Rule of Three: Direct and Inverse Proportion

At the end of a Magnado round, the result card shows 48 seconds alive and a highest mass of 68. If I had lasted twice as long, at the same pace, would the mass double too? That question is solved with the rule of three.

Here you get what the rule of three is, how to solve direct and inverse versions, how to tell which one to use and worked examples with the math checked.

Play Magnado

What is the rule of three?

The rule of three is a way to find a missing value when you know three values related by proportion. Two quantities are proportional when, if one doubles, the other doubles (or halves).

Direct proportion

Here the quantities grow together: more of one, more of the other. Set up a table, then cross-multiply.

Example: 3 pounds of apples cost $12. How much do 5 pounds cost? 3 is to 12 as 5 is to x. So x = 12 × 5 ÷ 3 = $20.

Recipe: 2 cups of flour make 12 cookies. For 30 cookies: x = 2 × 30 ÷ 12 = 5 cups.

Inverse proportion

Here, when one quantity grows, the other shrinks: more of one, less of the other. Instead of cross-multiplying, multiply straight across.

Example: 4 people do a job in 6 days. How many days do 8 people need? More people, fewer days. x = 4 × 6 ÷ 8 = 3 days.

How to tell direct from inverse

• If one goes up and the other goes up too (price and amount), it is direct.
• If one goes up and the other goes down (people and days, speed and time), it is inverse.

Step by step

1. Write the quantities in columns, with the same unit in each column.
2. Decide whether it is direct or inverse.
3. Set up the proportion.
4. Solve it and check that the result makes sense.

Common mistakes

• Mixing units, like hours with minutes.
• Using the direct rule when it was inverse.
• Forgetting to check that the result makes sense. If 8 people took more days than 4, something is wrong.

The rule of three in Magnado

The Magnado result card shows your highest mass, your time alive and your position in the match.

A proportion example: at the same pace, in 96 seconds (double 48) the mass would be 68 × 96 ÷ 48 = 136. It is only a sample calculation, since the pace changes in the game.

Polarzinho18 out of 25 is the same as 72 out of 100. The rule of three and percentages go together.

FAQ

What is the rule of three?

A method for finding a missing value when three values are related by proportion.

What is the difference between direct and inverse proportion?

In direct proportion, the quantities grow together. In inverse proportion, when one grows the other shrinks.

How do you solve a simple rule of three?

Set up a table and cross-multiply (direct) or multiply straight across (inverse).

How much do 5 pounds cost if 3 pounds cost $12?

$20.

Your turn

If 60 people set up a stage in 2 hours, how long do 40 people take? Answer: 3 hours.

Play Magnado