Calculating fractions

Fraction questions usually come down to two moves: taking a fraction of an amount, and finding what fraction one amount is of another.

"A fraction of a quantity" always means multiply.
To find $\frac{2}{3}$ of $27$, compute $\frac{2}{3} \times 27 = 18$.
It helps to read "of" as a multiplication sign every time it appears.

"What fraction is it?" means put the part over the whole, then simplify.
If $66$ of $84$ members went, the fraction is $\frac{66}{84}$, which reduces to $\frac{11}{14}$.
Always reduce the fraction to lowest terms at the end.

The most common slip is using the wrong whole in the denominator.
"What fraction of the whole team" divides by the full team size, while "what fraction of those who stayed" divides only by the ones who stayed.
Multi-step problems often ask you to first find the part — for instance adding two groups — and then divide by the correct total.

A garden is $40$ units and $\frac{1}{2}$ of it is weeded. How many units are weeded?
"A fraction of a quantity" means multiply: $\frac{1}{2} \times 40$.
So $20$ units are weeded.

Out of a team of $84$ members, $66$ ended up going to the competition. What fraction is that?
Put the part over the whole: $\frac{66}{84}$.
Dividing top and bottom by $6$, this simplifies to $\frac{11}{14}$.

A field is $50$ units in all, and $26$ units are weeded. What fraction is NOT weeded?
First find the un-weeded part: $50 - 26 = 24$ units.
Then the fraction is $\frac{24}{50} = \frac{12}{25}$.