Rule of three calculator
If 3 workers finish a job in 8 days, how long do 6 workers take? If 2 kg of flour makes 12 rolls, how much flour for 30 rolls?
How to solve a proportion
1. Identify whether the relationship is direct (more → more) or inverse (more → less).
2. Enter the three known values in the labeled fields.
3. Read the computed fourth value.
4. Sanity-check: does the answer scale in the right direction?
Proportion examples
Direct proportion — recipe scaling
2 cups sugar → 24 cookies; 5 cups sugar → ? cookies. Direct: (5 ÷ 2) × 24 = 60 cookies.
Inverse proportion — workers and days
4 workers → 12 days; 6 workers → ? days. Inverse: (4 × 12) ÷ 6 = 8 days.
Unit price comparison
$7.50 for 500 g; how much for 1.2 kg? Direct: (7.50 ÷ 500) × 1200 = $18.00.
When to use the rule of three
• When you scale ingredient lists or chemical mixtures by mass or volume.
• When you estimate project duration from known team-size tradeoffs (rough inverse models).
• When you convert quantities at a fixed ratio without reopening a spreadsheet.
Direct vs inverse in everyday problems
Direct: maps at 1:50,000 scale — double map distance means double real distance. Inverse: fixed pool volume — wider pipe (more flow) means less time to fill. Misclassifying direct as inverse is the most common student error; ask "if I double the first quantity, does the second double or halve?"
Frequently asked questions
What is direct proportion?
When one quantity increases, the other increases at a constant ratio. Example: more miles at the same speed means more time.
What is inverse proportion?
When one increases, the other decreases so their product stays constant. Example: more workers often means fewer days for the same job.
What is the cross-multiply formula?
Direct: a/b = c/x → x = (b × c) ÷ a. Inverse: a × b = c × x → x = (a × b) ÷ c.
Can I use this for currency exchange?
Yes at a fixed rate. Real markets fluctuate — refresh the rate for large transfers.
Why did my worker-days answer look wrong?
Real projects are not perfectly inverse — communication overhead and indivisible tasks break the simple model.