The quotient that you get of an dividing the reciprocal of the sum of `(-4)/(15) + (2)/(5) ` by the sum is

Options

A. 1
B. `-1`
C. `(225)/(4)`
D. none of these

Answer

To solve the problem step by step, we will first find the sum of the fractions, then calculate the reciprocal of that sum, and finally divide the reciprocal by the sum to find the quotient.

### Step 1: Find the sum of the fractions \(-\frac{4}{15}\) and \(\frac{2}{5}\).

To add the fractions, we need a common denominator. The least common multiple (LCM) of 15 and 5 is 15.

\[ -\frac{4}{15} + \frac{2}{5} = -\frac{4}{15} + \frac{2 \times 3}{5 \times 3} = -\frac{4}{15} + \frac{6}{15} \]

Now, we can combine the fractions:

\[ -\frac{4}{15} + \frac{6}{15} = \frac{-4 + 6}{15} = \frac{2}{15} \]

### Step 2: Find the reciprocal of the sum.

The sum we found is \(\frac{2}{15}\). The reciprocal of a fraction \(\frac{a}{b}\) is \(\frac{b}{a}\).

\[ \text{Reciprocal of } \frac{2}{15} = \frac{15}{2} \]

### Step 3: Divide the reciprocal by the sum.

Now we need to divide the reciprocal \(\frac{15}{2}\) by the sum \(\frac{2}{15}\):

\[ \frac{15}{2} \div \frac{2}{15} \]

To divide fractions, we multiply by the reciprocal of the second fraction:

\[ \frac{15}{2} \times \frac{15}{2} = \frac{15 \times 15}{2 \times 2} = \frac{225}{4} \]

### Final Answer:

The quotient that you get by dividing the reciprocal of the sum by the sum is:

\[ \frac{225}{4} \]

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