The quotient of two numbers is `(-5)/(7).` If the divident is `(-4)/(5)` and remainder is 0, then find the divisor.

Options

A. `(26)/(15)`
B. `(28)/(25)`
C. `-(28)/(25)`
D. `(25)/(28)`

Answer

To find the divisor given the quotient, dividend, and remainder, we can use the relationship between these quantities. The formula we will use is:

\[ \text{Dividend} = \text{Quotient} \times \text{Divisor} + \text{Remainder} \]

Given:
- Dividend = \(-\frac{4}{5}\)
- Quotient = \(-\frac{5}{7}\)
- Remainder = 0

Let's denote the divisor as \( x \).

### Step 1: Set up the equation
Using the formula, we can substitute the known values:

\[ -\frac{4}{5} = -\frac{5}{7} \times x + 0 \]

Since the remainder is 0, we can simplify the equation to:

\[ -\frac{4}{5} = -\frac{5}{7} \times x \]

### Step 2: Eliminate the negative sign
We can multiply both sides of the equation by -1 to eliminate the negative signs:

\[ \frac{4}{5} = \frac{5}{7} \times x \]

### Step 3: Solve for \( x \)
To isolate \( x \), we can multiply both sides by the reciprocal of \(\frac{5}{7}\):

\[ x = \frac{4}{5} \times \frac{7}{5} \]

### Step 4: Multiply the fractions
Now we multiply the fractions:

\[ x = \frac{4 \times 7}{5 \times 5} = \frac{28}{25} \]

### Conclusion
Thus, the divisor is:

\[ \text{Divisor} = \frac{28}{25} \]

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