Question

what is $3\frac{1}{3}-1\frac{1}{2}$? show your work.

Explanation:

Step1: Convert mixed numbers to improper fractions

To subtract mixed numbers, first convert them to improper fractions. For \(3\frac{1}{3}\), multiply the whole number \(3\) by the denominator \(3\) and add the numerator \(1\): \(3\times3 + 1 = 10\), so \(3\frac{1}{3}=\frac{10}{3}\). For \(1\frac{1}{2}\), multiply \(1\) by \(2\) and add \(1\): \(1\times2 + 1 = 3\), so \(1\frac{1}{2}=\frac{3}{2}\).

Step2: Find a common denominator

The denominators are \(3\) and \(2\), so the least common denominator (LCD) is \(6\). Convert \(\frac{10}{3}\) to a fraction with denominator \(6\) by multiplying numerator and denominator by \(2\): \(\frac{10\times2}{3\times2}=\frac{20}{6}\). Convert \(\frac{3}{2}\) to a fraction with denominator \(6\) by multiplying numerator and denominator by \(3\): \(\frac{3\times3}{2\times3}=\frac{9}{6}\).

Step3: Subtract the fractions

Now subtract the two fractions: \(\frac{20}{6}-\frac{9}{6}=\frac{20 - 9}{6}=\frac{11}{6}\).

Step4: Convert back to a mixed number (optional)

Convert \(\frac{11}{6}\) back to a mixed number: \(11\div6 = 1\) with a remainder of \(5\), so \(\frac{11}{6}=1\frac{5}{6}\).

Answer:

\(1\frac{5}{6}\) (or \(\frac{11}{6}\))