6.RP.3 — Ratios & Rates in the Real World
Practice solving real-world problems using ratios, unit rates, equivalent ratio tables, percent reasoning, and unit conversions to build proportional thinking skills.
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Three different problem sets — same skill, same layout, fresh numbers.
Preview — Set A
Read each problem carefully, then use ratio and rate reasoning to find the answer.
- 1.A car travels 180 miles in 3 hours at a constant speed. How many miles does the car travel per hour?
- 2.A grocery store sells 5 apples for $2.50. At this rate, how much would 12 apples cost?
- 3.A recipe calls for 3 cups of flour for every 2 cups of sugar. If a baker uses 9 cups of flour, how many cups of sugar are needed?
- 4.A runner completes 4 laps in 10 minutes. At this rate, how many laps will the runner complete in 25 minutes?
- 5.A map has a scale of 1 inch = 50 miles. Two cities are 7 inches apart on the map. What is the actual distance between the two cities?
- 6.A store is offering a 25% discount on a jacket that originally costs $80. How much money will a customer save?
- 7.There are 120 students in 6th grade. If 45% of them participate in after-school clubs, how many students participate in after-school clubs?
- 8.A faucet leaks at a rate of 3 gallons every 4 hours. How many gallons will leak in 24 hours?
- 9.A factory produces 560 toy cars in 8 hours. How many toy cars does it produce per hour?
- 10.A swimming pool is being filled at a rate of 150 gallons per hour. How many gallons will be in the pool after 6 hours?
- 11.At a fruit stand, oranges are sold at a ratio of 3 oranges for $1.50. Complete the equivalent ratio table: if you buy 6, 9, and 12 oranges, how much does each cost? What is the unit price per orange?
- 12.A cyclist rides 48 miles in 4 hours. At this same unit rate, how long will it take the cyclist to ride 72 miles?
- 13.A student answered 35 out of 40 questions correctly on a test. What percent of the questions did the student answer correctly?
- 14.A bag of dog food weighs 15 pounds. How many ounces does the bag weigh? (1 pound = 16 ounces)
- 15.A tank holds 6 liters of water. There are 1,000 milliliters in 1 liter. How many milliliters of water does the tank hold?
- 16.A school bought 8 boxes of markers. Each box contains 24 markers. The school paid a total of $48. What is the cost per marker?
- 17.A car uses 2 gallons of gas to travel 56 miles. How many miles per gallon does the car get, and how far can it travel on 7 gallons?
- 18.A class has 18 girls and 12 boys. Write the ratio of girls to boys in simplest form.
- 19.A store marks up the price of a shirt from $15 to $24. What is the percent increase in price?
- 20.It takes 5 workers 6 days to complete a project. If the same total amount of work is shared equally among 10 workers working at the same rate, how many days will it take them to finish?
- 21.A recipe that serves 4 people uses 2 pounds of pasta. How many pounds of pasta are needed to serve 14 people?
- 22.A store sells trail mix for $3.60 per pound. How much would 2.5 pounds of trail mix cost?
What this worksheet covers
Set A of this grade 6 word problems sheet holds 22 story problems on one printable page, with the answer key on the page behind it. Within that, every problem is set in a short situation, so the first decision is which operation it calls for and operands run to two decimal places, so the decimal points have to be lined up rather than the right-hand digits. Two problems from the middle of the page — "A faucet leaks at a rate of 3 gallons every 4 hours. How…" and "A tank holds 6 liters of water. There are 1,000 milliliters…" — show the range. It is written against Common Core 6.RP.3 — Ratios & Proportional Relationships, grade 6.
Skills practised
The grade 6 ratios and proportions sequence covers writing and simplifying ratios, equivalent ratios, ratio tables, unit rates and ratios as percents; this page sits inside it. What a student is asked to do here is ratios & Rates in the Real World. Working the page asks a student to read a situation and choose an operation before computing, keep the decimal points aligned, and carry money notation through to the answer.
About the word problems format
Story problems are set one to a line with room to work underneath, problem 8, "A faucet leaks at a rate of 3 gallons every 4 hours. How…" among them, and the key gives each of the 22 answers with its unit. Recipes, speeds and prices are where proportional reasoning is actually used, and where a wrong setup is obvious.
Set A, Set B and Set C
Set A is the original MathSheetLab worksheet; Sets B and C keep its structure and redraw the numbers, with each answer recomputed rather than copied. Where Set A's problem 12 is "A cyclist rides 48 miles in 4 hours. At this same unit…", Set B's is "A cyclist rides 108 miles in 3 hours. At this same unit…".
22 story problem(s) drawn from the 6.RP.3 context family (ratio, unit-rate and percent stories) — parameters inferred from the standard and grade
How to use this worksheet
Work it without a calculator. Every one of the 22 ratios and proportions problems is designed to be done by hand, and reaching for a calculator at grade 6 skips exactly the reasoning being built. Print Set B of this ratios and proportions word problems before writing on Set A; the same skill worked twice a week apart tells you far more than once.
One mistake to watch for
Equivalent ratios are made by adding the same number to both terms. On this grade 6 word problems, problem 15 ("A tank holds 6 liters of water. There are 1,000 milliliters…") is the kind of item where it shows.
Scaling and adding are being confused, as with fractions.
Build a ratio table by multiplying across a row and check that the columns keep the same relationship.
Other grade 6 ratios and proportions formats
The same skill in the other formats available at this grade.
- Drill — Grade 6 Ratios & Proportions Drill, 30 problems
- Timed Drill — Grade 6 Ratios & Proportions Timed Drill, 60 problems
- Missing Number — Grade 6 Ratios & Proportions Missing Number, 24 problems
- Mixed Review — Grade 6 Ratios & Proportions Mixed Review, 30 problems
A step either side
The same format one grade down and one grade up — the easier sheet is often the faster fix when this one is not landing.
- Grade 7 Ratios & Proportions Word Problems — grade 7, 10 problems
Word Problems sheets in other grade 6 topics
Free to download, print and photocopy for a whole class: three word problems sheets of grade 6 ratios and proportions, 22 problems each, keys included.