Question

find the sum and write the answer in simplest form. make sure to show all your work.
$4\frac{1}{3} + 3\frac{1}{2}$
(2 points)

Explanation:

Step1: Convert mixed numbers to improper fractions

To convert \(4\frac{1}{3}\) to an improper fraction, multiply the whole number (4) by the denominator (3) and add the numerator (1): \(4\times3 + 1 = 13\), so \(4\frac{1}{3}=\frac{13}{3}\).
To convert \(3\frac{1}{2}\) to an improper fraction, multiply the whole number (3) by the denominator (2) and add the numerator (1): \(3\times2 + 1 = 7\), so \(3\frac{1}{2}=\frac{7}{2}\).

Step2: Find a common denominator

The denominators are 3 and 2. The least common denominator (LCD) of 3 and 2 is 6.

Step3: Rewrite fractions with the LCD

Rewrite \(\frac{13}{3}\) with denominator 6: \(\frac{13}{3}=\frac{13\times2}{3\times2}=\frac{26}{6}\).
Rewrite \(\frac{7}{2}\) with denominator 6: \(\frac{7}{2}=\frac{7\times3}{2\times3}=\frac{21}{6}\).

Step4: Add the fractions

Add the numerators: \(\frac{26}{6}+\frac{21}{6}=\frac{26 + 21}{6}=\frac{47}{6}\).

Step5: Convert back to a mixed number (optional, but often preferred)

Divide 47 by 6: \(6\times7 = 42\), so \(47 - 42 = 5\). Thus, \(\frac{47}{6}=7\frac{5}{6}\).

Answer:

\(7\frac{5}{6}\)