Compare rational numbers

Key notes:

🔢 What are Rational Numbers?

• A rational number is any number that can be written as a fraction:
  👉 a/b, where a and b are integers and b ≠ 0
• Examples: 1/2, -3/4, 5, 0, -7/1

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📏 Convert to Same Form Before Comparing

To compare rational numbers, convert them into:

✔️ Fractions

✔️ Decimals

✔️ Like denominators

Example:
Compare 2/3 and 3/5 → Make denominators same or convert to decimals.

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🟰 Use Common Denominators

🌟 Rule: When denominators are the same,
➡️ The number with the bigger numerator is greater.
Example:

• 7/12 > 5/12 👍

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💡 Use Number Line

• Numbers on the right 👉 are greater than numbers on the left 👈.
• Example:
  • −2 is to the right of −5, so −2 > −5 😊

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🔍 Compare Using Decimals

Convert both numbers into decimals for easy comparison.
Example:

• 1/4 = 0.25
• 2/5 = 0.40
  So, 2/5 > 1/4 ✔️

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➕➖ Be Careful with Negative Rational Numbers

💥 Rule:

• The rational number closer to zero is greater when negative.
  Example:
• −1/3 > −1/2
  Because −1/3 is closer to 0.

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🔢 Cross Multiplication Method

Use when denominators are different:
Compare a/b and c/d
👉 Cross multiply: a × d and b × c

• If a × d > b × c, then a/b > c/d

Example:
Compare: 3/4 and 5/8

• 3 × 8 = 24
• 4 × 5 = 20
  ➡️ 24 > 20 so 3/4 > 5/8 🎉

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🎯 Remember the Order

👉 Smallest → Largest
👉 Negative < Zero < Positive

Example order:

• −3/2, −1/4, 0, 2/3, 5/4

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🌈 Summary Chart

Method	When to Use	Emoji
Common denominator	Comparing fractions	➗
Number line	Visual comparison	📉
Decimals	Easy comparison	🔢
Cross multiplication	Fast for unlike denominators	✖️

Learn with an example

Let’s practice!🖊️