What fraction of 30 is 25?
The Correct Answer and Explanation is:
To find what fraction of 30 is 25, we need to express the relationship between 25 and 30 as a fraction. This can be done by dividing 25 by 30:
[
\text{Fraction} = \frac{25}{30}
]
Now, to simplify the fraction, we need to find the greatest common divisor (GCD) of 25 and 30. The GCD is the largest number that divides both 25 and 30. To find the GCD, we list the factors of each number:
- The factors of 25 are 1, 5, and 25.
- The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.
The common factors of 25 and 30 are 1 and 5, and the greatest of these is 5.
Next, we divide both the numerator and the denominator of the fraction by the GCD (which is 5):
[
\frac{25}{30} = \frac{25 \div 5}{30 \div 5} = \frac{5}{6}
]
So, the fraction of 30 that is 25 is (\frac{5}{6}).
Explanation:
This problem is about expressing one number as a fraction of another. In this case, we are trying to find out what fraction 25 is of 30. To do this, we divide 25 by 30, which gives the fraction (\frac{25}{30}). However, to express this fraction in its simplest form, we need to simplify it. Simplifying a fraction involves dividing both the numerator (the top number) and the denominator (the bottom number) by their greatest common divisor (GCD).
The GCD of 25 and 30 is 5, so we divide both 25 and 30 by 5. This results in the simplified fraction (\frac{5}{6}), which represents the portion of 30 that is equivalent to 25. Thus, ( \frac{5}{6} ) is the correct answer.