A Fraction of a Number

What is three quarters of 20? Taking a fraction of a number is a multiplication, written $\frac{3}{4}\cdot 20$. To work it out, cut 20 into 4 equal parts, as the denominator says: $\frac{20}{4}$ is 5, so each quarter is 5.

Then take 3 of those parts, as the numerator says: $3\cdot 5$ is 15. So three quarters of 20 is 15. On the board that is two lines after the problem: $3\cdot 5$, then 15.

In short: divide by the bottom, then multiply by the top. That is exactly what the fraction means, since the bottom makes the equal parts and the top counts them, and dividing first keeps the numbers small. The word 'of' after a fraction always means multiply.