Scale a fraction without losing the whole
What stays the same when a reference batch changes?
Entering midway? Division asks how many equal parts or how much per part. A ratio compares quantities; percent means per hundred.
Start with a concrete question
Use an original synthetic batch calculation to connect a fraction, decimal, percentage and amount. All units are litres.
Try the initial inputs, then write a prediction before changing one setting. All calculations run locally on your CPU.
Go directly to the experiment · Review prerequisite mathematics and return here
What do you expect?
Predict whether doubling the reference batch changes the fraction or only the amount.
Change one thing. Inspect what happens.
- At 3/4 of 12 litres, predict the amount before checking.
- Use 6/8 with the same batch. Explain equivalent fractions.
- Try numerator larger than denominator and interpret an amount above the reference.
Your settingsMechanism
Calculation belowEvidence
Compare outcomes
Same ratio at different reference sizes
Horizontal: Reference batch (litres). Vertical: Scaled amount (litres).
- 1. Constant ratio (solid line)
- 2. Your batch (points)
Axes use the displayed ranges.
Read plotted values as a table
| Series | Reference batch (litres) | Scaled amount (litres) |
|---|---|---|
| Constant ratio | 0 | 0 |
| Constant ratio | 40 | 30 |
| Your batch | 12 | 9 |
Follow the calculation
- Fraction 3/4: divide 3 by 4 = 0.75.
- Percent means per hundred: 0.75 × 100 = 75%.
- Apply to a 12-litre reference batch: 12 × 3/4 = 9 litres.
A fraction names a ratio, not an absolute amount. Values above one represent more than the reference whole.
Captures keep your inputs, prediction and observation. Results are recalculated from those inputs. Resetting inputs keeps your captures and challenge history.
Explain the mechanism
Scale a fraction without losing the whole
Recap for entering here
Division asks how many equal parts or how much per part. A ratio compares quantities; percent means per hundred.
The concrete question
Use an original synthetic batch calculation to connect a fraction, decimal, percentage and amount. All units are litres.
Predict whether doubling the reference batch changes the fraction or only the amount.
Work through the mechanism
The denominator names the number of equal parts; the numerator counts those parts. Three quarters means three of four equal parts.
3/4 = 0.75 = 75%. Applied to 12 litres, each quarter is 3 litres, and three quarters total 9.
The ratio is a slope on the batch graph: every extra reference litre adds 0.75 scaled litres at this setting.
Formula and symbols
Fraction r = numerator/denominator; percentage = 100r; amount A = rB where B is reference litres and A is scaled litres.
Test the idea
At 3/4 of 12 litres, predict the amount before checking.
Use 6/8 with the same batch. Explain equivalent fractions.
Try numerator larger than denominator and interpret an amount above the reference.
Assumptions and boundaries
The denominator is positive; ratios with zero denominators are undefined.
A fraction above one is mathematically valid but may be infeasible for a fixed physical container.
Extend your investigation
High school: Scale an invented recipe and label every quantity.
College: Prove equivalent ratios by multiplying numerator and denominator by the same nonzero value.
Working professionals: Audit a percentage dashboard for changing denominators.
Try a fresh case
What is 5/8 of a 24-litre reference batch?
This is a public practice check. Retries support learning; matching a number does not certify independent proficiency.
Take the investigation further
Choose any extension. These are project prompts for you to carry out; they are not automatically assessed.
School investigation
Scale an invented recipe and label every quantity.
College investigation
Prove equivalent ratios by multiplying numerator and denominator by the same nonzero value.
Workplace investigation
Audit a percentage dashboard for changing denominators.
Keep the evidence, choose your next step
Completion records your own decision that you have worked through this investigation. Practice checks and independent project evidence are separate.