Let's solve this fraction problem step by step. We have four-fifths plus two-thirds plus one-fifth minus one-third. First, we'll group the fractions that have the same denominator. We put four-fifths and one-fifth together, and we group two-thirds and one-third together.
Now, let's add or subtract the fractions in each group. For the first group, we add four-fifths and one-fifth. Since they have the same denominator, we just add the numerators: four plus one equals five. So we get five-fifths, which simplifies to one. For the second group, we subtract one-third from two-thirds. Again, with the same denominator, we subtract the numerators: two minus one equals one. So we get one-third.
Now, let's add the results from each group. We have one from the first group and one-third from the second group. To add a whole number and a fraction, we need to convert the whole number to a fraction with the same denominator. One is equivalent to three-thirds. Now we can add three-thirds and one-third. With the same denominator, we add the numerators: three plus one equals four. So our final answer is four-thirds.
Let's summarize what we've learned about adding and subtracting fractions. We started with the problem: four-fifths plus two-thirds plus one-fifth minus one-third. First, we grouped fractions with the same denominator. Then, we added or subtracted within each group to get one plus one-third. Next, we converted the whole number to a fraction with the same denominator as one-third, giving us three-thirds plus one-third. Finally, we added these fractions to get our answer: four-thirds. Remember these key steps when working with fractions that have different denominators.