If Carol can write 3 articles for the newspaper every \(2 \frac{\mathrm{1} }{\mathrm{2} } \) hours, how many articles can she write in 10 hours?

If Carol can write 3 articles for the newspaper every \(2 \frac{\mathrm{1} }{\mathrm{2} } \) hours, how many articles can she write in 10 hours?

Detailed Explanation

Convert the mixed number to an improper fraction by multiplying the denominator by the base number and adding it to the numerator. \(2 \frac{\mathrm{1} }{\mathrm{2} } = \frac{\mathrm{2 \times 2 + 1} }{\mathrm{2} } = \frac{\mathrm{5} }{\mathrm{2}} \).

Divide 10 hours by 5/2.

Remember that when dividing by a fraction, you can multiply it by its reciprocal instead. \(10 \div \frac{\mathrm{5} }{\mathrm{2} } = 10 \times \frac{\mathrm{2} }{\mathrm{5} } = \frac{\mathrm{20} }{\mathrm{5} } = 4\) .

Since Carol can write 3 articles in each \(2 \frac{\mathrm{1} }{\mathrm{2} } \) hour time period, multiply 4 by 3 to find the total number of articles she can write in 10 hours. \(4 \times 3 = 12\) articles.

Divide 10 hours by 5/2.

Remember that when dividing by a fraction, you can multiply it by its reciprocal instead. \(10 \div \frac{\mathrm{5} }{\mathrm{2} } = 10 \times \frac{\mathrm{2} }{\mathrm{5} } = \frac{\mathrm{20} }{\mathrm{5} } = 4\) .

Since Carol can write 3 articles in each \(2 \frac{\mathrm{1} }{\mathrm{2} } \) hour time period, multiply 4 by 3 to find the total number of articles she can write in 10 hours. \(4 \times 3 = 12\) articles.