Question

1\frac{3}{4}+6\frac{1}{3}

Explanation:

Step1: Convert mixed numbers to improper fractions

To add mixed numbers, first convert them to improper fractions. For \(1\frac{3}{4}\), multiply the whole number \(1\) by the denominator \(4\) and add the numerator \(3\): \(1\times4 + 3 = 7\), so \(1\frac{3}{4}=\frac{7}{4}\). For \(6\frac{1}{3}\), multiply the whole number \(6\) by the denominator \(3\) and add the numerator \(1\): \(6\times3 + 1 = 19\), so \(6\frac{1}{3}=\frac{19}{3}\).

Step2: Find a common denominator

The denominators are \(4\) and \(3\), and the least common denominator (LCD) of \(4\) and \(3\) is \(12\). Convert \(\frac{7}{4}\) to a fraction with denominator \(12\) by multiplying the numerator and denominator by \(3\): \(\frac{7\times3}{4\times3}=\frac{21}{12}\). Convert \(\frac{19}{3}\) to a fraction with denominator \(12\) by multiplying the numerator and denominator by \(4\): \(\frac{19\times4}{3\times4}=\frac{76}{12}\).

Step3: Add the fractions

Now add the two fractions with the common denominator: \(\frac{21}{12}+\frac{76}{12}=\frac{21 + 76}{12}=\frac{97}{12}\).

Step4: Convert back to a mixed number (optional)

To convert \(\frac{97}{12}\) back to a mixed number, divide \(97\) by \(12\). \(12\times8 = 96\), so \(97\div12 = 8\) with a remainder of \(1\). Thus, \(\frac{97}{12}=8\frac{1}{12}\).

Answer:

\(8\frac{1}{12}\) (or \(\frac{97}{12}\))