You can multiply a fraction by a whole number, and you know a fraction is a division. Now find a fraction of a number, like $\frac{2}{3}$ of 12.
Idea clave
To find $\frac{a}{b}$ of a number, divide it into $b$ equal parts and take $a$ of them. $\frac{2}{3}$ of 12 is 2 groups of $\frac{1}{3}$ of 12: $2 \times 4 = 8$. This is the same as $\frac{2}{3} \times 12$.
Por qué funciona
$\frac{1}{3}$ of 12 means 12 split into 3 equal parts: $12 \div 3 = 4$. Two of those parts are $2 \times 4 = 8$. Multiplying first works too: $\frac{2 \times 12}{3} = \frac{24}{3} = 8$, because 2 copies of 12 split into 3 parts gives the same amount.
Worked examples
Ejemplo resuelto: A whole-number answer
What is $\frac{2}{3}$ of 12?
- $\frac{1}{3}$ of 12: $12 \div 3 = 4$.
- Two of those: $2 \times 4 = 8$.
Respuesta: $8$
Ejemplo resuelto: A story
A class has 30 students. $\frac{3}{5}$ of them ride the bus. How many ride the bus?
- $\frac{1}{5}$ of 30: $30 \div 5 = 6$.
- $\frac{3}{5}$ of 30: $3 \times 6 = 18$.
Respuesta: 18 students
Ejemplo resuelto: A fraction answer
What is $\frac{3}{4}$ of 10?
- $\frac{1}{4}$ of 10: $10 \div 4 = 2\frac{1}{2}$.
- Three of those: $3 \times 2\frac{1}{2} = 7\frac{1}{2}$. Or: $\frac{3 \times 10}{4} = \frac{30}{4} = 7\frac{1}{2}$.
Respuesta: $7\frac{1}{2}$
Error común
Dividing by the numerator instead of the denominator, like finding $\frac{2}{3}$ of 12 as $12 \div 2 = 6$. The denominator says how many equal parts to make. Check: $\frac{2}{3}$ is more than half, so the answer must be more than 6.