Simple Proportions Game
A proportion is an equation that states that two ratios (or fractions) are equal.
\( \frac{A}{B} = \frac{C}{D} \)
When you solve a proportion, you are finding the missing part (A, B, C, or D) that makes the two ratios equivalent.
In this game, one of the denominator (or numerator) is a multiple of the other. This means that it is possible to use equivalent fractions as a short cut to find the missing value. Check out this other Proportional Game where the solutions may be decimals.
Scroll down the page for a more detailed explanation.
 

Simple Proportions

Find the value of x.

Enable 60-Second Timer

Start Game

Score: 0 / 0

Time: 60

Find the value of x:

Check Next

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How to Play the Simple Proportions Game
The game will show you a proportion in the form:
\( \frac{A}{B} = \frac{C}{D} \)
You need to find the missing part (A, B, C, or D) that makes the two ratios (or fractions) equivalent.
In this game, one of the denominator (or numerator) is a multiple of the other. This means that it is possible to use equivalent fractions as a short cut to find the missing value.
Here’s how to play:

1. Timed Option: Check the timer if you want to enable the 60 second timer. Click “Start Game”.
   
2. Look at the Problem: You’ll see a proportion. Solve for the variable.
   
3. Enter Your Answer: Enter your answer at the (?).
   
4. Check Your Work: Click the Check button (or press the Enter key). The game will tell you if you’re correct. If you are wrong, you will be shown the correct answer.
   
5. Get a New Problem: Click the Next button for a new problem.
   Your score is tracked at the top, showing how many you’ve gotten right out of the total you’ve tried.
6. Back to Menu Click “Back to Menu” to restart the game.
    
   

How to solve Proportions
Method 1: Equivalent Fractions (The Shortcut)
This method is the fastest way to solve proportions, but it only works easily when one denominator (or numerator) is a multiple of the other. You ask yourself: “What did I multiply or divide by to get from one fraction to the other?"
Example: \( \frac{5}{7} = \frac{35}{x} \)
Step 1: Find the Scale Factor
Look at the numbers you know (the numerators, 5 and 35) and determine the relationship between them.
To get from 5 to 35, you multiply by 7 (5×7=35).
Step 2: Apply the Scale Factor
To keep the fractions equivalent, you must multiply the other pair of terms (the denominators) by the exact same scale factor.
\( \frac{5x7}{7x7} = \frac{35}{x} \)
Step 3: Calculate the Missing Value
7×7=49
x=49
 
Method 2: Cross-Multiplication (The Universal Method)
Cross-multiplication works for any proportion, regardless of the numbers involved. It turns the proportion into a simple linear equation.
The Rule
The cross-products of any proportion must be equal.
if \( \frac{A}{B} = \frac{C}{D} \) then AD = BC
Example: \( \frac{7}{19} = \frac{13}{x} \)
Step 1: Cross-Multiply
Multiply the diagonal terms and set them equal to each other.
7x = 13×19
Step 2: Isolate the Variable (x)
x = (13×19) ÷ 7 = 35.3 (correct to 1 decimal place)
 

The video gives a clear, step-by-step approach to solving proportions.

• Show Video

 

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