Worked Example 1
A Mixture
Punch is made with 3 cups of juice for every 5 cups of soda. How much juice is in 24 cups of punch?
- 1Each batch has 3 + 5 = 8 cups, and 38 of it is juice.
- 224 ÷ 8 = 3 batches
- 33 × 3 = 9
Answer: 9 cups of juice
Florida Grade 6 Math · Algebraic Reasoning
MA.6.AR.3.5: Ratio and Rate Problems
What this Grade 6 benchmark means, worked examples, common mistakes, and a free printable worksheet.
Created by a Florida mom · Published by Tropical Learning LLC
What Is Benchmark MA.6.AR.3.5?
Students solve problems with ratios, rates, and unit rates, including comparisons, mixtures, ratios of lengths, and conversions within the same measurement system (like feet to inches or meters to kilometers).
Tables, tape diagrams, and double number lines help organize the quantities.
Official benchmarkSolve mathematical and real-world problems involving ratios, rates and unit rates, including comparisons, mixtures, ratios of lengths and conversions within the same measurement system.
On the FAST test: part of the Grade 6 reporting category Algebraic Reasoning, which is about 25–36% of the test.
Worked Examples
Worked Example 2
Comparing Rates
Car A goes 280 miles on 10 gallons. Car B goes 325 miles on 13 gallons. Which gets better gas mileage?
- 1Car A: 280 ÷ 10 = 28 miles per gallon
- 2Car B: 325 ÷ 13 = 25 miles per gallon
Answer: Car A
Common Mistakes to Watch For
Using a part-to-part ratio as part-to-whole
Wrong:Juice is 35 of the punch.
3:5 compares juice to soda. Juice is 3 out of every 8 cups: 38 of the punch.
Converting in the wrong direction
Wrong:4.5 feet = 4.5 ÷ 12 inches
Inches are smaller, so there are more of them: 4.5 × 12 = 54 inches.
Helpful Math Tip
Draw a tape diagram: a bar split into 3 juice parts and 5 soda parts. It makes the whole (8 parts) easy to see.
Related Grade 6 Skills
Make Florida Math Practice More Fun
Help your child build math confidence with original interactive questions aligned with Florida's B.E.S.T. Mathematics Standards.
Start Practicing FreeIndependent Educational Platform. FastChomp is published by Tropical Learning LLC and is not affiliated with, sponsored by, or endorsed by the Florida Department of Education. FAST and Star assessment names are referenced for informational purposes only. FastChomp practice questions are original educational materials, not official Florida FAST assessment questions.