Evaluate one-quarter plus one-third plus three-quarters plus negative two-sixths, giving the answer in its simplest form.
Our usual method when adding and subtracting fractions is to find the lowest common denominator. This is the lowest common multiple from all the denominators. However, in this case, we noticed that two of the fractions already have the same denominator — one-quarter plus three-quarters. One-quarter plus three-quarters is equal to four-quarters. This is equal to one. Therefore, one-quarter plus three-quarters equals one.
The fraction negative two-sixths can be simplified to negative one-third. We can divide the numerator by two and the denominator by two. This means that the original question can be simplified to one plus one-third plus negative one-third. Simplifying this one stage further gives us one plus a third minus a third. As plus a third minus one-third is equal to zero, our final answer is equal to one. This means that one-quarter plus a third plus three-quarters plus negative two-sixths in its simplest form is equal to one.
The alternative method would’ve been to find the lowest common denominator — in this case 12. One-quarter is the same as three 12th, one-third is the same as four 12th, three-quarters is the same as nine 12th, and negative two-sixths is the same as negative four 12th.
We can then simplify the numerators. Three plus four plus nine minus four is equal to 12. So our answer is twelve 12th. Twelve 12th is the same as one. So our answer using this method is also one.