Here's an example: 23×47.
23×47=(2×4)×100+(2×7+3×4)×10+3×7.
Step 1: Start by multiplying the last digits of the two numbers: 3×7=21: write it down:
21
Step 2: The middle part (the tens part) is 2×7+3×4, so work out the multiplication first: 14+12 then do the addition: 14+12=26. This is the number of tens so add a zero on to the end: 260 and write down:
21+
260
Make sure the numbers line up as shown.
Step 3: Now we work out the hundreds by multiplying the first digits of the numbers: 2×4=8. This is the number of hundreds so we add two zeroes to the end: 800 and write this down:
21+
260+
800
Now we just add these numbers: 1+0+0 (in the ones position)=1, so the last digit in the result is 1.
Now add the tens: 2+6+0=8, which goes next the the 1: 81.
Finally add the hundreds: 2+8=10, so the final result= 1081.
FASTER METHOD
The method is shorter if steps 1 and 3 are combined.
Multiply the first digits and the last digits of the numbers and write the products alongside one another like this: 821 (2×4=8, 3×7=21).
Now do the middle part (cross-products):
2×7=14+
3×4=12
26, adding a zero to the end: 260
Final addition:
821+
260=
1081
Another example using the faster method: 89×76
5654 (7×8=56, 6×9=54).
Middle part:
6×8=48+
7×9=63=
111, then add in zero: 1110.
Final addition:
5654+
1110=
6764 final answer for 89×76.