Express `(-42)/(98)` as a rational number with denominator `7`.

Options

A. `(-4)/(7) `
B. `(-5)/(7) `
C. `(-3)/(7) `
D. `(-6)/(7) `

Answer

To express \(-\frac{42}{98}\) as a rational number with a denominator of \(7\), we can follow these steps:

### Step 1: Simplify the fraction \(-\frac{42}{98}\)

To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator.

**Calculation:**
- The GCD of \(42\) and \(98\) is \(14\).
- Now, divide both the numerator and the denominator by \(14\):

\[ -\frac{42 \div 14}{98 \div 14} = -\frac{3}{7} \]

### Step 2: Write the result

Now that we have simplified the fraction, we can express it as:

\[ -\frac{42}{98} = -\frac{3}{7} \]

### Final Answer

Thus, \(-\frac{42}{98}\) expressed as a rational number with a denominator of \(7\) is:

\[ -\frac{3}{7} \]

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