Question

1\frac{3}{4}+6\frac{6}{7}=

Explanation:

Step1: Convert mixed numbers to improper fractions

For \(1\frac{3}{4}\), the improper fraction is \(\frac{1\times4 + 3}{4}=\frac{7}{4}\). For \(6\frac{6}{7}\), the improper fraction is \(\frac{6\times7+6}{7}=\frac{48}{7}\).

Step2: Find a common denominator

The least common denominator of 4 and 7 is \(4\times7 = 28\).

Step3: Rewrite fractions with the common denominator

\(\frac{7}{4}=\frac{7\times7}{4\times7}=\frac{49}{28}\) and \(\frac{48}{7}=\frac{48\times4}{7\times4}=\frac{192}{28}\).

Step4: Add the fractions

\(\frac{49}{28}+\frac{192}{28}=\frac{49 + 192}{28}=\frac{241}{28}\).

Step5: Convert back to a mixed number

\(241\div28 = 8\) with a remainder of \(17\), so \(\frac{241}{28}=8\frac{17}{28}\).

Answer:

\(8\frac{17}{28}\)