Understanding word problems

A word problem is a math problem written in sentences.
The steps are always the same: understand what is asked, give the unknowns letters, translate the words into equations, solve, and answer in context.

Certain words map directly to operations, and it helps to see each one in action.
"Of" means multiply, so "half of $20$" is $\frac{1}{2} \times 20 = 10$.
"Is", "are", and "equals" mean the equals sign, so "a number is $7$" becomes $n = 7$.
"More than" and "sum" mean add, so "$5$ more than $x$" is $x + 5$, and "the sum of $a$ and $b$" is $a + b$.

Two of these need extra care.
"Less than" and "difference" mean subtract, but watch the order: "$5$ less than $x$" is $x - 5$, not $5 - x$.
"Per" and "each" signal a rate you multiply by, so at $3$ dollars per book, the cost is $3 \times$ the number of books.

You can combine these to translate a whole sentence at once.
Take "John has $5$ more than twice as many stamps as Sara".
Let Sara's stamps be $s$.
"Twice as many" is $2s$, and "$5$ more than" that is $2s + 5$, so John has $2s + 5$ stamps.

The average is a special phrase: it means the sum of the values divided by how many there are.
For example, the average of $4$, $6$, and $8$ is $\frac{4 + 6 + 8}{3} = 6$.
So "the average price of $12$ fruits is $40$ cents" means the total cost divided by $12$ equals $40$.

Finally, always answer the exact question asked, with units.
If the problem wants the number of eighth graders, give that number — not the total, and not some intermediate value you found along the way.

In a club of $30$ students, $\frac{2}{5}$ of them play a sport. How many students play a sport?
The word "of" means multiply.
So it is $\frac{2}{5} \times 30 = 12$ students.

Apples cost $30$ cents and bananas cost $50$ cents. Someone buys $12$ fruits at an average price of $40$ cents. Write an equation for this.
Let $a$ be the number of apples and $b$ the number of bananas.
"Average price is $40$" means the total cost over $12$ equals $40$, so $30a + 50b = 12 \times 40 = 480$.

A school has $600$ students. $\frac{1}{4}$ are ninth graders, and $\frac{2}{5}$ of the rest are in eleventh and twelfth grade. How many are in eleventh and twelfth grade?
Ninth graders: $\frac{1}{4} \times 600 = 150$, which leaves $600 - 150 = 450$.
Then $\frac{2}{5} \times 450 = 180$ students in eleventh and twelfth grade.