Ratios & Proportions Game/Worksheet

Ratios & Proportions Game/Worksheet
Welcome to the Ratios & Proportions Challenge! This is an interactive math game designed to test and sharpen your fractional number sense. Ratios are simply a way to compare two quantities. When two ratios scale up or down at the exact same rate, they are considered equivalent, meaning they form a true proportion. This game challenges you to look closely at pair comparisons across different difficulty levels to determine if they balance out perfectly or represent completely different scales. Scroll down the page for a more detailed explanation.

 

 

How to Play
Playing the game is straightforward, but it requires quick mathematical thinking:

1. Setup: On the home menu, choose whether you want to play with sound effects toggled on. You can also turn on the 60-Second Blitz Timer if you want an extra challenge against the clock. Click Initialize Game to begin.
   

2. The Main Screen: For each round, you will be shown two different fractions separated by a question mark. At the top, you can track your current problem number (1 through 10) and your current score.
   

3. Making a Choice: Below the fractions, click the YES (True) button if you believe the two ratios form a true proportion, or click the NO (False) button if they do not match.
   

4. Reviewing Explanations: After making your choice, a feedback screen will slide open. It provides a visual proof and a step-by-step mathematical breakdown explaining why the answer is correct. Click Advance to Next Node to move forward until you finish all 10 rounds and receive your final diagnostic score!
   

How the Math Works
To decide whether two ratios like \(\frac{a}{b}\) and \(\frac{c}{d}\) form a true proportion (\(\frac{a}{b} = \frac{c}{d}\)), you can use three techniques depending on how difficult the numbers look.

1. Scaling Factors (The Easy Method)
   For simpler fractions, check to see if one fraction is just the other fraction multiplied or divided by a whole number.
   Example: Do \(\frac{2}{4}\) and \(\frac{4}{8}\) form a proportion?
   Thinking: If you look at the first fraction, multiplying both the top number (2 × 2 = 4) and the bottom number (4 × 2 = 8) perfectly gives you the second fraction. Because they scaled up by the exact same multiplier, YES, they form a proportion.
   

2. Simplifying to Lowest Terms (The Reduction Method)
   If the scaling factor isn’t obvious, try simplifying both fractions to their absolute lowest terms to see if they turn into the exact same starting fraction.
   Example: Do \(\frac{4}{10}\) and \(\frac{6}{15}\) form a proportion?
   Thinking:
   Simplify \(\frac{4}{10}\) by dividing the top and bottom by \(2 \rightarrow \frac{2}{5}\)
   Simplify \(\frac{6}{15}\) by dividing the top and bottom by \(3 \rightarrow \frac{2}{5}\)
   Since both fractions reduce down to \(\frac{2}{5}\), YES, they are proportional.
   

3. Cross-Multiplication
   When the numbers get large or tricky, the most reliable strategy is to cross-multiply the opposite corners. Multiply the top-left number by the bottom-right number, and the bottom-left number by the top-right number. If the two resulting products match, it’s a true proportion.
   a × d = b × c
   

Example 1 (True Proportion):
Do \(\frac{12}{20}\) and \(\frac{15}{25}\) form a proportion?
Multiply top-left by bottom-right: 12 × 25 = 300
Multiply bottom-left by top-right: 20 × 15 = 300
Since 300 = 300, select YES.

Example 2 (False Proportion):
Do \(\frac{2}{5}\) and \(\frac{3}{7}\) form a proportion?
Multiply top-left by bottom-right: 2 × 7 = 14
Multiply bottom-left by top-right: 5 × 3 = 15
Since 14 does not equal 15, select NO.

Ratios & Proportions

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