Final answer:
When we add fractions with the same denominator, we add the numerators. So, 1/12 + 1/12 + 1/12 equals 3/12, which simplifies to 1/4 when both numerator and denominator are divided by their greatest common divisor, confirming the equality of these two expressions.
Step-by-step explanation:
To understand why 1/12 + 1/12 + 1/12 is the same as 1/4, we need to consider the concept of adding fractions. When we add fractions with the same denominator, we simply add the numerators together and keep the denominator the same. In this case, adding three 1/12s together gives us:
1/12 + 1/12 + 1/12 = (1+1+1)/12 = 3/12
Now, we can simplify the fraction 3/12 by dividing both the numerator and the denominator by their greatest common divisor, which is 3. So, we get:
3/12 = (3÷3)/(12÷3) = 1/4
Hence, after simplification, 3/12 is equivalent to 1/4. This is due to the rules of equivalence and simplification in fraction operations, and it relates back to the concept of reciprocals in multiplication and division. The process of simplifying fractions ensures that an expression remains an equality as long as we perform the same operation on both the numerator and the denominator.