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
- 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.
- 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:
$$ \frac{5}{24} $$
- 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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