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06-02-2025

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Simplifying 30/42: A Step-by-Step Guide

Title Tag: Simplify 30/42: Easy Steps & Explanation

Meta Description: Learn how to simplify the fraction 30/42 to its lowest terms. This step-by-step guide provides a clear explanation and examples, perfect for students and anyone needing a refresher on fraction simplification.

H1: Simplifying the Fraction 30/42

Finding the simplest form of a fraction, like 30/42, means reducing it to its lowest terms. This means finding the greatest common divisor (GCD) of the numerator (30) and the denominator (42) and dividing both by it.

H2: Finding the Greatest Common Divisor (GCD)

To simplify 30/42, we first need to find the greatest common divisor (GCD) of 30 and 42. There are a few ways to do this:

• Listing Factors: List all the factors of 30 (1, 2, 3, 5, 6, 10, 15, 30) and 42 (1, 2, 3, 6, 7, 14, 21, 42). The largest number that appears in both lists is the GCD. In this case, it's 6.

• Prime Factorization: Break down both numbers into their prime factors.

  • 30 = 2 x 3 x 5
  • 42 = 2 x 3 x 7 The common prime factors are 2 and 3. Multiply them together (2 x 3 = 6) to find the GCD.

• Euclidean Algorithm (for larger numbers): This is a more efficient method for larger numbers, but for 30 and 42, the above methods are quicker.

H2: Simplifying the Fraction

Now that we know the GCD is 6, we can simplify the fraction:

• Divide both the numerator (30) and the denominator (42) by the GCD (6):

30 ÷ 6 = 5 42 ÷ 6 = 7

Therefore, the simplified fraction is 5/7.

H2: Why Simplify Fractions?

Simplifying fractions makes them easier to understand and work with. A simplified fraction represents the same value as the original fraction, but in its most concise form. This is crucial for further calculations and comparisons.

H2: Practice Problems (with solutions)

Here are a few practice problems to test your understanding:

• Simplify 12/18: The GCD of 12 and 18 is 6. 12 ÷ 6 = 2; 18 ÷ 6 = 3. The simplified fraction is 2/3.

• Simplify 25/75: The GCD of 25 and 75 is 25. 25 ÷ 25 = 1; 75 ÷ 25 = 3. The simplified fraction is 1/3.

• Simplify 14/21: The GCD of 14 and 21 is 7. 14 ÷ 7 = 2; 21 ÷ 7 = 3. The simplified fraction is 2/3.

H2: Conclusion

Simplifying fractions like 30/42 is a fundamental skill in mathematics. By understanding the concept of the greatest common divisor and following the steps outlined above, you can easily reduce any fraction to its lowest terms. Remember to practice regularly to master this essential skill. This will make working with fractions much smoother in the future.