What is 12/14 in its simplest form
The Correct Answer and Explanation is:
To simplify the fraction 1214\frac{12}{14}1412, you need to find the greatest common divisor (GCD) of 12 and 14. The GCD is the largest number that divides both 12 and 14 evenly.
Step 1: 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 common factors are: 1 and 2.
- The greatest common factor is 2.
Step 2: Divide both the numerator and the denominator by the GCD (2).
- 1214÷2=12÷214÷2=67\frac{12}{14} \div 2 = \frac{12 \div 2}{14 \div 2} = \frac{6}{7}1412÷2=14÷212÷2=76.
Thus, the simplified form of 1214\frac{12}{14}1412 is 67\frac{6}{7}76.
Explanation:
Simplifying a fraction involves reducing it to its simplest form, which is achieved by dividing both the numerator and the denominator by their greatest common divisor. The GCD is a crucial part of this process because it ensures the fraction is reduced as much as possible while maintaining its value. In this case, the numerator (12) and denominator (14) share the common factor of 2, which we used to divide both terms. After performing the division, the fraction 1214\frac{12}{14}1412 is reduced to 67\frac{6}{7}76.
By simplifying fractions, we make them easier to work with, especially in more complex mathematical operations like addition, subtraction, or multiplication of fractions. The simplest form of a fraction is also useful when comparing different fractions.
