Question

The water level of a lake rose by (2 frac{1}{2}) inches during a (2 frac{6}{7}) week-long wet spell. Simplify the complex fraction below to find the average rate at which the water level changed every week:

[frac{frac{5}{2}}{frac{20}{7}}]

Answer 1

To simplify the complex fraction frac{frac{5}{2}}{frac{20}{7}}, you multiply the numerator by the reciprocal of the denominator to get frac{35}{40}, which simplifies to frac{7}{8} inches per week.

Step-by-step explanation:

To simplify the complex fraction frac{frac{5}{2}}{frac{20}{7}} to find the average rate at which the water level changed every week. To simplify this fraction, you divide the numerator by the denominator. This is done by multiplying the numerator by the reciprocal of the denominator. The reciprocal of frac{20}{7} is frac{7}{20}. Thus, the operation is frac{5}{2} times frac{7}{20}.

Now, multiply the numerators together and the denominators together:

• Numerator: 5 times 7 = 35
• Denominator: 2 times 20 = 40

So, we get the fraction frac{35}{40}, which can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 5:

• 35 ÷ 5 = 7
• 40 ÷ 5 = 8

So the simplified rate of change of the water level is frac{7}{8} inches per week.