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날짜별 학습 진행 상황 - 수능영어

날짜별 학습 진행 상황 - 수능영어 [riemann]

날짜	출제 문항 수	맞은 문항 수	백분율 점수
2007-09-02	50	48	96
2007-08-31	53	48	90
2007-08-30	44	41	93
2007-08-29	34	33	97
2007-08-27	33	26	78
2007-08-25	42	35	83
2007-08-24	37	35	94

곱셈법4

Using VERTICALLY AND CROSSWISE you do not need to the multiplication tables beyond 5 X 5.

• Suppose you need 8 x 7

  8 is 2 below 10 and 7 is 3 below 10.
  Think of it like this:
  
  The answer is 56.
  The diagram below shows how you get it.
  
  You subtract crosswise 8-3 or 7 - 2 to get 5,
  the first figure of the answer.
  And you multiply vertically: 2 x 3 to get 6,
  the last figure of the answer.

  That's all you do:

  See how far the numbers are below 10, subtract one
  number's deficiency from the other number, and
  multiply the deficiencies together.

• 7 x 6 = 42
  
  Here there is a carry: the 1 in the 12 goes over to make 3 into 4.

Here's how to use VERTICALLY AND CROSSWISE for multiplying numbers close to 100.

• Suppose you want to multiply 88 by 98.

  Not easy,you might think. But with
  VERTICALLY AND CROSSWISE you can give
  the answer immediately, using the same method
  as above.

  Both 88 and 98 are close to 100.
  88 is 12 below 100 and 98 is 2 below 100.

  You can imagine the sum set out like this:

  

  As before the 86 comes from
  subtracting crosswise: 88 - 2 = 86
  (or 98 - 12 = 86: you can subtract
  either way, you will always get
  the same answer).
  And the 24 in the answer is
  just 12 x 2: you multiply vertically.
  So 88 x 98 = 8624

Multiplying numbers just over 100.

• 103 x 104 = 10712

  The answer is in two parts: 107 and 12,
  107 is just 103 + 4 (or 104 + 3),
  and 12 is just 3 x 4.

• Similarly 107 x 106 = 11342

  107 + 6 = 113 and 7 x 6 =42

곱셈법3

An elegant way of multiplying numbers using a simple pattern.

• 21 x 23 = 483

  This is normally called long multiplication but
  actually the answer can be written straight down
  using the VERTICALLY AND CROSSWISE
  formula.

  We first put, or imagine, 23 below 21:

  

  There are 3 steps:

  a) Multiply vertically on the left: 2 x 2 = 4.
  This gives the first figure of the answer.
  b) Multiply crosswise and add: 2 x 3 + 1 x 2 = 8
  This gives the middle figure.
  c) Multiply vertically on the right: 1 x 3 = 3
  This gives the last figure of the answer.

And thats all there is to it.

• Similarly 61 x 31 = 1891
  

  

• 6 x 3 = 18; 6 x 1 + 1 x 3 = 9; 1 x 1 = 1

Multiply any 2-figure numbers together by mere mental arithmetic!

If you want 21 stamps at 26 pence each you can
easily find the total price in your head.

There were no carries in the method given above.
However, there only involve one small extra step.

• 21 x 26 = 546

The method is the same as above
except that we get a 2-figure number, 14, in the
middle step, so the 1 is carried over to the left
(4 becomes 5).

So 21 stamps cost £5.46.

33 x 44 = 1452

There may be more than one carry in a sum:

Vertically on the left we get 12.
Crosswise gives us 24, so we carry 2 to the left
and mentally get 144.

Then vertically on the right we get 12 and the 1
here is carried over to the 144 to make 1452

곱셉법2

Multiplying a number by 11.

To multiply any 2-figure number by 11 we just put
the total of the two figures between the 2 figures.

• 26 x 11 = 286

  Notice that the outer figures in 286 are the 26
  being multiplied.

  And the middle figure is just 2 and 6 added up.

• So 72 x 11 = 792

77 x 11 = 847

This involves a carry figure because 7 + 7 = 14
we get 77 x 11 = 7₁47 = 847

234 x 11 = 2574

We put the 2 and the 4 at the ends.
We add the first pair 2 + 3 = 5.
and we add the last pair: 3 + 4 = 7.