3 quick arithmetic questions, speed, I m in a hurry

Why don't you use the calculator that comes with the computer?。。

I took a look at the calculation method...

First of all 15x26

Step 1: The first product is multiplied by the tail product and written in parallel and then (1 2 5 6) 23o

Step 2: The sum of the first and last products is 10 is (1 6+2 5) 10=160

Step 3: 230 + 160 = 390

390x37

Step 1: The first product is multiplied by the mantissa and written in parallel with (3x3 9 7) 963

Step 2: The sum of the first and last products is 10 is (3 7+3 9) 10=480

Step 3: 963 + 480 = 1443

After that, add 0=14430

Question 2: 23 times 273 times 74

First, list the multipliers, one digit at a time, the number of repetitions is a number of digits, 2 digits, and the column is moved one place each time from the second row to the right.

Write to be multiplied, in a column-followed row.

3,2) (3,3) Multiply the number in ().

6) (9) Summing, pay attention to carrying.

4 2o 27 9

273x23=6279

First, list the multipliers, one digit at a time, the number of repetitions is a number of digits, 2 digits, and the column is moved one place each time from the second row to the right.

Write to be multiplied, in a column-followed row.

9,7) (9,4) multiply the number in ().

63) (36) Add and pay attention to carrying.

6279x74=46464

Question 3. 67x12=

First, list the multipliers, one digit at a time, the number of repetitions is a number of digits, 2 digits, and the column is moved one place each time from the second row to the right.

Write to be multiplied, in a column-followed row.

7,1) (7,2) multiply the number in () by two.

7) (14) Summing, pay attention to carrying.

67x12=804

804x24

First, list the multipliers, one digit at a time, the number of repetitions is a number of digits, 2 digits, and the column is moved one place each time from the second row to the right.

Write to be multiplied, in a column-followed row.

4,2) (4,4) Multiply the number in () by two.

8) (16) Summing, pay attention to carrying.

67x12=19296

Finally finished, whether the landlord will not, maybe it's been a day late, for my topic didn't see clearly, I spent 2 hours, to perfect it, thank you landlord!! Let me learn quick arithmetic, and pay tribute to the landlord again!!

It is all done according to the multiplicative distributive law, which is ab+ac=a(b+c) original formula = 2 999+2 1+4 999+4 1+6 1+6 999=2 (999+1)+4 (999+1)+6 (999+1)=2 1000+4 1000+6 1000=(2+4+6) 1000

Original = 3 998 + 3 2 + 4 998 + 4 2 + 6 998 + 6 2 = 3 (998 + 2) + 4 (998 + 2) + 6 (998 + 2) = (3 + 4 + 6) 1000

Original = 4 995 + 4 5 + 5 996 + 5 4 + 6 997 + 6 3 = 4 (995 + 5) + 5 (996 + 4) + 6 (997 + 3) = (4 + 5 + 6) 1000

Original = 5 999 + 3 998 + 997 + (5 + 3 2 + 3) = 5 (999 + 1) + 3 (998 + 2) + (997 + 3) = (5 + 3 + 1) 1000

o() o Alas, 2 x 999 is equal to 2x(1000-1).

And so on.

It only makes sense to do the question yourself.

These problems are solved in one way, such as 1 question, 2 (999 + 1) + 4 (999 + 1) + 6 (999 + 1) = 12000

1.Solution: Original = 2

2.Solution: Original =

3.Solution: Original =

4.Solution: Original =

5 * 999 + 3 * 998 + 997 + 14 = 9000 Give 14 points and 5 numbers to 5 * 999 and it will become 5 * 1000, and in the same way, divide six to three times nine hundred and eight to become three times one thousand, and the remaining three will be given to nine hundred and ninety-seven, a total of nine thousand!

Question 1:

2x-3y=8①

3y+2z=0②

x-z=-2③

Obtained by +: 2x+2z=8

From the formula to get x=z-2, bring in the formula to get: z=3 and then solve: x=1, y=-2, z=3, then xyz=-6 second problem:

From -2 , 2 respectively: x-4z=-11··· az-4x=-4 ·· b

From a+4b, we get: x=1, and then we bring in the problem and get :

x=1、y=2、z=3、u=4。

It is known that x, y, z satisfy the system of equations.

2x-3y=8①

3y+2z=0②

x-z=-2③

Then xyz=?

