Calculating rational numbers by mouth The more, the better!

Calculating rational numbers by mouth The more, the better!

Operational properties of subtraction
Subtraction has the following operational properties: 1. A number minus a number, plus the same number, a number remains unchanged, that is, (a-b) + B = A2. A number plus a number, minus the same number, a number remains unchanged, that is, (a + b) - B = A3. The sum of N numbers minus a number can be subtracted from any addend
Given a (- 2,1), if the line L passes through point a and the area of the triangle enclosed by the two coordinate axes in the first quadrant is 1 / 2, the equation of line L is obtained?
Let L: Y-1 = K (x + 2) y = KX + 2K + 1
When y = 0, KX + 2K + 1 = 0, x = - 1 / K-2 > 0 (the first quadrant)
For the first quadrant, y = 0 + 1
The area of the triangle formed in the first quadrant is 1 / 2
1/2(-1/k-2)(2k+1)=1/2
-2-1/k-4k-2=1
4k²+5k+1=0
(4k+1)(k+1)=0
k1=-1/4
k2=-1
Or equation: y = + 2x-1 + 1
Let the equation of line l be y = KX + B, substitute the coordinates of point a into - 2x + B = 1, the intercept on the x-axis is - B / K, the intercept on the y-axis is B, from the area of triangle is 1 / 2, deduce B ^ 2 / k = 1, then the equation can be solved
2000 rational numbers!
At least 2000,
Within 3 digits, including 3 digits
－44＋68＝ 93－7×4＝ 28÷4＋83＝12÷4－2＝ 4×4×2＝ 7×90÷9＝ 97－7－66＝60÷6－7＝ 8×27÷9＝ 81÷9÷1＝ 10÷1×8＝30÷10－1＝ 76＋57...
How many?
The law of multiplicative distribution is alphabetized as yes
（a+b)c=ac+bc
Or AC + BC = (a + b) C
For example, (4a + 3b) C = 4ac + 3bC
The reverse is true
When a line L passes through points (1,4), the area of the triangle formed by it and the coordinate axis in the first quadrant is the smallest, and the equation of L is obtained
Let the linear equation be ax + by + C = 0 (i.e. y = - A / b * x-C / b)
Because the line passes through point P (1,4)
So a + 4B + C = 0, C = - a-4b
The topic requires a triangle formed in the first quadrant on the coordinate axis
So - A / B0) (when a = B, a + B gets the minimum value, AB under the root sign of 2)
We know that when a / b = 16b / a (that is, a ^ 2 = 16b ^ 2) (because AB > 0, so a / b > 0, 16b / a > 0), s gets the minimum
So a = 4b, then C = - 8b
So the linear equation AX + by + C = 0 is 4x + Y-8 = 0
Give me 10 simple oral arithmetic of rational numbers
-2*(-99)=
5/(-2.5)=
45+(-49)=
120*(-1)=
18-32/8-(-4)*5=
17-8/(-2)+4*(-5)=
14*(-3)*(-3)-5*(-3)+6=
1/(-1)+0/4-(-4)*(-1)=
13*(-4)-28/7=
(-7)*(-5)-90/(-15)=
1+1
1+2
1+3
1+4
-1+5
-5+6
-9+8
5+-9
6-8
78-98
It is necessary to express the commutative law of multiplication with letters______ The distribution law of multiplication______ .
The commutative law of multiplication is a × B = B × a, and the distributive law of multiplication is (a + b) × C = a × C + B × C. so the answer is: a × B = B × a, (a + b) × C = a × C + B × C
If the line L passes through the fixed point a (- 2,3) and forms a triangle with two coordinate axes, and the area is 4, the equation of line L is obtained
Let the linear equation be XA + Yb = 1, ∵ the line L passes through the fixed point a (- 2,3), and the area of the triangle surrounding the two coordinate axes be 4, ∵ 2A + 3B = 112 | ab | = 4. The solution is a = - 43b = - 6 or a = 4B = 2, so the equation of the line L is x − 43 + y − 6 = 1 or X4 + y2 = 1, that is 9x + 2Y + 12 = 0, or x + 2y-4 = 0
Exercises of mixed operation of rational numbers in Volume 1 of junior high school
The more the better!
Don't be too complicated, just ordinary!
OK, I'll add points!
1.2100-21×53+2255 2.(103-336÷21)×15 3.800-(2000-9600÷8) 4.40×48-(1472+328)÷5 5.(488+344)÷(202-194) 6.2940÷28+136×7 7.605×(500-494)-1898 8.(2886+6618)÷(400-346) 9.9125-(182+35×22) 10.(154-7...