What is the fraction 12/30 in simplest form?
The Correct Answer and Explanation is :
To simplify the fraction ( \frac{12}{30} ), we need to divide both the numerator (12) and the denominator (30) by their greatest common divisor (GCD). The GCD of two numbers is the largest number that divides both of them without leaving a remainder.
Step 1: Find the GCD
We can find the GCD of 12 and 30 by listing the factors:
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
From the lists, the common factors are 1, 2, 3, and 6. The greatest of these is 6, so the GCD of 12 and 30 is 6.
Step 2: Divide by the GCD
Next, we simplify the fraction by dividing both the numerator and the denominator by their GCD:
[
\frac{12 \div 6}{30 \div 6} = \frac{2}{5}
]
Conclusion
Thus, the fraction ( \frac{12}{30} ) in simplest form is ( \frac{2}{5} ).
Explanation of Simplifying Fractions
Simplifying fractions is an essential mathematical skill that helps in understanding ratios and proportions. A fraction consists of two parts: the numerator, which represents the number of parts we have, and the denominator, which represents the total number of equal parts. When both the numerator and the denominator are divided by their GCD, the fraction is expressed in its simplest form, which makes it easier to compare with other fractions, perform operations, and interpret real-world situations involving ratios.
For instance, knowing that ( \frac{12}{30} ) simplifies to ( \frac{2}{5} ) can help us understand that for every 5 equal parts of a whole, 2 parts are being considered. Simplifying fractions not only provides clarity but also facilitates mathematical computations, especially in areas such as algebra, where fractions are frequently encountered.