What is the difference between a ratio and a proportion?

A ratio compares two amounts, while a proportion states that two ratios are equal. Saying there are 2 teachers for every 30 pupils gives a ratio, written 2 : 30 or 2/30. Writing 2/30 = 4/60 makes a proportion, because both ratios describe the same mix. The rule of three works on proportions, using three known numbers to find the fourth.

How do you solve a rule of three word problem?

To solve a rule of three word problem, find the value of one unit first, then multiply. Suppose 3 bags of rice weigh 12 kilograms, and you want the weight of 7 bags. One bag weighs 12 ÷ 3 = 4 kilograms, so 7 bags weigh 7 × 4 = 28 kilograms. As a proportion, that is 3/12 = 7/28, with bags on top on both sides.

Is there a quick trick for solving proportions?

Yes, cross multiplication solves any proportion, even when the numbers do not divide neatly. Multiply the two known numbers on one diagonal of the = sign, then divide by the number left over. For 6/9 = 4/?, multiply 9 × 4 = 36, then divide by 6 to get 6. To check, the other diagonal must match: 6 × 6 is also 36.

Why does my child add instead of multiplying in proportions?

Children often add because addition came first, so a jump from 2 to 4 looks like “add 2”. In 2/4 = 5/?, that gives 7, which is wrong. Bicycles show why: 2 bikes have 4 wheels, so 5 bikes have 10 wheels, not 7. Testing answers against real objects like this shows that proportions grow by multiplying.

Is this ratio and proportion game free to use with a class?

Yes, none of the three levels costs anything, and each runs straight from a web browser with nothing to install or register. For proportions practice at the board, draw a two-row table with 3 on top and 12 below. Pupils then add columns such as 5 over 20 and 7 over 28. After that, everyone fights on a tablet. A teacher dashboard showing who is improving comes with the schools plan, priced per student.

Math practice · reimagined

Rule of Three Game

In this rule of three fight, the gap always sits at the bottom of the second fraction, as in 4/12 = 5/?, and answers grow from 4 up to 240. Find the multiplier before your rival does, and your fighter turns your speed into damage.

Ages 4–99+ · no download · plays in your browser · 23 languages

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What is the rule of three?

The rule of three finds the fourth number of a proportion when you already know the other three. A proportion says that two ratios are equal, and a ratio compares two amounts, such as 3 glasses to 6 oranges. If 3 glasses of juice need 6 oranges, each glass needs 2. So 5 glasses need 10 oranges.

Every level of Rule of three

Example: 4/12 = 5/?, with the bottom number missing

Look down the first fraction: 4 × 3 = 12, so its bottom is 3 times its top.
The second fraction must keep the same link, so its bottom is also 3 times its top.
Its top is 5, and 5 × 3 = 15. Check it: 4/12 and 5/15 are both equal to 1/3.
The missing number is 15, so you type 15 on the keypad.

Learn it step by step

Two ratios that match — find the missing piece so they stay in balance.

If 2 apples cost 6 coins, what do 4 apples cost? Apples doubled (2 → 4), so the coins double too → 12. Figure out what you multiplied the first pair by, then do the same to the other.

This is the famous "rule of three." Type the missing number.

Tips and common mistakes

Read the first fraction as a times table fact: 6/30 says 6 × 5 = 30. The second fraction hides the same × 5, so 7/? gives 35.
A common mistake is mixing up the pairs. If 3 boxes hold 12 pens, keep boxes on top on both sides: 3/12 = 5/? gives 20 pens for 5 boxes.
Scale a recipe together. If pancakes for 2 people need 3 eggs, ask how many eggs 6 people need, then 8. Write each pair as a fraction: 2/3 = 6/9.

How to play

Two fractions stand side by side, such as 3/9 = 7/?, and the empty spot is always the bottom of the second one. Type the missing number on the keypad; on the top level it can run to three digits. Answer before your rival and Carrot strikes, with every second you save adding damage.

— Quick answers —

Rule of three: the short FAQ

What is the difference between a ratio and a proportion?: A ratio compares two amounts, while a proportion states that two ratios are equal. Saying there are 2 teachers for every 30 pupils gives a ratio, written 2 : 30 or 2/30. Writing 2/30 = 4/60 makes a proportion, because both ratios describe the same mix. The rule of three works on proportions, using three known numbers to find the fourth.
How do you solve a rule of three word problem?: To solve a rule of three word problem, find the value of one unit first, then multiply. Suppose 3 bags of rice weigh 12 kilograms, and you want the weight of 7 bags. One bag weighs 12 ÷ 3 = 4 kilograms, so 7 bags weigh 7 × 4 = 28 kilograms. As a proportion, that is 3/12 = 7/28, with bags on top on both sides.
Is there a quick trick for solving proportions?: Yes, cross multiplication solves any proportion, even when the numbers do not divide neatly. Multiply the two known numbers on one diagonal of the = sign, then divide by the number left over. For 6/9 = 4/?, multiply 9 × 4 = 36, then divide by 6 to get 6. To check, the other diagonal must match: 6 × 6 is also 36.
Why does my child add instead of multiplying in proportions?: Children often add because addition came first, so a jump from 2 to 4 looks like “add 2”. In 2/4 = 5/?, that gives 7, which is wrong. Bicycles show why: 2 bikes have 4 wheels, so 5 bikes have 10 wheels, not 7. Testing answers against real objects like this shows that proportions grow by multiplying.
Is this ratio and proportion game free to use with a class?: Yes, none of the three levels costs anything, and each runs straight from a web browser with nothing to install or register. For proportions practice at the board, draw a two-row table with 3 on top and 12 below. Pupils then add columns such as 5 over 20 and 7 over 28. After that, everyone fights on a tablet. A teacher dashboard showing who is improving comes with the schools plan, priced per student.

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