`7/8 ` is what % of ` 3/4 ` ?

Options

A. `116 (1)/(3)%`
B. `116%`
C. `116 (3)/(2) %`
D. `116(2)/(3) %`

Answer

To find out what percentage \( \frac{7}{8} \) is of \( \frac{3}{4} \), we can follow these steps:

### Step 1: Set up the equation
We want to find \( x \) such that:
\[ \frac{7}{8} = x \% \text{ of } \frac{3}{4} \]
This can be rewritten as:
\[ \frac{7}{8} = \frac{x}{100} \times \frac{3}{4} \]

### Step 2: Rewrite the equation
To simplify, we can express \( x \% \) as \( \frac{x}{100} \):
\[ \frac{7}{8} = \frac{x}{100} \times \frac{3}{4} \]

### Step 3: Multiply both sides by 100
To eliminate the fraction on the right side, multiply both sides by 100:
\[ 100 \times \frac{7}{8} = x \times \frac{3}{4} \]
This simplifies to:
\[ \frac{700}{8} = \frac{3x}{4} \]

### Step 4: Simplify \( \frac{700}{8} \)
Now, simplify \( \frac{700}{8} \):
\[ \frac{700}{8} = 87.5 \]
So we have:
\[ 87.5 = \frac{3x}{4} \]

### Step 5: Multiply both sides by 4
To isolate \( x \), multiply both sides by 4:
\[ 4 \times 87.5 = 3x \]
Calculating the left side gives:
\[ 350 = 3x \]

### Step 6: Solve for \( x \)
Now, divide both sides by 3 to find \( x \):
\[ x = \frac{350}{3} \]
Calculating this gives:
\[ x \approx 116.67 \]

### Step 7: Convert to percentage
Thus, \( \frac{7}{8} \) is approximately \( 116.67\% \) of \( \frac{3}{4} \).

### Final Answer
Therefore, \( \frac{7}{8} \) is \( 116 \frac{2}{3} \% \) of \( \frac{3}{4} \).

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