what is 19/40 in simplest form as a fraction

Natashya

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26-12-2024

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The fraction 19/40 is already in its simplest form. Let's explore why and understand how to determine the simplest form of any fraction.

Understanding Simplest Form

A fraction is in its simplest form (or lowest terms) when the greatest common divisor (GCD) of the numerator (top number) and the denominator (bottom number) is 1. In other words, there's no whole number other than 1 that can divide both the numerator and the denominator evenly.

Finding the GCD of 19 and 40

To check if 19/40 can be simplified, we need to find the greatest common divisor (GCD) of 19 and 40.

The number 19 is a prime number, meaning its only divisors are 1 and itself. Let's look at the factors of 40:

• 1, 2, 4, 5, 8, 10, 20, 40

Since 19 doesn't appear in the list of factors of 40, and the only common factor of 19 and 40 is 1, their GCD is 1.

Conclusion: 19/40 is Already Simplified

Because the greatest common divisor of 19 and 40 is 1, the fraction 19/40 is already in its simplest form. There's no way to reduce it further. Therefore, the answer is 19/40.

Further Exploration: Simplifying Other Fractions

Let's look at an example of a fraction that can be simplified:

Example: Simplify 12/18

1. Find the GCD: The factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 18 are 1, 2, 3, 6, 9, and 18. The greatest common factor is 6.

2. Divide: Divide both the numerator and the denominator by the GCD (6): 12 ÷ 6 = 2 and 18 ÷ 6 = 3

3. Simplest Form: The simplified fraction is 2/3.

This process of finding the GCD and dividing is essential for simplifying fractions. However, as we've seen with 19/40, sometimes a fraction is already in its simplest form!