Alexis had 5/12 of a cake. She ate 4/7 of the remaining cake. How much of the original cake did Alexis eat? Bookyeuwaa baked 542 meat pies and planned to serve 7 friends equally. How many meat pies wi

The initial amount of cake in the fridge was $\frac{5}{12}$.

Alexis ate $\frac{4}{7}$ of the leftover cake, which is $\frac{5}{12}$. To find out how much she ate, we multiply these fractions.

Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 4.

Alexis had $\frac{5}{21}$ of the original cake.

The amount of cake Alexis had was $\boxed{\frac{5}{21}}$.

5.
This question asks about "donuts" but the context is about "meat pies". Assuming "donuts" is a typo and it should be "meat pies", we will calculate the number of meat pies Bookyeuwaa is left with.

Bookyeuwaa baked 542 meat pies.

She planned to serve 7 friends equally.

We divide the total pies by the number of friends:

This means each of the 7 friends will receive 77 meat pies, and there will be a remainder of 3 meat pies.
Bookyeuwaa will be left with the remainder.

Bookyeuwaa will be left with $\boxed{3 \text{ meat pies}}$.

6.

To find the quotient, we divide 88,668 by 9.

The quotient of 88,668 and 9 is $\boxed{9,852}$.

7a.

The given expression is $\frac{4}{5} + \frac{3}{9}$.
The fraction $\frac{3}{9}$ can be simplified by dividing both the numerator and the denominator by 3:

So the expression becomes:

The least common multiple of 5 and 3 is 15.
Convert each fraction to an equivalent fraction with a denominator of 15.
For $\frac{4}{5}$:

For $\frac{1}{3}$:

Now add the fractions with the common denominator:

The fraction $\frac{17}{15}$ can also be written as a mixed number:

The simplified sum is $\boxed{\frac{17}{15}}$ or $\boxed{1 \frac{2}{15}}$.