36:99 in its simplest form

lucas.M

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22-01-2025

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Fractions represent parts of a whole. Sometimes, fractions can be simplified to make them easier to understand and work with. This article explains how to simplify the fraction 36/99 to its simplest form. We'll cover the steps involved and why this simplification is important.

Understanding Fraction Simplification

Simplifying a fraction means reducing it to its lowest terms. This means finding the greatest common divisor (GCD) of both the numerator (top number) and the denominator (bottom number) and dividing both by that number. The resulting fraction will be equivalent to the original but will be expressed in a simpler, more manageable way.

Finding the GCD of 36 and 99

To simplify 36/99, we need to find the greatest common divisor (GCD) of 36 and 99. One way to do this is by listing the factors of each number:

• Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
• Factors of 99: 1, 3, 9, 11, 33, 99

The largest number that appears in both lists is 9. Therefore, the GCD of 36 and 99 is 9.

Alternatively, you can use the Euclidean algorithm to find the GCD more efficiently, especially for larger numbers.

Simplifying 36/99

Now that we know the GCD is 9, we divide both the numerator and the denominator of the fraction by 9:

36 ÷ 9 = 4

99 ÷ 9 = 11

Therefore, the simplified form of 36/99 is 4/11.

Why Simplify Fractions?

Simplifying fractions makes them easier to:

• Understand: 4/11 is much easier to visualize and comprehend than 36/99.
• Compare: Comparing 4/11 to other fractions is simpler than comparing 36/99.
• Calculate: Calculations involving 4/11 are generally quicker and less prone to errors.

Conclusion

Simplifying the fraction 36/99 to its simplest form, 4/11, involves finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by that GCD. This process results in an equivalent fraction that is easier to understand and work with in various mathematical operations. Remember, simplifying fractions is a fundamental skill in mathematics with numerous practical applications.