id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
28,677 |
1/100 \cdot 10000 + 10000 = \left(1 + 1/100\right) \cdot 10000
|
-12,908 |
\frac{5}{8} = \frac{15}{24}
|
4,584 |
-22 \cdot x^2 - x \cdot x = -23 \cdot x^2
|
1,668 |
-\phi^2/2 (-\phi^2) = e^{-\phi^2} \phi^3
|
28,370 |
2 \cdot x \cdot c = (x + x) \cdot c = x \cdot c + x \cdot c = 2 \cdot x \cdot c
|
28,100 |
\tan^{-1}{\sqrt{3}/3} = \frac{\pi}{6}
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-7,381 |
\frac{5}{14}\cdot \frac{4}{13} = \dfrac{10}{91}
|
1,829 |
7/36*(\frac{15}{4})^2 = 175/64
|
21,511 |
\cos^3{π} = (-1) \cdot (-1) \cdot (-1) = -1
|
-6,038 |
\dfrac{8(x + 4)}{(x + 10)(x + 4)} + \dfrac{4(x + 10)}{(x + 10)(x + 4)} - \dfrac{8}{(x + 10)(x + 4)} = \dfrac{ 8(x + 4) + 4(x + 10) - 8}{(x + 10)(x + 4)}
|
-1,583 |
\pi \cdot \frac{19}{12} = 5/6 \cdot \pi + \pi \cdot 3/4
|
-4,048 |
\frac{54*g^4}{g^2*30} = \frac{g^4}{g^2}*\frac{54}{30}
|
17,520 |
(z_i + y_i)*c_i = z_i*c_i + c_i*y_i
|
11,032 |
2 \cdot g \cdot f + 2 \cdot g \cdot h + 2 \cdot f \cdot h = 4 \cdot g + 4 \cdot f + 4 \cdot h = g \cdot f \cdot h
|
7,325 |
\tau + 1 - p > 0 \Rightarrow \tau \gt p + \left(-1\right)
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-18,332 |
\dfrac{y\cdot (y + 10)}{(y + 3) (y + 10)} = \frac{1}{30 + y^2 + 13 y}(y\cdot 10 + y^2)
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4,324 |
-4 C + A\cdot 2 + 2 B = 0 \Rightarrow -2 C + A + B = 0 \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots\cdot 3
|
868 |
(1/a)^n = a^{-n} = \frac{1}{a^n}
|
34,026 |
(1 + k)*k! = (k + 1)!
|
8,630 |
\frac{86}{100}*114/100 x = x
|
6,047 |
-h_1 \cdot f_1 + f_2 \cdot h_2 = -f_1 \cdot h_1 + f_2 \cdot h_2 - f_1 \cdot h_2 + f_1 \cdot h_2
|
24,509 |
103/165 = \dfrac{1}{11} + 1/3 + \frac15
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-2,104 |
17/12*\pi = 17/12*\pi + 0
|
29,103 |
1 = a^0 = a^{1 + (-1)} = \dfrac1a*a^1 = \frac{a}{a}
|
15,109 |
3 \cdot (-1) + x = 0 \implies x = 3
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-9,640 |
-\dfrac{4}{5} = -\frac{1}{25}*20
|
-2,650 |
\sqrt{11}\times 6 = \sqrt{11}\times \left(1 + 3 + 2\right)
|
-22,255 |
n^2 + n*5 + 6*(-1) = ((-1) + n)*\left(6 + n\right)
|
-3,466 |
\dfrac{4 \cdot 2}{5 \cdot 2} = \frac{8}{10}
|
-1,139 |
\dfrac{1}{\left(-4\right)*1/9}*((-1)*9*1/7) = -9/7*(-\tfrac94)
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10,500 |
xl + x = x \cdot \left(1 + l\right)
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-9,433 |
-20\cdot x \cdot x + 6\cdot x = -x\cdot 2\cdot 2\cdot 5\cdot x + x\cdot 2\cdot 3
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9,464 |
\frac{1}{3!}\cdot \left(\binom{202}{2} - 3\cdot 101\right) = \frac{1}{6}\cdot (20301 + 303\cdot (-1)) = 3333
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25,220 |
(Z_2 + Z_1)^2 - 2\cdot Z_1\cdot Z_2 = Z_2^2 + Z_1^2
|
1,411 |
\left(\sin^{-1}(1) = y rightarrow \sin(y) = 1\right) rightarrow y = \pi/2
|
13,915 |
\frac{1}{4} \pi + \pi = \frac{\pi\cdot 5}{4}
|
10,884 |
a \cdot \mu_T = \mu_Z \Rightarrow a = \frac{\mu_Z}{\mu_T}
|
1,822 |
2^2\cdot l + ((-1) + l)^2 = (1 + l)^2
|
24,565 |
y\times (y + 1) = y\times (y + 1) = y^2 + y
|
8,119 |
\frac{4 \cdot 4 \cdot 4}{3 \cdot 3 \cdot 3} = (4/3)^3
|
-21,923 |
-\dfrac{1}{6} + \dfrac{8}{5} = - {\dfrac{1 \times 5}{6 \times 5}} + {\dfrac{8 \times 6}{5 \times 6}} = - {\dfrac{5}{30}} + {\dfrac{48}{30}} = - \dfrac{{5} + {48}}{30} = \dfrac{43}{30}
|
3,286 |
\frac{1}{h\cdot x\cdot f} = \dfrac{1/h}{f}\cdot \frac{1}{x}
|
17,872 |
28 = 1 + 3^{3 + 6 \cdot 0}
|
33,189 |
\left(x * x + y^2\right)*(-\dfrac{y}{x} + 1) = (-\frac{1}{x}*y + 1)*((x^2 + y * y)^{1/2})^2
|
20,328 |
8 + 2*\dfrac{8}{14} = 64/7
|
-16,328 |
i = 3 s = s + 4
|
-1,641 |
3/4 \pi = -\pi*2 + \dfrac1411 \pi
|
-26,248 |
1 = H \cdot e^{7 \cdot 0} = H
|
15,351 |
-\sin{x}\cdot \sin{y} + \cos{y}\cdot \cos{x} = \cos\left(x + y\right)
|
-7,909 |
\frac{1}{5 - 3\cdot i}\cdot \left(25 + i\cdot 19\right)\cdot \frac{5 + 3\cdot i}{3\cdot i + 5} = \frac{25 + i\cdot 19}{5 - i\cdot 3}
|
14,382 |
\frac{5!}{10} \cdot 2 \cdot 5! = 5! \cdot 5!/5 = 4! \cdot 5!
