Word Problem Wizard (Percent, Ratio, Speed, Concentration)

Use the relation part = whole × rate . If you need the whole, compute whole = part ÷ rate . If you need the rate, compute rate = part ÷ whole .

First add the ratio parts ( a+b ). One part is total ÷ (a+b) . Multiply that by a and b to get each share.

Quick start

Template

Settings

Prefer fractions Decimal places Show percent

Teacher mode Reduced motion

Enter numbers as 12, 0.25, 1/4, or 25%.

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How should I organize a word problem?

Identify what is given, what is unknown, and the units. Then pick a matching template and translate it into a diagram and a short set of formulas.

How do I choose between part, whole, and rate in percent problems?

Use the relation part = whole × rate. If you need the whole, compute whole = part ÷ rate. If you need the rate, compute rate = part ÷ whole.

What does “per part” mean when splitting by ratio?

First add the ratio parts (a+b). One part is total ÷ (a+b). Multiply that by a and b to get each share.

Why is average speed total distance ÷ total time?

Average speed depends on the whole trip. Add distances and times first, then divide.

Why do salt-solution mixtures add solute amounts?

Mixing does not change the amount of salt. Compute salt in each solution and add them. The mixed concentration is total salt ÷ total amount.

How can I avoid mistakes with unit conversion?

Convert to consistent base units first (e.g., meters and seconds). The wizard normalizes units internally and shows the result in your chosen unit.