Long Multiplication

Split 18 into 10 and 8 and multiply in two steps:

$23\times 8=184$ (from $3\times 8=24$: write 4, carry 2; then $2\times 8=16$, plus the carried 2 gives 18).

$23\times 10=230$: the placeholder zero is what makes this row ten times bigger.

Add the rows: $184+230=414$. So $23\times 18=414$.

Split 15 into 10 and 5 and multiply in two steps:

$52\times 5=260$ (from $2\times 5=10$: write 0, carry 1; then $5\times 5=25$, plus the carried 1 gives 26).

$52\times 10=520$: the placeholder zero is what makes this row ten times bigger.

Add the rows: $260+520=780$. So $52\times 15=780$.

Set it out as long multiplication.

First multiply by the units digit: $36\times 4=144(6\times 4=24$, write 4 and carry 2; $3\times 4=12$, plus the carried 2 gives 14).

Then multiply by the tens digit, remembering the placeholder zero: $36\times 20=720$.

Add the two rows: $144+720=864$.

Set it out as long multiplication.

First multiply by the units digit: $19\times 7=133(9\times 7=63$, write 3 and carry 6; $1\times 7=7$, plus the carried 6 gives 13).

Then multiply by the tens digit, remembering the placeholder zero: $19\times 40=760$.

Add the two rows: $133+760=893$.

Set it out as long multiplication.

First multiply by the units digit: $103\times 6=618(3\times 6=18$, write 8 and carry 1; $0\times 6=0$, plus the carried 1 gives 1; $1\times 6=6)$.

Then multiply by the tens digit, remembering the placeholder zero: $103\times 20=2060$.

Add the two rows: $618+2060=2678$.

Set it out as long multiplication.

First multiply by the units digit: $263\times 5=1315(3\times 5=15$, write 5 and carry 1; $6\times 5=30$, plus the carried 1 gives 31, write 1 and carry 3; $2\times 5=10$, plus the carried 3 gives 13).

Then multiply by the tens digit, remembering the placeholder zero: $263\times 30=7890$.

Add the two rows: $1315+7890=9205$.