What is
12
14
simplified to its simplest form?
The Correct Answer and Explanation is :
To simplify the fraction ( \frac{12}{14} ), you need to find the greatest common divisor (GCD) of the numerator (12) and the denominator (14) and then divide both by that number.
- Find the GCD of 12 and 14:
- The factors of 12 are: 1, 2, 3, 4, 6, 12.
- The factors of 14 are: 1, 2, 7, 14.
- The largest common factor between them is 2.
- Divide the numerator and denominator by 2:
- ( \frac{12 \div 2}{14 \div 2} = \frac{6}{7} ).
So, the fraction ( \frac{12}{14} ) simplified to its simplest form is ( \frac{6}{7} ).
Explanation
Simplifying a fraction means expressing it in the smallest possible terms, where the numerator and denominator have no common factors other than 1. In this case, the fraction ( \frac{12}{14} ) has both the numerator (12) and the denominator (14) that can be divided by 2, their GCD. This process of dividing by the GCD removes any common factors, resulting in ( \frac{6}{7} ).
The importance of simplifying fractions lies in making them easier to understand, compare, and use in calculations. For instance, in math or science problems, using simplified forms helps avoid large numbers, which could complicate computations and potentially lead to errors. When fractions are reduced, they represent the same ratio or proportion, just in a more straightforward form.
For example, if you have a recipe that calls for ( \frac{12}{14} ) of a cup of an ingredient, simplifying it to ( \frac{6}{7} ) of a cup makes it clearer and easier to measure. Simplified fractions are especially important in real-world applications like budgeting, engineering, and cooking, where precision and ease of understanding make a difference.