To determine how much of the cake was left after Aliyah's siblings and friends ate it, we need to know the total amount of cake and how much was eaten.
Let's denote the whole cake as 1 (i.e., a whole).
- Aliyah's siblings ate \( \frac{14}{1} = 14 \) of the cake.
- Aliyah's friends ate \( \frac{23}{1} = 23 \) of the cake.
Now, we add the amounts eaten: \[ 14 + 23 = 37 \text{ of the cake} \]
Since a whole cake is represented as 1, if we take into account that more than one whole cake was eaten, we need to consider how much cake these portions represent in terms of whole cakes.
If \( 14 + 23 = 37 \), we can conclude:
- The total cake consumed is more than 1 whole cake.
Since the options given are fractions, we need to express the eaten portions in fractions of a cake.
To illustrate:
- If you have 1 cake and you consumed 37 units, the question is how much of a whole cake is left from the total eaten rates.
- The total amount eaten compared to just one whole cake may not yield traditional fractions.
However, if we presume that the problem intended 14ths and 23rds are meant to be expressed as fractions of a whole cake and thus we must simplify these numbers into a singular format to represent leftover cake.
Therefore, to calculate how much is "left" comes down to: If there was initially 1 whole cake and 37 is the total rate of whole cakes eaten as there is no defined denominator outlined as only one cake reference at the start.
Under the options given, we evaluate if any of the options represent reality of consumed cake over what remained in traditional fractions.
Since as stated "how much cake left?" would be: \[ \text{Leftover} = 1 - \text{Total Consumed} \]
And that ultimately the traditional fraction perspective remains undefined, thus none of the provided options represent a scenario where a defined leftover of cake exists or matches against consumed cakes based fit of the standard amount left after each sibling/friend consumed their portion in whole regardless of fraction nature.
None of the presented options (56, 5/6, 34, 3/4, 12, 1/2, 112) appear logical, they do not handle the calculation of whole consumption vs remaining clearly. Please verify extravagantly initially given or simplistically how many cakes were stated, in coherence to how cakes were presented.
In a standard question format typically a simple resolution if based correctly can derive left from defining actual whole cakes.
If the context you wish to seek the cake relation based amid actual 1 whole vs share each sibling respectively to the normalised equally, please dispense a breakdown or query output return for clarity on whole definitions in relation to fractions stated or simplified result metric for result verification.