Fractions - Problem Solving


How many minutes are there in \(50\%\) of a third of the entire day?

Details and assumptions

An entire day consists of \(24\) hours.

In a certain positive fraction \( \frac{a}{b} \), the numerator is 2 less than the denominator. If the numerator and denominator are interchanged, the fraction is increased by \( 1 \frac{1}{15} \). Find \( a + b \).

Details and assumptions

A positive fraction is a fraction that has a positive value. For example, \( \frac {10}{12} \) and \( \frac { - 2.3}{-0.3} \) are both positive fractions.

It takes \(3\) hours for Amy and Beth to water their garden together every weekend. One Saturday, Amy had already been working for \(5\) hours alone when Beth woke up late. Then they worked together for \(1\) hour(s) to finish the job. If Amy works alone, how many hours would it take to water their garden?

The area of South Korea is \(\frac{10}{37}\) of the area of Japan. The area of North Korea is \(\frac{12}{25}\) of the area of Texas. If the area of Texas is \(\frac{25}{37}\) of that of Japan and the area of Japan is \(\frac{37}{982}\) of that of the United States, what fraction of Korean peninsular is South Korea?

Note: All the measurements given in this problem are approximate values.

Find the greatest number given by multiplying three of the following four rational numbers: \[-\frac{2}{3}, 21, -4, 18?\]


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