Arliss has two pieces of carpet runner. One is yards long and the other is yards long. She needs 10 yards of carpet runner altogether. How much more does she need to buy?

Given:

10 yards required

5 2/3 yards on hand.

We need to subtract the yards on hand from the total yards required.

First, we need to convert the mixed fraction into an improper fraction.

5 2/3 = ((5*3) + 2) / 3 = (15+2) / 3 = 17/3

Second, we need to multiply 10 by a fraction that will give us the denominator of 3.

10 * 3/3 = (10*3) / 3 = 30/3

Third, we do subtraction using our derived fractions.

30/3 - 17/3 = (30-17) / 3 = 13/3

Lastly, we simplify the improper fraction. Improper fraction is a fraction whose numerator is greater than its denominator. Its simplified form is a mixed fraction.

13/3 = 4 1/3

Arliss needs to buy 4 1/3 yards more to complete the required yard length.