Which number should come in place of `""^(**)` ?
`(**)/(4)+(1)/(6)+(5)/(12)=1 (1)/(3)`

Options

A. 5
B. 7
C. 3
D. 1

Answer

To solve the equation \( \frac{(**)}{4} + \frac{1}{6} + \frac{5}{12} = 1 \frac{1}{3} \), we will follow these steps:

### Step 1: Convert the mixed number to an improper fraction
The mixed number \( 1 \frac{1}{3} \) can be converted to an improper fraction:
\[ 1 \frac{1}{3} = \frac{3 \times 1 + 1}{3} = \frac{4}{3} \]

### Step 2: Rewrite the equation
Now we can rewrite the equation as:
\[ \frac{(**)}{4} + \frac{1}{6} + \frac{5}{12} = \frac{4}{3} \]

### Step 3: Move the fractions on the right-hand side
We will move \( \frac{1}{6} \) and \( \frac{5}{12} \) to the right-hand side:
\[ \frac{(**)}{4} = \frac{4}{3} - \frac{1}{6} - \frac{5}{12} \]

### Step 4: Find a common denominator
To subtract the fractions on the right, we need a common denominator. The least common multiple (LCM) of 3, 6, and 12 is 12. We will convert each fraction:
- \( \frac{4}{3} = \frac{4 \times 4}{3 \times 4} = \frac{16}{12} \)
- \( \frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12} \)
- \( \frac{5}{12} = \frac{5}{12} \)

### Step 5: Substitute back into the equation
Now substitute these values back into the equation:
\[ \frac{(**)}{4} = \frac{16}{12} - \frac{2}{12} - \frac{5}{12} \]

### Step 6: Perform the subtraction
Now perform the subtraction:
\[ \frac{(**)}{4} = \frac{16 - 2 - 5}{12} = \frac{9}{12} \]

### Step 7: Simplify the fraction
We can simplify \( \frac{9}{12} \):
\[ \frac{9}{12} = \frac{3}{4} \]

### Step 8: Solve for \( ** \)
Now we have:
\[ \frac{(**)}{4} = \frac{3}{4} \]
To find \( ** \), we multiply both sides by 4:
\[ ** = 3 \]

### Final Answer
The number that should come in place of \( ** \) is \( 3 \).

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