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A farmer's land is separated into sections of size
2(3)/(7) acres. Suppose there are
2(4)/(5) such sections. How many acres of land does the farmer own?
Write your answer as a mixed number in simplest form.

A farmer's land is separated into sections of size $2 \frac{3}{7}$ acres. Suppose there are $2 \frac{4}{5}$ such sections. How many acres of land does the farmer own? $\newline$ Write your answer as a mixed number in simplest form.

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Multiplication with rational exponents

Full solution

Q. A farmer's land is separated into sections of size

2 \frac{3}{7}

acres. Suppose there are

2 \frac{4}{5}

such sections. How many acres of land does the farmer own?

\newline

Write your answer as a mixed number in simplest form.

Convert to Improper Fractions: Convert mixed numbers to improper fractions for easier multiplication. $\newline$ $2\frac{3}{7} = \frac{2\times7 + 3}{7} = \frac{17}{7}$ acres per section. $\newline$ $2\frac{4}{5} = \frac{2\times5 + 4}{5} = \frac{14}{5}$ sections.
Multiply Fractions: Multiply the fractions to find the total acres. $\newline$ $(\frac{17}{7}) \times (\frac{14}{5}) = \frac{17\times14}{7\times5} = \frac{238}{35}$ acres.
Simplify Fraction: Simplify the fraction to a mixed number. $\newline$ $238 \div 35 = 6$ remainder $28$ , so it's $6\left(\frac{28}{35}\right)$ . $\newline$ Reduce $\frac{28}{35}$ by dividing both numerator and denominator by their GCD, which is $7$ . $\newline$ $28 \div 7 = 4$ and $35 \div 7 = 5$ . $\newline$ So, $\frac{28}{35}$ simplifies to $\frac{4}{5}$ .

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