In Grade 4 you multiplied two-digit numbers with partial products in an area model. The standard algorithm is the same idea written in a compact stack: one row for each digit of the bottom number.
Idea clave
Multiply the top number by the ones digit of the bottom number. Then multiply by the tens digit, starting that row with a 0 because you are multiplying by tens. Add the rows.
Por qué funciona
In $346 \times 27$, the 2 in 27 is really 20. So the second row is $346 \times 20$, which is $346 \times 2$ tens: $692$ tens, or $6{,}920$. The 0 at the end holds the ones place. The two rows are the two parts of the area model, $346 \times 7$ and $346 \times 20$.
Worked examples
Ejemplo resuelto: Two digits by two digits
Multiply $54 \times 36$.
- Ones row: $54 \times 6 = 324$.
- Tens row: $54 \times 30 = 1{,}620$ (write the 0 first, then $54 \times 3 = 162$).
- Add: $324 + 1{,}620 = 1{,}944$.
- Estimate: $50 \times 40 = 2{,}000$. Close.
Respuesta: $1{,}944$
Ejemplo resuelto: Three digits by two digits
Multiply $346 \times 27$.
- Ones row: $346 \times 7 = 2{,}422$.
- Tens row: $346 \times 20 = 6{,}920$.
- Add: $2{,}422 + 6{,}920 = 9{,}342$.
- Estimate: $350 \times 30 = 10{,}500$. Close.
Respuesta: $9{,}342$
Error común
Leaving out the placeholder 0, so $346 \times 27$ becomes $2{,}422 + 692 = 3{,}114$. That treats the 2 in 27 as 2 instead of 20. Check with an estimate: $350 \times 30$ is about 10,000, so 3,114 is far too small.