Class Note: How to Simplify Fractions with Large Numbers

Objective

Learn how to simplify fractions, especially those with large numbers, using basic divisibility rules.

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Steps to Simplify Fractions

1. Check for Even Numbers

   • If both the numerator and denominator are even, divide both by 2.
   • Repeat this process until at least one of the numbers is no longer even.

2. Check for Divisibility by Other Numbers

   • Once you cannot divide by 2, check if both numbers are divisible by 3.
   • If so, divide both by 3.

3. Check if Numbers End in 5 or 0

   • If both numbers end in 5 or 0, they can be divided by 5.

4. Repeat as Needed

   • Continue the process with other common factors if possible, or until the fraction cannot be simplified further.

5. Shortcut

   • If you can recognize a larger common factor early (e.g., 8 in both 40 and 64), divide by it directly.

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Examples

Example 1: 36 / 48

• Both even ⇒ divide by 2: 18 / 24
• Still even ⇒ divide by 2: 9 / 12
• Both divisible by 3 ⇒ divide by 3: 3 / 4

Answer: 3 / 4

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Example 2: 40 / 64

• Both even ⇒ divide by 2: 20 / 32

• Both even ⇒ divide by 2: 10 / 16

• Both even ⇒ divide by 2: 5 / 8

  Shortcut: Recognize both are multiples of 8 and divide at once: 40 / 8 = 5, 64 / 8 = 8

Answer: 5 / 8

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Example 3: 21 / 45

• Not even, but both divisible by 3: 21 / 3 = 7, 45 / 3 = 15

Answer: 7 / 15

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Example 4: 35 / 75

• Not even, not divisible by 3; both end with 5 ⇒ divide by 5: 35 / 5 = 7, 75 / 5 = 15

Answer: 7 / 15

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Example 5: 55 / 90

• Both end in 5 or 0 ⇒ divide by 5: 55 / 5 = 11, 90 / 5 = 18

Answer: 11 / 18

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Key Tips

• Even Numbers: Start by dividing by 2.
• Divisible by 3: Check if both can be divided by 3.
• Ends with 5 or 0: Try dividing by 5.
• Know your multiplication tables for quickly spotting common factors.
• Most problems can be handled with factors of 2, 3, and 5.

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Practice: Apply these rules to any given fraction to simplify it.