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15/72 simplified

Understand the Problem

The question is asking for the simplification of the fraction 15/72 to its lowest terms, which involves finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by it.

Answer

The simplified form of the fraction is $\frac{5}{24}$.
Answer for screen readers

The simplified form of the fraction $\frac{15}{72}$ is $\frac{5}{24}$.

Steps to Solve

  1. Finding the GCD To simplify the fraction, we first need to find the greatest common divisor (GCD) of the numerator (15) and the denominator (72).

The factors of 15 are: 1, 3, 5, 15.
The factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.

The highest common factor between both sets is 3.

  1. Dividing Both Parts by the GCD Now that we have the GCD (3), we can simplify the fraction by dividing both the numerator and the denominator by this GCD:

$$ \frac{15 \div 3}{72 \div 3} $$

This results in:

$$ \frac{5}{24} $$

  1. Final Check We should check if the fraction $\frac{5}{24}$ can be simplified further. The factors of 5 are 1 and 5, while the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. Since 5 has no common factors with 24 other than 1, the fraction is in its simplest form.

The simplified form of the fraction $\frac{15}{72}$ is $\frac{5}{24}$.

More Information

The process of simplifying fractions is commonly used in mathematics, helping to express ratios and divisions in their most reduced form, making calculations easier and more understandable.

Tips

  • Forgetting to find the GCD correctly, which can lead to an incorrect simplification. Always double-check the factors.
  • Dividing only one part of the fraction by the GCD instead of both the numerator and the denominator.
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