You can multiply fractions and rename mixed numbers as fractions. Multiplying mixed numbers uses both skills.
Idea clave
Rename each mixed number as a fraction greater than 1, multiply the numerators and the denominators, then simplify and write the answer as a mixed number.
Por qué funciona
$2\frac{1}{2} \times 2\frac{1}{2}$ is the area of a square with sides $2\frac{1}{2}$. Splitting each side into $2 + \frac{1}{2}$ gives four parts: $2 \times 2 = 4$, two strips of $2 \times \frac{1}{2} = 1$, and a corner of $\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$. Total $6\frac{1}{4}$. Renaming as $\frac{5}{2} \times \frac{5}{2} = \frac{25}{4}$ gives the same, with less work.
Worked examples
Ejemplo resuelto: A whole number times a mixed number
Find $3 \times 2\frac{1}{4}$.
- $2\frac{1}{4} = \frac{9}{4}$.
- $3 \times \frac{9}{4} = \frac{27}{4}$.
- $\frac{27}{4} = 6\frac{3}{4}$.
Respuesta: $6\frac{3}{4}$
Ejemplo resuelto: Two mixed numbers
Find $1\frac{1}{2} \times 2\frac{2}{3}$.
- $1\frac{1}{2} = \frac{3}{2}$ and $2\frac{2}{3} = \frac{8}{3}$.
- $\frac{3}{2} \times \frac{8}{3} = \frac{24}{6}$.
- $\frac{24}{6} = 4$.
Respuesta: $4$
Error común
Multiplying the whole numbers and the fractions separately: $2\frac{1}{2} \times 2\frac{1}{2} = 4\frac{1}{4}$. The area model shows the two middle strips worth 1 each are missing. Check with an estimate: $2\frac{1}{2} \times 2\frac{1}{2}$ is more than $2 \times 3 = 6$.