Calculate eight and two-fifths plus the negative of four and three-fifths. Give your answer as a mixed number.
Adding a negative number is the same as subtracting the number. This means that we can rewrite our calculation as eight and two-fifths minus four and three-fifths. There are lots of ways of approaching this problem from this point. One way is to turn both fractions into improper or top-heavy fractions. We can convert the mixed number, eight and two-fifths, into an improper fraction by multiplying eight by five and then adding two. Eight multiplied by five is equal to 40. Adding two to this gives us 42. Therefore, eight and two-fifths is equal to forty-two fifths.
We can do the same with the fraction four and three-fifths. Four multiplied by five is equal to 20. And, adding three to this gives us 23. Therefore, four and three-fifths is equal to twenty-three fifths. This comes from the general rule that any fraction in the form 𝑎 plus 𝑏 over 𝑐 is equal to 𝑎𝑐 plus 𝑏 over 𝑐. We multiply the whole number by the denominator and add this to the numerator. The denominator of the fraction stays the same.
Eight and two-fifths minus four and three-fifths is equal to forty-two fifths minus twenty-three fifths. As the denominator of both fractions is the same, we just need to subtract the numerators. 42 minus 23 is equal to 19. Therefore, our answer, as an improper fraction, is nineteen-fifths or 19 over five.
We were asked to give our answer as a mixed number. We do this by dividing 19 by five, the numerator by the denominator. 19 divided by five is equal to three remainder four. This means that the fraction 19 over five or nineteen-fifths is equal to three and four-fifths. The remainder becomes the numerator of our fraction, and the denominator stays the same.
We can check this by multiplying three by five and adding four. Three multiplied by five is equal to 15. And, adding four to this gives us 19. Therefore, our answer is correct. Eight and two-fifths plus negative four and three-fifths, written as a mixed number, is three and four-fifths.