All the Math You'll Ever Need. Steve Slavin

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Название All the Math You'll Ever Need
Автор произведения Steve Slavin
Жанр Математика
Серия
Издательство Математика
Год выпуска 0
isbn 9781119719199



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below. Others will come up in Chapter 4, “Focus on Division.” It's fair to say that division with larger numbers is one task for which calculators are helpful. If you're going to use a calculator, you'll want to be able to estimate the answer, so that you can see if the answer on the calculator is reasonable. Errors, even as simple as a typing error, can give you a wildly wrong answer.

      Estimation

      Short Division

      In a division problem, you have a dividend, a divisor, a quotient, and a remainder. You don't need those labels all that often but we'll need them to talk about how to divide. If you want to divide 785 by 5, the 785 is the dividend and 5 is the divisor. If the dividend is large but the divisor is small, you can use what's called short division. It's a method that uses regrouping and compresses the work.

      Set up with the dividend inside and the divisor outside, like this:

. Look at the first digit in the dividend, 7. Can you divide 7 by 5? There is one 5 and 2 left over. Show that like this:

      Those 2 hundreds that were left get regrouped as 20 tens so now that middle number is not just 8 but 28. Divide 28 by 5, and you get 5 with 3 left over.

      Divide 35 by 5 to get 7.

      Problem 1:

      What is the result of dividing 161 by 7?

       Solution:

      Divide 7 into 16. It goes twice, so place the 2 up top, but 7 × 2 = 14, so there will be 2 left over. Write the 2 beside the 1 and divide 7 into 21. That gives you 3.

      Problem 2:

       Solution:

      Estimate your answer by thinking about how many times 30 could be subtracted from 1,800 or by thinking that 18 ÷ 3 = 6 and so 1,800 ÷ 30 would need a 6 and another zero. 1,800 ÷ 30 = 60, so expect a quotient close to 60. This one may be hard to keep all in your head, so write down as you go.

      You're probably tempted to start with a 6, but if you check 6 × 31 = 186, and you're trying to divide into 182, so 6 is too big. Drop down to 5, and place 5 × 31 = 155 under the 182.

      Subtract 182 – 155 = 27 and bring down the 9. Three goes into 27 nine times so there's a good chance 31 goes into 279 nine times. Multiply to check it.

      If this longer division is giving you trouble, there's more on this in Chapter 4, “Focus on Division.” In the meantime, try Self-Test 2.2.

      SELF-TEST 2.2

      1 Subtract 384 from 497.

      2 What is the difference between 2,857 and 6,793?

      3 Divide 4,816 by 8.

      4 When 3,751 is divided by 31, what is the result?

      5 Divide 1,911 by 21.

      ANSWERS TO SELF-TEST 2.1

      1 1,428

      2 2,662

      3 51,612

      4 26,730

      5 15,120

      ANSWERS TO SELF-TEST 2.2

      1 113

      2 3,936

      3 602

      4 121

      5 91

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