$4 \frac{1}{12} \times 2 \frac{3}{10} \approx 4 \times[?]$ $\newline$ The estimated product is [ ] .

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4 \frac{1}{12} \times 2 \frac{3}{10} \approx 4 \times[?]

\newline

The estimated product is [ ] .

Convert to Improper Fractions: First, let's convert the mixed numbers to improper fractions to make the multiplication easier. $\newline$ $4\left(\frac{1}{12}\right)$ can be converted to an improper fraction by multiplying the whole number $4$ by the denominator $12$ and then adding the numerator $1$ . $\newline$ So, $4\left(\frac{1}{12}\right) = \left(4\times12 + 1\right)/12 = \left(48 + 1\right)/12 = 49/12$ .
Multiply Improper Fractions: Similarly, convert $2\left(\frac{3}{10}\right)$ to an improper fraction by multiplying the whole number $2$ by the denominator $10$ and then adding the numerator $3$ . So, $2\left(\frac{3}{10}\right) = \left(2\times10 + 3\right)/10 = \left(20 + 3\right)/10 = 23/10$ .
Estimate Product: Now, multiply the two improper fractions together. $(\frac{49}{12}) \times (\frac{23}{10}) = (\frac{49\times23}{12\times10})$ .
Estimate Product: Now, multiply the two improper fractions together. $\newline$ $(\frac{49}{12}) \times (\frac{23}{10}) = (\frac{49\times23}{12\times10})$ .Before multiplying the numerators and denominators, we can estimate the product by rounding the fractions to the nearest whole number. $\newline$ $\frac{49}{12}$ is approximately equal to $4$ because $49$ is close to $48$ , which is $4$ times $12$ . $\newline$ $\frac{23}{10}$ is approximately equal to $2$ because $23$ is close to $\frac{49}{12}$ $0$ , which is $2$ times $\frac{49}{12}$ $2$ .
Estimate Product: Now, multiply the two improper fractions together. $\newline$ $(\frac{49}{12}) \times (\frac{23}{10}) = (\frac{49\times23}{12\times10})$ .Before multiplying the numerators and denominators, we can estimate the product by rounding the fractions to the nearest whole number. $\newline$ $\frac{49}{12}$ is approximately equal to $4$ because $49$ is close to $48$ , which is $4$ times $12$ . $\newline$ $\frac{23}{10}$ is approximately equal to $2$ because $23$ is close to $\frac{49}{12}$ $0$ , which is $2$ times $\frac{49}{12}$ $2$ .Now, multiply the estimated values. $\newline$ Estimated product = $\frac{49}{12}$ $3$ .