Sure! Let's go through the multiplication of the two mixed numbers step-by-step.
### Problem
Multiply the mixed numbers [tex]\( 2 \frac{5}{6} \)[/tex] and [tex]\( 3 \frac{7}{8} \)[/tex].
### Step-by-Step Solution
1. Convert the Mixed Numbers to Improper Fractions:
- For [tex]\( 2 \frac{5}{6} \)[/tex]:
- The whole number part is [tex]\( 2 \)[/tex].
- The fraction part is [tex]\( \frac{5}{6} \)[/tex].
- Convert to an improper fraction:
[tex]\[
\frac{\text{whole number} \times \text{denominator} + \text{numerator}}{\text{denominator}} = \frac{2 \times 6 + 5}{6} = \frac{12 + 5}{6} = \frac{17}{6}
\][/tex]
- For [tex]\( 3 \frac{7}{8} \)[/tex]:
- The whole number part is [tex]\( 3 \)[/tex].
- The fraction part is [tex]\( \frac{7}{8} \)[/tex].
- Convert to an improper fraction:
[tex]\[
\frac{\text{whole number} \times \text{denominator} + \text{numerator}}{\text{denominator}} = \frac{3 \times 8 + 7}{8} = \frac{24 + 7}{8} = \frac{31}{8}
\][/tex]
2. Multiply the Improper Fractions:
- The fractions to multiply are [tex]\( \frac{17}{6} \)[/tex] and [tex]\( \frac{31}{8} \)[/tex].
- Multiply the numerators:
[tex]\[
17 \times 31 = 527
\][/tex]
- Multiply the denominators:
[tex]\[
6 \times 8 = 48
\][/tex]
- The product of the two fractions is:
[tex]\[
\frac{527}{48}
\][/tex]
### Result
So, the multiplication of [tex]\( 2 \frac{5}{6} \times 3 \frac{7}{8} \)[/tex] results in the improper fraction [tex]\( \frac{527}{48} \)[/tex].
Therefore, the final answer is:
[tex]\[
2 \frac{5}{6} \times 3 \frac{7}{8} = \frac{527}{48}
\][/tex]