②：2x+2z=8 x+z=4④③+2x=2 x=1

Substitute x=1 into z=3

Substitute x=1 into y=-2

xyz=-6

Solve the equation x+2y=5

y+2z=8②

z+2u=11③

u+2x=6④

2*②+4*③-8*④：x-8*2x=5-2*8+4*11-8*6

15x=-15 x=1

y=2z=3u=4

Answer: Solution: (1) Bo1C=N-1N 180°+1N A, BoN-1C=1N 180°+N-1N A (2) When N=4, Bo3C=14 180°+34 A Prove:

Left side of the equation = bo3c = 180° - (o3bc + o3cb) = 180° - 34 ( b + c) = 180° - 34 (180° - a) = 14 180° + 34 a = right side of the equation When n = 4, bo3c = 14 180° + 34 a Comment: This problem comprehensively uses the concept of the inner angles and theorems of triangles and the equinometric angles of n.

Solution: (1) The angular bisector of abc and acb intersects at the point O, 2 obc= abc, 2 ocb= acb, a+ abc+ acb=180°, a+2 obc+2 ocb=180°, obc+ ocb=90°-1 2 a, boc=180°-(obc+ ocb)=90°+1 2 a, a=x°, boc=(90+1 2 x)°;

2) The tripartite lines of ABC and ACB intersect at the points O1, O2, O1BC=2 3 ABC, O1CB=2 3 ACB, 3 2 O1BC= ABC,3 2 O1CB= ACB, A+ ABC+ ACB=180°, A+3 2 O1BC+3 2 O1CB=180°, O1BC+ O1CB=2 3(180°- A), BOC=180°-(O1BC+ O1CB)=60°+2 3 A, A=X°, boc=（60+2 3 x）°；

3) The law that can be obtained from (1) and (2) is:

If the n-bisector lines of ABC and ACB intersect at the points O1, O2, 、..., on-1, then x is used to represent bo1c=(n-1) n*180+1 n* a bon-1c=1 n*180+(n-1) n* a boic=(n-i) n*180+i n* a. If you agree with my answer.

Knowing a=2, c=4, a=30°, we can get that the height of the AC edge is h=4*sin(30°)=2, which means that h=bc=a, abc is a right triangle. BC is perpendicular to AC, therefore, the area of the triangle is: . where (3) is the root number three.

cos30=b c = half of the root number 3, c = 4, b = two root number three, known a, b, c then the area is sixteen root number three.

a/c=sina/sinc

The solution is that sinc=1 and c=90° are right-angled triangles.

b = 2 3 area = 1 2 * 2 * 2 3 = 2 3

First a sina=a sinc

Get sinc=90 degrees.

Get b = 2 times the root number 3

S triangle abc = ab 2 = 2 times the root number 3

Hello!

Solution: 1, 4=120°, 3+ 4=180° 3=180- 4=180-120=60° 2= 3

1 = 2 = 60° (equal to the apex angle).

2. There are 4 pairs, which are, 1 and coe, 4 and aod, 3 and coe, 2 and aod

3. Let coe=x°, then aoc=30°+x°, boc=2(30 x)°+30°

aoc+∠boc=180

30+x+2（30＋x）+30=180

30+60+3x+30=180

3x=60x=20

dof= coe=20° (equal to apex angle) hope it helps you

The degree of angle 1 is because, angle one and angle two are opposite the top angle, so angle one is equal to angle two equals angle three, because angle three plus angle four is equal to 180 degrees, angle four is equal to 120 degrees, so angle one is equal to angle three is equal to 180 - angle four is equal to 60 degrees.

1 pair, which are the horn eob and the horn boa, the angle is not so sure.

Let the angle EOC be equal to X degrees, the angle COB is equal to X + EOC and multiplied by 2+30, the angle COB + X is equal to 150 degrees, so 2 (X + 30) + 30 + X is equal to 150 degrees, so X is equal to 20 degrees, because the angle OEC and the angle DOF are the top angles, so the angle DOF is equal to 20 degrees.

1, 1= 2= 3, while 3+ 4=180°, 4=120°, so 3=60°, so 1=60°

2, 1 with coe, 4 with aod, 3 with coe, 2 with aod3, dof= eoc

boc+ aoc=180°, boc=2 aoc+30°, so aoc=50°, so eoc= dof=20°

1.4 120 (known).

3 180 - 4 60 (definition of complementary angles).

2 3 1 = 2 (known).

1 3 60 (equivalent substitution).

2., 1 with coe, 4 with aod, 3 with coe, 2 with aod3Solution: Let aoc x boc 2x+30x+2x+30=180

x+2x=150

x=50∠aoc＝x=50

AOE 30 (known).

EOC 50 AOE 20 (Equation Definition) DOF is EOC to apex angle (known).

EOC DOF=20 (equal to the vertex angle).

48/192*9=1728

Represents divided by.

Represents multiplied by.