Basic Math & Pre-Algebra All-in-One For Dummies (+ Chapter Quizzes Online). Mark Zegarelli

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Basic Math & Pre-Algebra All-in-One For Dummies (+ Chapter Quizzes Online) - Mark  Zegarelli


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can subtract math, and place this result in the ones’ column below the line:

math

      Next, you want to subtract math in the tens’ column. Again, you need to borrow 1 from the column to the left, changing 8 to 7, and adding 10 to the 4, making it 14:

math

      Now, you can subtract math, placing 8 in the tens’ column below the line:

math

      To complete the problem, subtract math in the hundreds’ column:

math

      Therefore, math.

      Calculating with stacked multiplication

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

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

math

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

math

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

math

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

math

      Therefore, math.

math

      Next, multiply math:

math

      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:

math

      Therefore, math.

      Understanding long division

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

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

math

      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:

math

      Now, multiply math, placing this result below 34:

math

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

math

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

math

      To finish up the problem, subtract math:

math

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

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

math

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

math

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

math

      To


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