If `3(1)/2 xx 3(1)/2 =1(1)/3 xx` _____ then the number in blank space is

Options

A. `147/16`
B. `148/17`
C. `145/16`
D. `145/17`

Answer

To solve the equation \( 3\frac{1}{2} \times 3\frac{1}{2} = 1\frac{1}{3} \times \_\_\_\_ \), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we convert the mixed numbers into improper fractions.

- For \( 3\frac{1}{2} \):
\[ 3\frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{6 + 1}{2} = \frac{7}{2} \]

- For \( 1\frac{1}{3} \):
\[ 1\frac{1}{3} = \frac{1 \times 3 + 1}{3} = \frac{3 + 1}{3} = \frac{4}{3} \]

### Step 2: Substitute the Improper Fractions into the Equation
Now we substitute these values back into the equation:
\[ \frac{7}{2} \times \frac{7}{2} = \frac{4}{3} \times A \]

### Step 3: Calculate the Left Side
Next, we calculate the left side:
\[ \frac{7}{2} \times \frac{7}{2} = \frac{49}{4} \]

### Step 4: Set Up the Equation
Now we have:
\[ \frac{49}{4} = \frac{4}{3} \times A \]

### Step 5: Solve for A
To find \( A \), we can multiply both sides by the reciprocal of \( \frac{4}{3} \):
\[ A = \frac{49}{4} \times \frac{3}{4} \]
\[ A = \frac{49 \times 3}{4 \times 4} = \frac{147}{16} \]

### Conclusion
Thus, the number in the blank space is \( \frac{147}{16} \).

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