18 ÷ 6 = 3 miles per minute.