Compare and order rational numbers

Key Notes :

🔢 What are Rational Numbers?

• Numbers that can be written as p/q, where p and q are integers and q ≠ 0.
• Examples: 1/2, -3/4, 0, 5

📏 Comparison Symbols

• > : Greater than
• < : Less than
• = : Equal to

🧮 Step 1: Same Denominator

• Compare fractions directly if denominators are the same.
• ✅ Example: 3/7 > 2/7 (because 3 > 2)

🧮 Step 2: Different Denominator

Find LCM of denominators to make denominators the same.

✅ Example: Compare 2/3 and 3/4

• LCM of 3 & 4 = 12
• Convert: 2/3 = 8/12, 3/4 = 9/12 → 8/12 < 9/12

➕ Step 3: Use Decimal Form

• Convert fractions/integers to decimals to compare.
• ✅ Example: 1/2 = 0.5, 2/5 = 0.4 → 0.5 > 0.4

➖ Step 4: Consider Negative Numbers

• On the number line, numbers to the right are greater, numbers to the left are smaller.
• ✅ Example: -2 < -1 (because -2 is left of -1)

📏 Step 5: Compare Mixed Numbers

• Convert mixed numbers to improper fractions first.
• ✅ Example: 1 1/2 = 3/2, 1 2/3 = 5/3 → 3/2 < 5/3

📊 Quick Tip: Number Line Method

• Plot numbers on a number line → easier to see which is greater.
• 🔹 Right → bigger
• 🔹 Left → smaller

💡 Remember:

• Positive > Negative
• Bigger numerator (same denominator) → bigger fraction
• Smaller denominator (same numerator) → bigger fraction

🎯 Practice Makes Perfect

• Always convert or plot before comparing!

Learn with an example

Let’s practice!🖊️