Real-World Ratio and Rate Problems: Sample FAST Questions
Students solve mathematical and real-world problems involving ratios, rates, and unit rates, including comparisons, mixtures, ratios of lengths, and conversions within the same measurement system. Examples include comparing paint mixtures for color strength and converting feet to inches or grams to kilograms.
How the FAST tests this benchmark
The FAST tests this with multi-step word problems in multiple choice and equation editor formats, including mixture comparisons and measurement conversion questions.
Skills students need
Solve ratio comparison problems
Solve mixture problems
Convert units within the same measurement system
Try 4 real MA.6.AR.3.5 questions
These come straight from Algebro's question bank. Pick an answer to check it instantly.
Question 1EasyMultiple Choice
On Quiz A, a student got 6 out of 10 questions correct. On Quiz B, the same student got 7 out of 12 correct. Which quiz had a higher correct rate?
Correct answer: B. Quiz A, because 106>127
This explanation shows one way to solve the problem.
Convert Quiz A's ratio to a decimal: 106=0.60.
Convert Quiz B's ratio to a decimal: 7÷12≈0.583.
Compare: 0.60>0.583, so Quiz A had the higher correct rate.
Final Answer
Quiz A, because 106>127
Question 2MediumEquation Editor
A tape diagram is shown. The ratio of tea drinkers to coffee drinkers in an office is shown. If there are 77 people in total, how many coffee drinkers are there?
Figure: a tape diagram.
Enter the number only. Do not include units like $, %, or ft²
Correct answer: 63
This explanation shows one way to solve the problem.
Count the total parts in the tape diagram: Tea: 2 parts. Coffee: 9 parts. Total: 2+9=11 parts.
Find the value of one part: 77÷11=7 people per part.
Find the coffee drinkers: Coffee =9×7=63.
Final Answer
63
Question 3MediumEquation Editor
A tape diagram is shown. The ratio of math minutes to reading minutes in a study plan is shown. If there are 55 minutes in total, how many math minutes are there?
Figure: a tape diagram.
Enter the number only. Do not include units like $, %, or ft²
Correct answer: 22
This explanation shows one way to solve the problem.
Count the total parts in the tape diagram: Math: 2 parts. Reading: 3 parts. Total: 2+3=5 parts.
Find the value of one part: 55÷5=11 minutes per part.
Find the math minutes: Math =2×11=22 minutes.
Final Answer
22
Question 4HardMultiple Choice
A tank holds 2,400 gallons of water. Water drains out at 6 quarts per minute. How many minutes will it take to drain the tank?
Correct answer: C. 1,600 minutes
This explanation shows one way to solve the problem.
These are 4 of the 100+ questions Algebro has for this benchmark alone. Take the diagnostic, get a study plan that targets your gaps, and practice with an AI tutor that explains every step.
