Therefore, .

      Calculating with stacked multiplication

      Stacked multiplication provides a systematic way to multiply a pair of larger numbers.

      For example, to multiply , set up the multiplication as shown here, then begin by multiplying as follows:

      Next, multiply . Because this result is more than one digit, place the 2 next to the 8 and carry the 1, as you would when adding:

      Now, multiply , then add the 1 you carried, . This time, write the 9 below the line and carry the 2:

      To finish the problem, multiply , then add the 2 you carried, , completing the problem as follows:

      Therefore, .

When multiplying by a number that has more than one digit, multiply each digit in turn by the top number, and then finish by adding the results. For example, to multiply , begin by multiplying as follows:

      Next, multiply :

      Before moving on, notice that I have lined up this result, 658, with the multiplier, 7. To complete the problem, add these two results as follows:

      Therefore, .

      Understanding long division

      Long division allows you to divide larger numbers in a systematic way.

      For example, to divide , set up the problem as follows:

      Begin by trying to divide 6 into the first digit of 347 by itself. Because 3 is less than 6, this division doesn’t work. Next, try dividing 6 into 34. In this case, 6 goes into 34 as many as 5 times, so record this answer over the 4:

      Now, multiply , placing this result below 34:

      To complete this step, subtract and bring down the 7 next to this result:

      At this point, you have a new number to try dividing 6 into: 6 goes into 47 no more than 7 times. Now, multiply :

      To finish up the problem, subtract :

      Thus, — that is, 57 with a remainder of 5.

      As another example, suppose you want to divide . Set up the problem as follows:

      To begin, note that you can divide 1,006 into 7,458 a maximum of 7 times. Thus, write 7 above the 8, multiply , then subtract and bring down the 5:

      Now, you can divide 1,006 into 4,165 a maximum of 4 times. So write 4 above the line after the 7, multiply , then subtract and bring down the 3:

      To

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