By what number must `-(5)/(8)` be multiplied, so that the product is `(3)/(4)`

Options

A. `-(6)/(7)`
B. `-(6)/(5)`
C. `-(3)/(5)`
D. `-(6)/(16)`

Answer

To solve the question "By what number must \(-\frac{5}{8}\) be multiplied so that the product is \(\frac{3}{4}\)?", we can follow these steps:

### Step 1: Set up the equation
Let the unknown number be \(x\). According to the problem, we can write the equation as:
\[ -\frac{5}{8} \times x = \frac{3}{4} \]

### Step 2: Isolate \(x\)
To find \(x\), we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by \(-\frac{5}{8}\):
\[ x = \frac{\frac{3}{4}}{-\frac{5}{8}} \]

### Step 3: Simplify the right side
Dividing by a fraction is the same as multiplying by its reciprocal. Therefore, we can rewrite the equation as:
\[ x = \frac{3}{4} \times -\frac{8}{5} \]

### Step 4: Perform the multiplication
Now, we can multiply the fractions:
\[ x = \frac{3 \times -8}{4 \times 5} = \frac{-24}{20} \]

### Step 5: Simplify the fraction
Next, we simplify \(\frac{-24}{20}\):
\[ x = \frac{-24 \div 4}{20 \div 4} = \frac{-6}{5} \]

### Final Answer
Thus, the number that must be multiplied by \(-\frac{5}{8}\) to get \(\frac{3}{4}\) is:
\[ x = -\frac{6}{5} \]

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