Long Multiplication
1. Arrange the numbers one on top of the other and line up the place values in columns. The number with the most digits is usually placed on top as the multiplicand.
This will be written as follows:
467
x 48
---------------
2. Starting with the ones digit of the bottom number, the multiplier, multiply it by the last digit in the top number.
This product is 8*7 = 56
3. If that answer is greater than nine, write the ones place as the answer and carry the tens digit.
We should write 6 and carry 5:
467
x 48
---------------
6 (carry 5)
4. Proceed right to left. Multiply the ones digit of the bottom number to the next digit to the left in the top number. If you carried a digit, add it to the result and write the answer below the equals line. If you need to carry again, do so.
The next product is 8*6 = 48. Adding the carry: 48+5=53, Write 3, carry 5:
467
x 48
---------------
36 (carry 5)
Multiply 8*4 = 32. Add the carry 5: 32+5 = 37. Write the full number because it's the last of the products of this step:
467
x 48
---------------
3736
5. When you've multiplied the ones digit by every digit in the top number, move to the tens digit in the bottom number.
Multiply as above, but this time write your answers in a new row, shifted one digit place to the left.
Multiply 4*7 = 28. Write 8, carry 2.
467
x 48
---------------
3736
8 (carry 2)
Multiply 4*6=24. Add 2: 24+2=26. Write 6, carry 2:
467
x 48
---------------
3736
68 (carry 2)
Multiply 4*4=16. Add 2: 16+2=18. Write the full number:
467
x 48
---------------
3736
1868
6. When you finish multiplying, draw another answer line below your last row of answer numbers.
467
x 48
---------------
3736
1868
----------------
7. Use long addition to add your number columns from right to left, carrying as you normally do for long addition.
467
x 48
---------------
3736
1868
----------------
22416