Q. \(8\frac{3}{4} \times 5\frac{5}{8}\) double window envelopes.

Interpret the notation. The expression 8-3/4 × 5-5/8 denotes the product of the mixed numbers 8 3/4 and 5 5/8.

Convert each mixed number to an improper fraction. For a mixed number A B/C, compute A×C + B over C.

\[8\frac{3}{4} = \frac{8\times 4 + 3}{4} = \frac{32 + 3}{4} = \frac{35}{4}\]

\[5\frac{5}{8} = \frac{5\times 8 + 5}{8} = \frac{40 + 5}{8} = \frac{45}{8}\]

Multiply the two improper fractions: multiply numerators together and denominators together.

\[\frac{35}{4}\times\frac{45}{8} = \frac{35\times 45}{4\times 8} = \frac{1575}{32}\]

Reduce the fraction if possible. Since 32 is a power of 2 and 1575 is odd (not divisible by 2), there is no common factor of 2, so the fraction is already in lowest terms:

\[\frac{1575}{32}\text{ is in simplest form.}\]

Convert the improper fraction to a mixed number by dividing 1575 by 32. The quotient is 49 and the remainder is 7, because 32×49 = 1568 and 1575 − 1568 = 7.

\[\frac{1575}{32} = 49\frac{7}{32}\]

Optional: express as a decimal. Compute 7 divided by 32 = 0.21875, so

\[49\frac{7}{32} = 49.21875\]