Primary Mathematics Olympiad Simple Calculation Process

<>2), (3) questions are not in parentheses, I don't understand well.

4) Refer to my question.

1.=4/3x2/3x5/4x3/4x……x101/100x99/100

4/3x5/4x6/5x……x100/99x101/100)x(2/3x3/4x4/5x……x98/99x99/100)

101/3x2/100

2.Did you forget to put brackets? （1999+2000x1998）/（1999x2000-1）

2000-1)+2000x(2000-2)]/[2000x(2000-1)-1]

2000x2000+2000-2000x2-1)/(2000x2000-2000-1)

2000x2000-2000-1)/(2000x2000-2000-1)

3.(2002x1999-1957)/(42+1999x2001)

2002x1999-1999+42)/(2001x1999+42)

2002-1)x1999+42]/(2001x1999+42)

1/4x(1/2+1/6+1/12+1/20+1/30)

1/4x(1x1/2+1/2x1/3+1/3x1/4+1/4x1/5+1/5x1/6)

1/4x(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6)

1/4x(1-1/6)

Question 4: It is estimated that the question was copied incorrectly!

1/2x4+1/4x6+1/6×8+1/8x10+1/10x12

The rest is omitted.

1. Multiplication:

1.The equation for the factor contains 25 and 125:

For example: 25 42 4

We keep in mind that 25 4 = 100, so we swap the factor positions so that the equation becomes 25 4 42

For equations that also contain the factor 125, use 125 8=1000 first.

For example: 25 32

At this point, we need to split 32 into 4 8 according to 25 4 = 100, and the original becomes 25 4 8.

For example: 72 125

We split 72 into 8 9 based on 125 8 = 1000, and the original becomes 8 125 9.

Key examples: 125 32 25

2.The equation for a factor containing 5 or so on:

For example: 35 16

We split 16 into 2 8 as needed, so that the original becomes 35 2 8. Because in this way, you can get the number of whole tens first, and it is easier to calculate.

3.Application of the multiplicative distribution rate:

For example: 56 32+56 68

Notice that the equation on both sides of the plus sign contains 56, which means what is the sum of 32 56s plus 68 56s, so we can propose 56 to change the equation to 56 (32+68).

If it is 56 132 — 56 32

The same as 56 is considered to be 56 (132-32).

Note: 56 99+56

Imagine that 99 56s plus 1 56 should be 100 56s, so the original becomes 56 (99+1).

Or 56 101-56

Also pay attention to the comprehensive application, such as:

4.Another application of multiplicative distribution rates:

For example: 102 47

Let's start by splitting 102 into 100+2

The equation becomes (100+2) 47

Then take care to match each item in parentheses with the outside of the parentheses. Multiply 47 and the equation becomes:

For example: 99 69

We turn 99 into 100-1

The equation becomes (100-1) 69

Then multiply the numbers in parentheses by 69, note that the minus sign in the middle, and the equation becomes:

2. Division:

1.Dividing by two numbers in a row is equal to dividing by the product of these two numbers:

For example: 32000 125 8

We can change the equation to 32000 (125 8) = 32000 1000

2.For example: 630 18

We can split 18 into 9 2

At this point, the original formula becomes 630 (9 2).

Note that to add parentheses, then turn on the parentheses, and the original becomes 630 9 2 = 70 2

3. Multiplication and division synthesis:

For example, 6300 (63 5).

We need to open the parentheses, and now we need to change the multiplication sign in the parentheses to the division sign, and the original form will become.

Let's start with a more common topic, take the topic I talked about on a small piece of paper as an example:

First of all, the reason why we can cross out a 0 of the dividend and the divisor at the same time is because we follow the rule that "the dividend and the number of jujube yards are reduced by the same multiple at the same time, and the quotient does not change". So, if you remove a 0 at the same time, it doesn't affect the result, so the original 65100 210 now becomes 6510 21, but the result is the same. Calculate 6510 21 and the final result is 310, so 65100 210 310.

Here's an example of a mistake: pay attention to the 0 at the end of the quotient, don't write it, because although the single digit still exists, there is no longer a number on the single digit.

Let's look at the second example.

3620÷50＝72...20, this is what we did with the previous method, there are no problems, the final result is 72 out of 20, but, looking further down, the new easy way.

Here's the new easy way: the final remainder is 2, is there something wrong with our calculations? Or is our new approach wrong?

In fact, it's not, how to understand it, first of all, the divisor is reduced by the dividend by the same multiple, the quotient is unchanged, and Yan Xiao is to say, in the vertical type, the quotient is a few, we can copy it directly, but the remainder is different, as I said above, although the 0 in the dividend is crossed out, but the digit is still there, our remainder 2, on the ten, represents 2 10, so it is 20. Summed up in one sentence:

Use a simple way to do pen calculations, the quotient is a few, directly copied in the horizontal back, but the remainder must be careful to see which digit it is in, like this topic, 2 in the ten digit, it represents 20, so the remainder 20.

