`1//8` of a number equals `2//5 div 1//20` What is the number?

Options

A. 54
B. 64
C. 88
D. 98

Answer

To solve the equation \( \frac{1}{8} \) of a number equals \( \frac{2}{5} \div \frac{1}{20} \), we can follow these steps:

### Step 1: Define the variable
Let the unknown number be \( x \).

### Step 2: Set up the equation
According to the problem, we can write the equation as:
\[ \frac{1}{8} \times x = \frac{2}{5} \div \frac{1}{20} \]

### Step 3: Simplify the right side
To simplify \( \frac{2}{5} \div \frac{1}{20} \), we can convert the division into multiplication by taking the reciprocal of \( \frac{1}{20} \):
\[ \frac{2}{5} \div \frac{1}{20} = \frac{2}{5} \times 20 \]

### Step 4: Perform the multiplication
Now we can multiply:
\[ \frac{2 \times 20}{5} = \frac{40}{5} = 8 \]

### Step 5: Substitute back into the equation
Now we have:
\[ \frac{1}{8} \times x = 8 \]

### Step 6: Solve for \( x \)
To find \( x \), we can multiply both sides of the equation by 8:
\[ x = 8 \times 8 = 64 \]

### Conclusion
The number is \( 64 \).

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