Calculate one-fourth plus one-third.
We need to think about the steps that we need to follow when we add and subtract fractions. First, we check to see if the fractions have common denominators, and if they don’t, we need to rename our fractions with a common denominator. One-fourth and one-third do not share common denominator, which means we need to rename them so that they do have a common denominator. 12 is a multiple of four and three: three times four equals 12 and four times three equals 12.
But remember if we multiply the denominator by something, we also need to multiply the numerator by the same amount. In this case, we multiply one times three, and one-fourth becomes three-twelfths. And then we multiply one by four; one-third becomes four-twelfths. Everything we did in this step was part of finding the common denominator.
It’s time for step two: to add or subtract. In our case, we’re adding, and now we’re adding three-twelfths plus four-twelfths. Three plus four equals seven. And when we’re adding and subtracting fractions, the denominator does not change. So we bring 12 across. This was our adding step.
Our third and final step is to simplify this number or reduce it if that’s possible. We asked the question, can this value, seven-twelfths, be reduced? The answer here is no. Seven-twelfths is already in its simplest form. This means that one-fourth plus one-third equals seven-twelfths. Seven-twelfths is your final answer.