$3 \frac{7}{8} \times 4 \frac{4}{5}$

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02-11-2026
Mathematics

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$3 \frac{7}{8} \times 4 \frac{4}{5}$

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-02T17:32:22-05:00

Convert the mixed numbers $3 \frac{7}{8}$ and $4 \frac{4}{5}$ to improper fractions $\frac{31}{8}$ and $\frac{24}{5}$.
Multiply these fractions to get $\frac{31 \times 24}{8 \times 5} = \frac{93}{5}$.
Simplify the fraction by dividing to find the mixed number form, which results in $\boxed{18 \frac{3}{5}}$.

Explanation

Converting Mixed Numbers to Improper Fractions

To compute the product of two mixed numbers, $3 \frac{7}{8}$ and $4 \frac{4}{5}$, we first convert them into improper fractions. An improper fraction is a fraction where the numerator is greater than or equal to the denominator, and it can be written as $\frac{A \cdot C + B}{C}$ for a mixed number $A \frac{B}{C}$. Applying this to our values:

For $3 \frac{7}{8}$, we have $\frac{3 \times 8 + 7}{8} = \frac{24 + 7}{8} = \frac{31}{8}$.
For $4 \frac{4}{5}$, we have $\frac{4 \times 5 + 4}{5} = \frac{20 + 4}{5} = \frac{24}{5}$.

Multiplying the Fractions

Now that we have the two improper fractions, we multiply them by multiplying their numerators together and their denominators together:
\[\frac{31}{8} \times \frac{24}{5} = \frac{31 \times 24}{8 \times 5}\]
Before performing the full multiplication, we can simplify the expression. Notice that $24$ and $8$ have a common factor of $8$:
\[\frac{31 \times 24}{8 \times 5} = \frac{31 \times 3}{1 \times 5} = \frac{93}{5}\]

Converting to a Mixed Number and Final Result

The improper fraction $\frac{93}{5}$ can be converted back to a mixed number by dividing the numerator by the denominator:
$93 \div 5 = 18$ with a remainder of $3$.
Thus, the fraction is equivalent to $18 \frac{3}{5}$.
The final result is $\boxed{18 \frac{3}{5}}$.

Examples

In a kitchen, if a recipe calls for $3 \frac{7}{8}$ cups of flour and you need to make $4 \frac{4}{5}$ times the amount for a large event, you need to calculate exactly how much flour to use. By converting mixed numbers to improper fractions, you can perform the multiplication easily to determine that you need exactly $18 \frac{3}{5}$ cups of flour. This method is essential for scaling measurements in cooking, construction, and other practical daily tasks.