`(1)/(4)` th of a pizza was eaten by Renu. The rest was equally distributed among 12 children. What part of the pizza did each of these children get?

Options

A. `(1)/(16) th`
B. `(1)/(32) th`
C. `(3)/(16)th`
D. `(1)/(8) th`

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Determine the total amount of pizza
The total amount of pizza is represented as 1 whole pizza.

### Step 2: Calculate the amount of pizza eaten by Renu
Renu ate \( \frac{1}{4} \) of the pizza.

### Step 3: Calculate the remaining pizza
To find out how much pizza is left after Renu ate her portion, we subtract the amount eaten from the total pizza:
\[ \text{Remaining pizza} = 1 - \frac{1}{4} \]
To perform this subtraction, we need a common denominator. The common denominator for 1 and \( \frac{1}{4} \) is 4. Thus, we can rewrite 1 as \( \frac{4}{4} \):
\[ \text{Remaining pizza} = \frac{4}{4} - \frac{1}{4} = \frac{3}{4} \]

### Step 4: Distribute the remaining pizza among the children
The remaining \( \frac{3}{4} \) of the pizza is to be distributed equally among 12 children. To find out how much each child receives, we divide the remaining pizza by the number of children:
\[ \text{Amount per child} = \frac{3}{4} \div 12 \]
Dividing by a whole number is the same as multiplying by its reciprocal:
\[ \text{Amount per child} = \frac{3}{4} \times \frac{1}{12} \]

### Step 5: Multiply the fractions
Now we multiply the fractions:
\[ \text{Amount per child} = \frac{3 \times 1}{4 \times 12} = \frac{3}{48} \]

### Step 6: Simplify the fraction
Next, we simplify \( \frac{3}{48} \):
\[ \frac{3}{48} = \frac{1}{16} \]

### Conclusion
Each child receives \( \frac{1}{16} \) of the pizza.

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