Add & Subtract Rational Numbers Game/Worksheet

Add & Subtract Rational Numbers Game/Worksheet
Welcome to the Add & Subtract Rational Numbers Challenge! This game is an interactive math game designed to add and subtract rational numbers. It mixes fractions, decimals, and integers together in the same problems (e.g., subtracting a decimal from a negative fraction). It forces students to think critically about conversion strategies (whether to convert everything to decimals or fractions). Scroll down the page for a more detailed explanation.

 

 

How to Play
The game is structured as a 10-stage diagnostics run. Each stage presents a new scenario and a fresh dataset plotted on your dashboard.

1. Analyze the Coordinates: Each round presents an addition or subtraction puzzle containing two different types of rational numbers (for example, an integer combined with a fraction, or a fraction combined with a decimal).
   

2. Choose Your Strategy: Look at the options and decide if it is easier to solve the problem using Fraction Format or Decimal Format. Click the corresponding toggle button to swap your input fields at any time.
   

3. Use the Scratchpad: If you need help converting a fraction to a decimal to see how it looks, type the numerator and denominator into the Quick Conversion Scratchpad at the bottom and click “Convert."
   

4. Lock It In: Enter your calculated answer (simplify your fractions if you are in fraction mode!) and click Verify Coordinates. The game will check your accuracy, award you 100 points for a correct trajectory, and reveal a step-by-step math blueprint explaining the conversion strategy.
   

How the Math Works
Method 1: The Fraction Route (Exact and Reliable)
Fractions are excellent because they can represent any rational number perfectly without any awkward rounding.

Converting Integers: Any whole number or integer can be instantly turned into a fraction by putting it over 1. For example, 5 becomes \(\frac{5}{1}\), and -3 becomes \(\frac{-3}{1}\).

Converting Decimals: Read the decimal by its place value. The number 0.5 is read as “five tenths,” which means it is \(\frac{5}{10}\) (simplifying to \(\frac{1}{2}\)). A negative decimal like -1.5 is -1 \(\frac{5}{10}\), which converts to the improper fraction \(\frac{-15}{10}\) (simplifying to \(\frac{-3}{2}\)).

The Final Step: Once everything is a fraction, find a common denominator, rewrite your terms, and add or subtract the numerators while keeping the denominator the same.

Method 2: The Decimal Route (Fast and Visual)
Decimals can be much faster to add and subtract mentally, but they only work smoothly if the fractions in the problem can turn into “terminating” decimals (decimals that end, like 0.25 or 0.4).

Converting Fractions: Divide the top number by the bottom number. For instance, if you see \(\frac{3}{4}\), computing 3 ÷ 4 gives you 0.75.

The Final Step: Line up the decimal points carefully, remember your rules for handling negative numbers (like how subtracting a negative is the same as adding a positive), and calculate your final value.

Add and Subtract Rational Numbers

• Show Video

 

Check out our most popular games!

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.