In Grade 3 you split a rectangle to find its area in parts. Now use the same idea for bigger numbers: split a factor by place value, find each part with tens and hundreds facts, and add.
Idea clave
To multiply $4 \times 236$, split $236 = 200 + 30 + 6$. Multiply each part: $4 \times 200$, $4 \times 30$, $4 \times 6$. Then add the partial products.
Por qué funciona
A rectangle 4 units wide and 236 units long can be cut into three smaller rectangles, 200 long, 30 long and 6 long. Cutting does not change the total area, so the three areas add up to $4 \times 236$. This is the distributive property.
Ejemplo resuelto: Three partial products
Find $4 \times 236$.
- Split 236 by place value: $200 + 30 + 6$.
- $4 \times 200 = 800$, $4 \times 30 = 120$, $4 \times 6 = 24$.
- Add: $800 + 120 + 24 = 944$.
Respuesta: $944$
Ejemplo resuelto: A zero in the middle
Find $7 \times 2{,}045$.
- Split: $2{,}000 + 40 + 5$. There are no hundreds, so there is no hundreds part.
- $7 \times 2{,}000 = 14{,}000$, $7 \times 40 = 280$, $7 \times 5 = 35$.
- Add: $14{,}000 + 280 + 35 = 14{,}315$.
Respuesta: $14{,}315$
Error común
Multiplying only the first part, as in $4 \times 200 + 30 + 6$. Every part of the split must be multiplied. Check with an estimate: $4 \times 236$ is a bit less than $4 \times 250 = 1{,}000$.