Write the fraction in lowest terms.
$\frac{8}{12}$
Answer (1)
Find the greatest common divisor (GCD) of the numerator and denominator.
Divide both the numerator and the denominator by their GCD.
Simplify the fraction to its lowest terms.
The fraction 12 8 in lowest terms is 3 2 .
Explanation
Understanding the Problem We are asked to write the fraction 12 8 in its lowest terms. This means we need to find a fraction that is equivalent to 12 8 but has the smallest possible numerator and denominator. To do this, we will find the greatest common divisor (GCD) of the numerator and the denominator and then divide both by that GCD.
Finding the Greatest Common Divisor (GCD) To find the greatest common divisor (GCD) of 8 and 12, we can list the factors of each number. The factors of 8 are 1, 2, 4, and 8. The factors of 12 are 1, 2, 3, 4, 6, and 12. The common factors are 1, 2, and 4. The greatest of these is 4. Therefore, the GCD of 8 and 12 is 4.
Dividing by the GCD Now, we divide both the numerator and the denominator by the GCD, which is 4. So, we have 12 ÷ 4 8 ÷ 4 = 3 2 .
Final Answer The fraction 3 2 is in its lowest terms because the GCD of 2 and 3 is 1. Therefore, the fraction 12 8 in lowest terms is 3 2 .
Examples
Fractions are used in everyday life, such as when cooking, measuring ingredients, or splitting a bill with friends. Simplifying fractions helps us understand proportions and ratios more easily. For example, if you have 8 slices of pizza and want to share it equally among 12 people, each person gets 12 8 of the pizza. Simplifying this fraction to 3 2 tells you that each person gets 2 out of every 3 slices.
