Answer :
Step-by-step explanation:
To simplify the expression \(1 \frac{5}{6} \times 2 \frac{3}{4} + 1 \frac{5}{6} \times 1 \frac{3}{4}\), we can follow these steps:
Step 1: Convert mixed numbers to improper fractions:
\[1 \frac{5}{6} = \frac{6}{6} + \frac{5}{6} = \frac{6 + 5}{6} = \frac{11}{6}\]
\[2 \frac{3}{4} = \frac{8}{4} + \frac{3}{4} = \frac{8 + 3}{4} = \frac{11}{4}\]
\[1 \frac{3}{4} = \frac{4}{4} + \frac{3}{4} = \frac{4 + 3}{4} = \frac{7}{4}\]
Step 2: Perform the multiplications:
\[1 \frac{5}{6} \times 2 \frac{3}{4} = \frac{11}{6} \times \frac{11}{4}\]
\[1 \frac{5}{6} \times 1 \frac{3}{4} = \frac{11}{6} \times \frac{7}{4}\]
Step 3: Multiply the fractions:
\[\frac{11}{6} \times \frac{11}{4} = \frac{121}{24}\]
\[\frac{11}{6} \times \frac{7}{4} = \frac{77}{24}\]
Step 4: Add the results:
\[\frac{121}{24} + \frac{77}{24} = \frac{121 + 77}{24} = \frac{198}{24}\]
Step 5: Simplify the fraction:
\[\frac{198}{24} = \frac{198 \div 6}{24 \div 6} = \frac{33}{4}\]
So, \(1 \frac{5}{6} \times 2 \frac{3}{4} + 1 \frac{5}{6} \times 1 \frac{3}{4}\) simplifies to \( \frac{33}{4} \).