Ratios and proportional relationships are the first big domain of sixth grade math. Students learn to describe a ratio relationship between two quantities (Common Core 6.RP.A.1), understand unit rates such as miles per hour or price per item (6.RP.A.2), and solve real problems with tables of equivalent ratios, tape diagrams, double number lines and percents (6.RP.A.3). These ideas lead straight into proportional relationships in seventh grade and slope in eighth grade.
This set includes simplifying a ratio, finding unit rates and unit prices, completing a ratio table, sharing a total in a given ratio, percent of a number and finding the whole from a percent. A tape diagram is the most reliable tool for sharing problems: draw one box for each part of the ratio, find the value of one box, then scale up. For percents, remember that percent means per hundred, so 30% of 80 is 30 hundredths of 80. Each question is checked instantly and explained step by step.
Choose an option or type your answer, then press Check. Capital letters and extra spaces do not matter in typed answers, and units are optional.
Answer: B) 4:5
Girls to boys is 12:15. Both numbers divide by 3, giving 4:5. 12:15 is the same ratio but not in simplest form, and 5:4 is in the wrong order.
Answer: 60 (also accepted: 60 miles per hour, 60 mph)
Unit rate = miles / hours = 240 / 4 = 60 miles per hour.
Answer: B) 9:15
Multiply both parts of 3:5 by 3 to get 9:15. 6:8 adds 3 to each part instead of multiplying, 5:3 is reversed and 12:15 only multiplies one part.
Answer: 24
10% of 80 is 8, so 30% is 3 x 8 = 24.
Answer: A) $0.25
Price per pencil = total cost / number of pencils = $2.00 / 8 = $0.25.
Answer: 12 (also accepted: 12 cups)
8 cups of milk is 4 times 2 cups. Multiply the flour by 4 as well: 3 x 4 = 12 cups of flour.
Answer: B) 75%
Write it as a fraction: 45/60. Simplify to 3/4, and 3/4 = 75/100 = 75%.
Answer: 60
25% is one quarter. If one quarter is 15, the whole is 4 x 15 = 60.
Answer: B) 4
There are 2 + 7 = 9 parts. 18 / 9 = 2 marbles per part. Red has 2 parts: 2 x 2 = 4 red marbles.
Answer: 29 (also accepted: 29 miles per gallon, 29 mpg)
Miles per gallon = miles / gallons = 87 / 3 = 29.
Answer: B) 15
y is always 5/2 times x (the unit rate is 2.5). When x = 6, y = 6 x 2.5 = 15. Equivalently, 6 is 3 times 2, so y is 3 times 5.
Answer: 75% (also accepted: 75, 75 percent)
Make the denominator 100: 3/4 = 75/100. Percent means per hundred, so 3/4 = 75%.
Answer: A) 30
Pages per hour = 45 / 1.5 = 30. Check: 30 pages in 1 hour plus 15 pages in half an hour makes 45.
Answer: 48 (also accepted: 48 inches)
The rate is 12 inches per foot, so 4 feet = 4 x 12 = 48 inches.
"Girls to boys" means girls first. 12 girls and 15 boys is 12:15 (or 4:5), not 5:4.
If 2 becomes 6, the ratio was multiplied by 3, so 5 becomes 15, not 9.
For red:blue = 2:7 with 18 in total, divide by 2 + 7 = 9 parts, not by 2 or 7.
Miles per gallon is miles divided by gallons. 87 miles on 3 gallons is 87 / 3 = 29, not 3 / 87.
Turn ratios and rates into a printable, differentiated worksheet with an answer key, matched to grade 6.
Make a worksheet βBuild a test or quiz on this topic that students answer online and that marks itself, with a class summary for you.
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Open the student portal βA rate for one unit of the second quantity, such as 60 miles per 1 hour or $0.25 per pencil. You find it by dividing the first quantity by the second.
They are closely related but not the same. The ratio 3:5 compares two parts; as a fraction of the whole, the first part is 3/8, not 3/5.