If Arnav ate `5/(12)` of the cake and Shreya ate `3/(12)` of the cake, how much cake was left over?

Answer

To find out how much cake was left after Arnav and Shreya ate their portions, we can follow these steps:

1. **Identify the portions eaten**:
- Arnav ate \( \frac{5}{12} \) of the cake.
- Shreya ate \( \frac{3}{12} \) of the cake.

2. **Add the portions eaten**:
- To find the total amount of cake eaten, we add the fractions:
\[ \text{Total eaten} = \frac{5}{12} + \frac{3}{12} \]

3. **Combine the fractions**:
- Since the denominators are the same (12), we can simply add the numerators:
\[ \text{Total eaten} = \frac{5 + 3}{12} = \frac{8}{12} \]

4. **Calculate the remaining cake**:
- The total cake is considered to be 1 (or \( \frac{12}{12} \)). To find out how much cake is left, we subtract the total eaten from the whole cake:
\[ \text{Cake left} = 1 - \frac{8}{12} \]

5. **Convert 1 to a fraction with the same denominator**:
- We can write 1 as \( \frac{12}{12} \):
\[ \text{Cake left} = \frac{12}{12} - \frac{8}{12} \]

6. **Subtract the fractions**:
- Now, subtract the numerators:
\[ \text{Cake left} = \frac{12 - 8}{12} = \frac{4}{12} \]

7. **Simplify the fraction**:
- We can simplify \( \frac{4}{12} \) by dividing both the numerator and the denominator by 4:
\[ \text{Cake left} = \frac{4 \div 4}{12 \div 4} = \frac{1}{3} \]

Thus, the amount of cake left over is \( \frac{1}{3} \).