Welcome to two-digit times three-digit multiplication! Today we'll learn the standard vertical method for multiplying these numbers. Let's start with an example: twenty-three times four hundred fifty-six. First, we set up the problem vertically with the larger number on top.
Now we multiply four hundred fifty-six by three, which is the ones digit of twenty-three. Six times three equals eighteen, write eight and carry one. Five times three equals fifteen, plus the carried one makes sixteen, write six and carry one. Four times three equals twelve, plus the carried one makes thirteen. So our first partial product is one thousand three hundred sixty-eight.
Next, we multiply four hundred fifty-six by two, which is the tens digit of twenty-three. Six times two equals twelve, write two and carry one. Five times two equals ten, plus the carried one makes eleven, write one and carry one. Four times two equals eight, plus the carried one makes nine. This gives us nine hundred twelve. Since we're multiplying by the tens digit, we shift this result one place to the left, making it nine thousand one hundred twenty.
Now we add our two partial products together. We have one thousand three hundred sixty-eight plus nine thousand one hundred twenty. Starting from the right: eight plus zero equals eight. Six plus two equals eight. Three plus one equals four. One plus nine equals ten, so we write zero and carry one. This gives us our final answer: ten thousand four hundred eighty-eight.
Let's summarize the method for multiplying a two-digit number by a three-digit number. First, set up the problem vertically. Second, multiply by the ones digit to get the first partial product. Third, multiply by the tens digit and shift the result one place left. Finally, add the partial products together. Our example of twenty-three times four hundred fifty-six equals ten thousand four hundred eighty-eight. Now try practicing with thirty-four times five hundred sixty-seven. Remember the key points: align digits properly, shift for the tens digit, and add carefully. With practice, this method becomes quick and reliable!