Grade 6 Math · Topic 07
Real-world ratio problems often give you a comparison and one missing piece. Your job: pick a strategy — equivalent ratios, a ratio table, or unit rates — and find the missing value. Always check that your answer is in the same units as the question.
Lesson alignment: 6.RP.A.3 · 6.RP.A.3.d · Take your time. You can return to this lesson whenever you need it.
Explore visually
Choose a conversion and amount. Follow the scale factor while the starting units cancel.
Think first: Predict what will change when you adjust one value, then use the model to check your idea.
Swipe horizontally to see the full diagram.
Turn on JavaScript to adjust this model. The examples and practice below work without it.
Grade 6 core skill · 6.RP.A.3.d
A conversion factor names two equal measurements. Choose the form that cancels the starting unit and leaves the unit you need.
1 meter = 100 centimeters, so multiply by a ratio equal to 1:
2.4 m × 100 cm / 1 m = 240 cm
The meter units cancel. The number gets larger because centimeters are smaller units.
Check the direction: converting to a smaller unit usually gives more units; converting to a larger unit gives fewer. Keep the unit labels in every line.
1 foot = 12 inches, so 3 × 12 = 36 inches. Feet cancel when you multiply by 12 inches per foot.
Read each step, then cover the explanation and see if you can explain why it works.
Worked example 1
Set up equivalent ratios first so the matching parts are clear: 4:5 = ?:30. Since 5 × 6 = 30, multiply nuts by 6 too: 4 × 6 = 24. So 24 cups of nuts are needed.
Answer: 24 cups
Worked example 2
Start with the unit rate so the scale-up step is clear: 30 ÷ 45 = 2/3 minute per page. For 90 pages: 90 × 2/3 = 60 minutes. (Or notice 90 = 45 × 2, so time doubles: 30 × 2 = 60.)
Answer: 60 minutes
Work these on paper first. Open “Check” when you are ready to compare your answer.
30
35
45
55
49
15
12
10
A blueprint uses 1 inch to represent 4 feet. How many feet does 7.5 inches represent?
Answer: 30 feet.
Scale up by 7.5: 1 × 7.5 = 7.5 inches matches 4 × 7.5 = 30 feet.
A printer uses 3 ink cartridges every 1200 pages. How many cartridges does it use for 4800 pages?
Answer: 12 cartridges.
Start by writing the calculation clearly: 1200 × 4 = 4800, so multiply cartridges by 4: 3 × 4 = 12.
Fresh questions · saved on this device
Try a fresh set each time. Answer one question, check your thinking, and read the explanation. If you miss one, return to the visual model and try another round.
Answer these five questions on your own. You can review the explanations after you submit and try again whenever you like. This short check is for practice, not a grade.
Try the linked topic quiz for more practice. If something is tricky, return to the example and look for the step that changes the numbers or representation.
Your checkmark, skill-practice sessions, and best exit-check score are saved on this browser and device. The course page can download a progress report to share with a tutor or teacher.
Use these free materials if you want another explanation, extra paper practice, or a broader review.