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  • Multiplying 2- and 3-Digit Numbers

Multiplication and Division

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Multiplying 2- and 3-Digit Numbers

Using Carrying

On the last page, you practiced multiplying vertically stacked numbers. Some problems need an extra step. For example, can you multiply the numbers in this expression?

f

If you tried to multiply 9 x 5, you might have noticed that there was no room to write the product, 45. When the product of two numbers is greater than 9, you'll need to use a technique called carrying. If you know how to add large numbers, you might remember using carrying in addition too. Let's see how it works in multiplication.

  • Let's try the problem we just looked at, 29 x 5.

  • As usual, we'll start by multiplying the 5 by the top-right digit, 9.

  • According to our times table, 5 x 9 is 45, but there's no room to write both digits underneath the 5 and 9.

  • We'll write the right digit, 5, under the line...

  • We'll write the right digit, 5, under the line...then we'll carry the left digit, 4, up to the next set of digits in the problem.

  • See how it works? We multiplied 5 and 9 to get 45. We put the 5 underneath the line, carried the 4 and placed it above the next set of digits.

  • Now it's time for the next step. It's the same as with any other multiplication problem. We'll multiply 5 x 2.

  • 5 x 2 = 10. However, we won't write 10 under the line yet - there's one more step.

  • Remember the number we carried, 4?

  • We have to add it to our product, 10.

  • 4 + 10 is 14. 

  • We'll write 14 beneath the line.

  • Our total is 145. We now know that 29 x 5 = 145.

  • Let's try another problem, just for practice. 208 x 6.

  • First, we multiply the bottom number, 6, by the digit on the top right. That's 8.

  • 6 x 8 is 48.

  • We'll write the 8 under the line...

  • We'll write the 8 under the line...and carry the 4. We'll place it above the next digit.

  • The next digit is 0.

  • Anything times zero is 0, so we know that 7 x 0 = 0.

  • Remember, we don't write that 0 beneath the line yet. We have to add it to the 4 we just carried.

  • 4 + 0 = 4. We'll write 4 beneath the line.

  • Finally, we multiply 6 and 2.

  • 6 x 2 = 12, so we'll write 12 beneath the line.

  • We're done! The answer is 1248, or one thousand, two hundred and forty-eight. 208 x 6 = 1248.

 

Now you try it. See if you can solve these problems. Remember, you can always use your times table for help.
















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