Question

subtract. write your answer as a fraction or as a whole or mixed number.
$19\frac{1}{3} - 8\frac{2}{3} = \square$

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \(19\frac{1}{3}\) and \(8\frac{2}{3}\) to improper fractions. The formula for converting a mixed number \(a\frac{b}{c}\) to an improper fraction is \(\frac{a\times c + b}{c}\).

For \(19\frac{1}{3}\):
\(19\times3 + 1 = 57 + 1 = 58\), so \(19\frac{1}{3}=\frac{58}{3}\)

For \(8\frac{2}{3}\):
\(8\times3 + 2 = 24 + 2 = 26\), so \(8\frac{2}{3}=\frac{26}{3}\)

Step2: Subtract the improper fractions

Now subtract the two improper fractions: \(\frac{58}{3}-\frac{26}{3}=\frac{58 - 26}{3}=\frac{32}{3}\)

Step3: Convert the improper fraction back to a mixed number (if needed)

Convert \(\frac{32}{3}\) to a mixed number. Divide 32 by 3: \(32\div3 = 10\) with a remainder of \(2\), so \(\frac{32}{3}=10\frac{2}{3}\)

Alternatively, we can also subtract the whole numbers and the fractions separately. Let's check that method:

Alternative Step1: Subtract whole numbers and fractions separately

Subtract the whole numbers: \(19 - 8 = 11\)

Subtract the fractions: \(\frac{1}{3}-\frac{2}{3}\). Since \(\frac{1}{3}<\frac{2}{3}\), we need to borrow 1 from the whole number part of \(19\frac{1}{3}\). So \(19\frac{1}{3}=18 + 1+\frac{1}{3}=18+\frac{3}{3}+\frac{1}{3}=18\frac{4}{3}\)

Now subtract: \(18\frac{4}{3}-8\frac{2}{3}=(18 - 8)+(\frac{4}{3}-\frac{2}{3}) = 10+\frac{2}{3}=10\frac{2}{3}\)

Answer:

\(10\frac{2}{3}\)