Exercises: Ratio and Rate Reasoning
Show your work for each problem. Include units in your answers where applicable.
Warm-Up: Review What You Know
These problems review skills you have already learned.
A ratio table shows the relationship between cups of orange juice and cups of water. The first row is 2 cups orange juice to 6 cups water. Which row correctly extends this table?
A car travels 150 miles in 3 hours at a constant speed. What is the unit rate in miles per hour?
A store sells 4 apples for $2.00. What is the unit price in dollars per apple?
Fluency Practice
Apply ratio and rate reasoning to each problem. Show your work.
A recipe uses 3 cups of flour for every 2 cups of sugar. Complete the ratio table: if you use 9 cups of flour, how many cups of sugar do you need?
A punch recipe calls for 4 cups of grape juice for every 10 cups of lemonade. If you want to make a batch using 6 cups of grape juice, how many cups of lemonade do you need?
Pairs from a ratio table are plotted on a coordinate plane with the first quantity on the horizontal axis and the second on the vertical axis. The pairs are (1, 3), (2, 6), (3, 9), and (4, 12). Which statement best describes the pattern?
It takes a printer 6 minutes to print 8 pages. At that rate, how many pages can it print in 21 minutes?
Store A sells 5 lb of rice for $4.50. Store B sells 8 lb of rice for $6.80. Which store has the lower price per pound? What is that price per pound?
What is 40% of 85?
A board is 96 inches long. How many feet long is it? (Use: 1 foot = 12 inches)
Mixed Practice
These problems test the same skills in different ways.
A ratio table for a paint mixture shows 2 cups red paint for every 5 cups white paint. Fill in the missing values: for 6 cups red paint, you need ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ cups white paint. For 10 cups red paint, you need ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ cups white paint.
Two students, Amara and Ben, each mix a trail mix. Amara uses 3 cups of nuts for every 7 cups of dried fruit. Ben uses 4 cups of nuts for every 9 cups of dried fruit. Which mix has a higher ratio of nuts to dried fruit?
A cyclist rides at a constant rate of 15 miles per hour. In 3 hours, the cyclist travels ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ miles. To travel 60 miles takes ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ hours.
There are 240 students at a school. 30% of them participate in an after-school club. How many students participate in an after-school club?
A shopper saved $12, which was 15% off the original price. What was the original price?
Jalen wants to convert 2.5 miles to feet. He knows that 1 mile = 5,280 feet. Which setup correctly converts 2.5 miles to feet?
Word Problems
Read each problem carefully. Decide what operation to use, then solve.
A garden store sells soil by the bag. A 3-bag set costs $7.50. Fatima needs 8 bags for her garden.
How much will 8 bags cost at the same unit price?
Priya and Marcus are comparing two types of granola at the grocery store. Brand A: 12 ounces for $3.60. Brand B: 18 ounces for $4.86.
What is the unit price (dollars per ounce) for Brand A?
Brand B costs $4.86 for 18 ounces. Its unit price is $0.27 per ounce. Which brand is the better deal, and by how much per ounce?
A class of 25 students took a science quiz. The teacher announced that 60% of the students scored 80 or above.
How many students scored 80 or above?
The teacher also said that 18 students brought their lunch from home, which was 45% of all students at school that day. How many students total were at school that day?
Find the Mistake
Each problem shows a student's work that contains an error. Find and explain the mistake.
Maya solved: "What is 25% of 60?"
Maya's work: 25 × 60 = 1,500
What mistake did Maya make?
Tanaka solved: "A trail is 3.5 miles long. How many feet is that?" (1 mile = 5,280 feet)
Tanaka's work: 3.5 ÷ 5,280 = 0.000663 feet
What mistake did Tanaka make?
Challenge Problems
These problems require multiple steps and careful reasoning.
A recipe is designed for 8 servings and uses 2.5 cups of broth and 1.5 cups of cream. Yuki wants to make the recipe for 14 servings. How many total cups of liquid (broth + cream) does she need? Round to the nearest tenth.
A car's speed is 60 miles per hour.
Miles per minute: ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲
Miles traveled in 7 minutes: ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