How to multiply 3 digit by 2 digit numbers

Understand the Problem

The question is asking for a method or steps to multiply three-digit numbers by two-digit numbers. It seeks guidance on the multiplication process, likely for educational purposes.

Answer

$5535$

Steps to Solve

Understand the multiplication setup

To multiply a three-digit number by a two-digit number, start by writing the numbers in a vertical format. For example, if we were multiplying 123 by 45, we write:

   123
 x  45

Multiply the ones place

Begin by multiplying the three-digit number by the ones place of the two-digit number. For instance, multiply 123 by 5 (the ones place of 45).

$$ 123 \times 5 = 615 $$

Write this result below the line:

   123
 x  45
 ------
   615  ← (Result from 5)

Multiply the tens place

Next, multiply the three-digit number by the tens place of the two-digit number. Multiply 123 by 4 (the tens place of 45), but remember it represents "40" because it's in the tens place.

$$ 123 \times 4 = 492 \quad \text{(This represents 4920 when shifted left)} $$

Write this result one place to the left:

   123
 x  45
 ------
   615  
+4920  ← (Result from 40)

Add the results

Finally, add the two results together:

$$ 615 + 4920 = 5535 $$

So the final answer is:

   123
 x  45
 ------
  5535

The final answer to the multiplication of 123 by 45 is $5535$.

More Information

Multiplying larger numbers can initially seem daunting, but breaking it down into smaller, manageable steps makes it easier. This method is useful in everyday calculations, such as working with prices or measurements.

Tips

Forgetting to shift the tens place multiplication result to the left, which leads to miscalculating the overall sum.
Misplacing values in the addition step. It's important to align numbers correctly based on their place values.

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