Find the missing number :

`16 + 1(1/6) + 33 + 1(1/6) = 15(1/2) +` ?

Options

A. `26(1/2)`
B. 51
C. `57(1/2)`
D. `66(1/2)`

Answer

To find the missing number in the equation:

\[ 16 + 1\frac{1}{6} + 33 + 1\frac{1}{6} = 15\frac{1}{2} + ? \]

Let's break it down step by step.

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

1. \( 1\frac{1}{6} = \frac{6 \times 1 + 1}{6} = \frac{7}{6} \)
2. \( 15\frac{1}{2} = \frac{2 \times 15 + 1}{2} = \frac{31}{2} \)

Now, rewrite the equation:

\[ 16 + \frac{7}{6} + 33 + \frac{7}{6} = \frac{31}{2} + ? \]

### Step 2: Combine Like Terms on the Left Side
Next, we combine the whole numbers on the left side:

1. \( 16 + 33 = 49 \)

So the equation now looks like:

\[ 49 + \frac{7}{6} + \frac{7}{6} = \frac{31}{2} + ? \]

### Step 3: Add the Fractions on the Left Side
Now, add the fractions:

1. \( \frac{7}{6} + \frac{7}{6} = \frac{14}{6} = \frac{7}{3} \)

Now the equation is:

\[ 49 + \frac{7}{3} = \frac{31}{2} + ? \]

### Step 4: Convert Whole Number to Fraction
Convert 49 into a fraction with a common denominator. The least common multiple of 3 and 2 is 6.

1. \( 49 = \frac{49 \times 6}{6} = \frac{294}{6} \)
2. \( \frac{7}{3} = \frac{7 \times 2}{6} = \frac{14}{6} \)

Now combine them:

\[ \frac{294}{6} + \frac{14}{6} = \frac{308}{6} \]

### Step 5: Convert \( \frac{31}{2} \) to a Fraction with Denominator 6
Convert \( \frac{31}{2} \) to a fraction with a denominator of 6:

1. \( \frac{31}{2} = \frac{31 \times 3}{2 \times 3} = \frac{93}{6} \)

### Step 6: Set Up the Equation
Now we have:

\[ \frac{308}{6} = \frac{93}{6} + ? \]

### Step 7: Solve for the Missing Number
To find the missing number, subtract \( \frac{93}{6} \) from \( \frac{308}{6} \):

\[ ? = \frac{308}{6} - \frac{93}{6} = \frac{308 - 93}{6} = \frac{215}{6} \]

### Step 8: Convert Back to Mixed Number
Convert \( \frac{215}{6} \) back to a mixed number:

1. Divide 215 by 6, which gives 35 with a remainder of 5.
2. So, \( \frac{215}{6} = 35\frac{5}{6} \)

### Final Answer
Thus, the missing number is:

\[ 35\frac{5}{6} \]

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