Basic word problem comprehension

The hardest part of a word problem is usually just translating the words into math. A few phrases come up again and again.

'Less than' means subtract and 'more than' means add. 'Twice' or 'double' means multiply by $2$. 'A third of' means multiply by $\frac{1}{3}$, and 'three-quarters of' means multiply by $\frac{3}{4}$. 'For each' tells you to multiply by the number of items.

Give the unknown a letter, then turn each sentence into math.
Suppose Tom is $3$ times as old as Sam, and Sam is $8$.
'Times as old' means multiply, so Tom is $3 \times 8 = 24$.

When a problem asks for a fraction or percentage but gives no actual amounts, you can pick a convenient number, because the answer does not depend on the real size.
For example: in a school, $\frac{2}{3}$ of the students take science, and $\frac{1}{2}$ of those also take art. What fraction of all the students take both?
Pick a school of $6$ (a number both $3$ and $2$ divide): science $= \frac{2}{3} \times 6 = 4$, and both $= \frac{1}{2} \times 4 = 2$. So $\frac{2}{6} = \frac{1}{3}$ take both.
Any starting number gives the same fraction, which is why picking one is safe here.

Sara has $5$ fewer apples than Tom, and Tom has $12$.
How many apples does Sara have?
'Fewer than' means subtract.
So Sara has $12 - 5 = 7$.

A shirt costs $40$ dollars and is on sale for three-quarters of the price.
What is the sale price?
'Three-quarters of' means multiply by $\frac{3}{4}$.
So the sale price is $\frac{3}{4} \times 40 = 30$ dollars.

One-quarter of a garden is planted, and two-thirds of the planted part has flowers.
What fraction of the whole garden has flowers?
Pick a size the denominators divide into, say $12$: planted $= \frac{1}{4} \times 12 = 3$, and flowers $= \frac{2}{3} \times 3 = 2$.
So $\frac{2}{12} = \frac{1}{6}$ of the garden.