Multiplying numbers with more than one digit can be done using various methods. Here's a straightforward approach commonly taught in schools, known as the standard algorithm:
Example: Multiply 23 by 45
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Write the numbers vertically and align them by the right.
23 x 45 -
Multiply the bottom number's rightmost digit (5 in this case) by each digit of the top number (23).
- 5 × 3 = 15. Write down 5 and carry over 1.
- 5 × 2 = 10, plus the 1 you carried over equals 11. Write 11 next to the 5.
23 x 45 ------ 115 (This is 23 * 5) -
Multiply the next digit of the bottom number (4 in this case), but remember that this represents 40 (since it’s in the tens place). So you'll place a zero for the next line.
- Start by writing 0 under the last digit in the previous line:
23 x 45 ------ 115 +920 (This is 23 * 4, shifted one position to the left) -
Add the two results together.
115 + 920 ------ 1035
So, 23 multiplied by 45 equals 1035.
Step-by-step Process:
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Break down the multiplication:
- Multiply each digit of the bottom number starting from the right.
- Keep track of place values by shifting results to the left (adding zeros).
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Carry over when needed:
- If the product of any single-digit multiplication exceeds 9, carry the tens digit over to the next multiplication.
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Add the results:
- Align the results properly and perform column addition to find the final answer.
You can also use other methods like the lattice method or area model if you prefer visual aids or different techniques. However, the standard algorithm is widely used because it is systematic and efficient.