32/68 simplified

Art Scpae

less than a minute read

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08-10-2024

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Simplifying Fractions: A Step-by-Step Guide with 32/68

Fractions are a fundamental part of mathematics, and simplifying them is a crucial skill. Let's explore how to simplify the fraction 32/68.

Understanding the Concept:

Simplifying a fraction means finding an equivalent fraction with the smallest possible numerator and denominator. This is achieved by dividing both the numerator and denominator by their greatest common factor (GCD).

Finding the Greatest Common Factor (GCD):

• Prime Factorization: One way to find the GCD is through prime factorization. Let's break down 32 and 68:
  • 32 = 2 x 2 x 2 x 2 x 2
  • 68 = 2 x 2 x 17
• Identify Common Factors: We see that both 32 and 68 share the factors 2 x 2 x 2 = 8. Therefore, the GCD of 32 and 68 is 8.

Simplifying the Fraction:

• Divide by the GCD: Divide both the numerator and denominator of 32/68 by 8:
  • 32 ÷ 8 = 4
  • 68 ÷ 8 = 17
• Simplified Fraction: The simplified form of 32/68 is 4/17.

Example:

Imagine you have 32 cookies and need to share them equally among 68 people. Simplifying the fraction 32/68 to 4/17 tells us that each person would receive 4 cookies for every 17 people.

Key Takeaways:

• Simplify to Understand: Simplifying fractions makes them easier to understand and compare.
• Efficiency: Working with simplified fractions often leads to simpler calculations.
• Practical Applications: Simplifying fractions is used in various real-world applications like cooking, construction, and finance.

Beyond 32/68:

The same principles apply to simplifying any fraction. Practice finding the GCD and dividing to make fractions as simple as possible. Remember, a simplified fraction is a more efficient and understandable representation of the same value.