A ratio compares quantities; it does not automatically tell you their total. A unit rate tells you how much corresponds to one unit. Decide which of those jobs a problem asks you to do before multiplying across numbers.
Original foundation practice · choose by prerequisite skill.
PREDICT · CHANGE · EXPLAIN
A recipe uses 3 cups of water for each cup of concentrate. The model is water=3 × concentrate; the recipe ratio stays fixed.
The curve shows this simplified model over the labelled range. Read the exact point below; the sketch is not a measuring instrument.
Water: 6 cups
Double the concentrate. What must happen to the water to preserve the taste ratio?
Now close the explanation and try the independent retest. Moving a slider alone does not check your understanding.
Start here if you confuse part-to-part with part-to-whole ratios, or compare pack prices using only the total cost. This is a prerequisite repair for proportional reasoning, including corresponding sides in similar triangles.
Red:blue counters = 2:3. What fraction of all counters is red? Explain what the denominator counts.
You will need: Multiplication, division and simple fractions.
Attempt each task before opening a hint. If you need help, reveal the first hint, then the setup, then compare your written steps with the solution. Finish with the retests without referring back.
A ratio 2:3 has five total parts. The first quantity is 2/5 of the combined total, not 2/3.
Equivalent ratios multiply every part by the same scale factor. Adding the same number to both parts generally does not preserve the ratio.
Direct proportion assumes a constant unit rate. This can model a fixed-price purchase, but not a situation with a separate delivery fee or bulk discount unless those are handled explicitly.
First count total parts.
Five parts together cost ₹60.
60/5=₹12.
A gets 2 × 12=₹24; B gets 3 × 12=₹36.
Answer: A ₹24, B ₹36
Before moving on: can you explain why your method works, as well as give the answer?
Write a method as well as an answer. The tasks change the reasoning, not just the numbers.
Find one notebook's price.
80/5=₹16.
Each notebook costs ₹16.
8 × 16=₹128.
Answer: ₹128
Before moving on: can you explain why your method works, as well as give the answer?
Scale both parts by 3.
Water is four times the concentrate.
1 becomes 3, so multiply by 3.
4 × 3=12 cups.
Answer: 12 cups
Before moving on: can you explain why your method works, as well as give the answer?
Count all ratio parts.
There are 3+5=8 parts.
The total includes both colours.
Red occupies three of eight parts.
Answer: 3/8
Before moving on: can you explain why your method works, as well as give the answer?
A tempting claim: “A 2:3 ratio means the first share is 2/3 of the total.”
The denominator for the total share is the sum of the parts, 5.
These changed questions test whether you can reconstruct the method. If you use a hint, record where you got stuck and retry later. Completing this small set does not establish full chapter mastery.
There are seven total parts.
84/7=12.
₹12.
3 × 12=36 and 4 × 12=48.
Answer: ₹36 and ₹48
Could you solve this without the earlier example? If not, revisit the first line where you got stuck.
Divide price by quantity for each.
42/6 and 64/8.
A costs ₹7 each; B costs ₹8 each.
A is cheaper per pencil.
Answer: Pack A
Could you solve this without the earlier example? If not, revisit the first line where you got stuck.
Try the two retests with examples closed. If the same error returns, correct that step and retry later; this short practice is not a diagnostic score or a grade assessment.
Ask what each number compares. Correct scaling is useful only if the learner has identified the two quantities and kept their units consistent.
If the retests are independent, return to the problem that brought you here. The linked Class 10 application is optional for learners already studying that topic; younger learners should use their current school exercise.
No. A fixed delivery fee, minimum charge or quantity discount can break direct proportion. Check the situation before applying a constant unit rate.
Yes. Use the two print buttons above. The question sheet leaves working space and hides solutions; the worked-solutions option includes the solution steps. Your browser can save either view as a PDF.
PERSONAL SUPPORT
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