Question 1, original formula = 1 3 (1 (1*2*3)-1 (2*3*4)+1 (2*3*4)-1 (3*4*5)+.1/（7*8*9）-1/8*9*10））

Question 2: Original formula = 10 + 1 7 + 10 + 1 6 + 10 + 1 5 + 10 + 1 4 = 40 + (1 7 + 1 6 + 1 5 + 1 4) = 40 + 319 420

Question 3: Original formula = (26 5) * (5 16) - (5 3) * (7 10) = 13 8-7 6

1 Use this formula to set 1 n(n+1)(n+2)=1 2[1 n(n+1)-1 (n+1)(n+2)].

Hope it helps.

Each item under observation is (n+1) 3-n, and you can try it all at once!

Apply the formula for summing continuous cubes and equal difference sequences.

1x2+2x3+3x4+4x5+..2002x2003

A and B respectively set off from AB and traveled in the same direction, their speed ratio was 3:2 when they started, after the encounter, A's speed increased by 1 5, B's speed increased by 2 5, and when A arrived at B, B was still 26km away from A. How many kilometers are the two places apart?

Let AB and the two places be separated by x kilometers.

2/(3+2)x]/[3×(1+1/5)]=[3/(3+2)x-26]/[2×(1+2/5)]

x/9=3x/14-130/14

13x/126=130/14x=90

A, B, and C went shopping together, and 1 2 of A's money was equal to 1 3 of B's money, and 3 4 of B's money was equal to 3 5 of C's spending, and C spent 98 yuan more than A, and asked them how much money they had spent.

490 yuan. A and B run a 100-meter run (assuming their speed remains the same), and when A runs 75 meters, B runs 60 meters. So, how many meters did B run when A reached the finish line?

80 meters. 1/6 + 1/12 + 1/24 + 1/48 + 1/96 + 1/192

The number of factor 5 determines the number of 0 at the end.

2008 5 = 401 (rounded).

2008 25=80 (rounded).

2008 125 = 16 (rounded).

2008 625 = 3 (rounded).

401 + 80 + 16 + 3 = 500.

1*2*3*4*5*6*……There were 500 zeros at the end of 2008

If a car drives from A to B, if the speed is increased by 20%, it can arrive 1 hour earlier than the original time, and if it travels 120 kilometers at the original speed and then increases the speed by 25%, it can arrive 40 minutes in advance.

40 minutes = 2 3 hours.

Original time: 1 [1-1 (1+20%)] = 6 hours.

The original speed [120-120 (1+25%)] 6-2 3-6 (1+25%)] = 24 8 15 = 45 km/h.

A and B are 45 6 = 270 kilometers apart.

The average score of the class in the final test of mathematics for class four (1) is 92 points, the number of boys who took the test is 18, the average score is 89 points, and the average score of girls is 94 points

92-89) 18 (94-92) = 27 people.

Chen Ming traveled 38 kilometers a day on flat roads and 23 kilometers a day on mountain roads, a total of 450 kilometers in 15 days. Asked how many kilometers of mountain roads he had walked during this time.

38*15-450) (38-23)*23=8*23=184km.

(1) Solution: Let a = 3 + 6 + 12 + 24 + ....+3072 then 2a = 6 + 12 + 24 + ...3072+6144 then a=2a-a

2) Solution: Let a = 1792 + 896 + 448 + ....+7 then 2a = 3584 + 1792 + 896 + 448 + ....+14 then a = 2a-a

3) Solution: Let a=1+3+9+27+81+....+177147 then 3a = 3 + 9 + 27 + 81 + ....+177147+531441 then a=(3a-a) 2

(1) Let a=3+6+12+24+...3072 so 2a = 6 + 12 + 24 + ...3072+6144a=2a-a=(6+12+24+..

2) Let a=1792+896+448+.14 + 7 so 2a = 3584 + 1792 + 896 + ...14a=2a-a=(3584+1792+896+..

3) Let a=1+3+9+27+81+...177147 so 3a = 3 + 9 + 27 + 81 + ...177147+5314412a=3a-a=(3+9+27+81+..

a=2a/2=265720

1986 3 2 = 331 331 * 3 = 993 It means that 1986 can be divided into 1986 3 groups of numbers in multiples of 3, that is, all the numbers you listed (excluding plus and minus signs) When considering the plus and minus signs, the sum of each adjacent two numbers is 3 Two numbers in a group, a total of 1986 3 2 groups, the result is multiplied by 3 over

Find the pattern from behind, (6-3) + (12-9) + (18-15) +1986-1983）

A total of 1986 6 3

So 1986 6*3=993