What is the simplified fraction for 12/16
The Correct Answer and Explanation is:
The simplified fraction for 12/16 is 3/4.
To reduce a fraction to its simplest form, the numerator and the denominator must be divided by their greatest common divisor (GCD). In this case, 12 and 16 are both divisible by 4, which is their GCD.
First, identify the factors of each number:
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 16: 1, 2, 4, 8, 16
The largest factor that both numbers share is 4.
Next, divide the numerator and the denominator by 4: 12÷416÷4=34\frac{12 ÷ 4}{16 ÷ 4} = \frac{3}{4}16÷412÷4=43
Thus, 12/16 simplifies to 3/4.
This simplification indicates that the two fractions—12/16 and 3/4—are equivalent in value but differ in form. The simplified version uses the smallest whole numbers possible for both numerator and denominator without changing the value of the fraction.
Understanding simplification helps improve clarity in mathematical communication. For instance, when dealing with measurements, ratios, or portions in everyday problems, working with reduced fractions makes calculations faster and interpretation easier.
Another method involves prime factorization:
- 12 = 2 × 2 × 3
- 16 = 2 × 2 × 2 × 2
By canceling out the common prime factors (two 2s), the result also becomes 3/4.
Simplifying fractions is a key skill in arithmetic, algebra, and beyond. It ensures that results are presented in their cleanest, most efficient form, which is especially useful when comparing values or performing additional operations like addition or multiplication of fractions.