|
-14,593 |
528 = 4\times 82 + 2\times 100
|
16,887 |
\sin(\vartheta_1 + \vartheta_2) = \sin{\vartheta_2}\cdot \cos{\vartheta_1} + \cos{\vartheta_2}\cdot \sin{\vartheta_1}
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-21,871 |
\frac16*4 - \frac{9}{2} = 4/(6) - 9*3/\left(2*3\right) = 4/6 - \frac{27}{6} = \frac16*(4 + 27*(-1)) = -\frac{23}{6}
|
6,948 |
\sqrt{t + 1} = 1 + t/2 + \ldots
|
32,121 |
(x + 1)^3 \cdot 4 = (1 + x)^2 \cdot (4 + x \cdot 4)
|
24,719 |
x^2 + a^2 + b b + h^2 = 0 \implies a = b = h = x = 0
|
20,345 |
\left(3\cdot (-1) + j\right)\cdot (1 + j) = j^2 - 2\cdot j + 3\cdot (-1)
|
-16,345 |
6*75^{1 / 2} = 6*(25*3)^{\frac{1}{2}}
|
33,784 |
C\cdot C/(C\cdot m)/(C\cdot x) = \frac{1}{m\cdot C\cdot x}\cdot C
|
29,533 |
90/11.25 = \frac{90}{45*1/4} = 4*90/45 = 4*2 = 8
|
13,359 |
(n + \frac{1}{2})^2 = n^2 + n + 1/4
|
20,940 |
295 = 5*59
|
-1,584 |
\pi\cdot 9/4 = \frac13\cdot 2\cdot \pi + 19/12\cdot \pi
|
33,174 |
(-(-5)^{1/2} + 1)\cdot (1 + \left(-5\right)^{1/2}) = 6
|
-20,610 |
\frac{-5 \cdot p + 7}{7 - 5 \cdot p} \cdot \left(-\frac{1}{4} \cdot 9\right) = \tfrac{63 \cdot (-1) + 45 \cdot p}{-p \cdot 20 + 28}
|
21,740 |
\mathbb{E}(B)^4 = \mathbb{E}(B^4)
|
20,670 |
\tfrac{3}{100}\cdot 3/100 = 9/10000 = 0.0009
|
13,227 |
\sin{2\cdot r} = 2\cdot \cos{r}\cdot \sin{r}
|
29,989 |
-\dfrac{1}{2} + \dfrac32 = 1
|
15,639 |
(-1) + x^4 = (1 + x) (x^2 + 1) (x + (-1))
|
38,409 |
-\tfrac{\pi}{4} = \frac{\pi\cdot (-1)}{4}
|
15,780 |
A\cdot \varepsilon = \varepsilon\cdot A
|
15,878 |
(n^2 + \frac12 \cdot n)^2 = n^4 + n^3 + n^2/4 < n^4 + n^3 + n \cdot n + n + 1
|
1,666 |
\sin{3x} = -4\sin^3{x} + 3\sin{x}
|
35,034 |
8 = 5*3 + 5 (-1) + 3 (-1) + 1
|
4,669 |
158/24 = \tfrac{1}{24} \cdot \left(12 \cdot 12 + 2^2 + 10\right)
|
544 |
(x * x + 1 + (-1)) x = x^2 * x
|
27,353 |
(hk)^g := hgk/g := \frac{h}{g}g kg/g
|
2,485 |
\left(d + b\right)^2 = d^2 + 2db + b^2
|
20,556 |
(z + 1) z \cdots\cdot ((-1) + z + l) = z^l
|
14,780 |
0 = \frac{1}{f} \cdot ((f - b) \cdot x + b^2) - b = (f - b)/f \cdot x + \frac{b^2}{f} - b
|
-4,522 |
-\frac{2}{3 + x} - \frac{1}{x + 1}\cdot 2 = \frac{1}{3 + x^2 + x\cdot 4}\cdot (-x\cdot 4 + 8\cdot (-1))
|
7,554 |
a \times 2^0 = a
|
22,495 |
\sin{y} = \sin(y\times 2 - y)
|
-6,725 |
\frac{1}{10}\times 8 + 9/100 = \frac{1}{100}\times 80 + 9/100
|
-24,035 |
9 + 7 \cdot 4 = 9 + 28 = 9 + 28 = 37
|
19,935 |
\frac{1}{24} (27 + 24 (-1)) = \dfrac{3}{24} = \frac18 = 12.5
|
23,858 |
h - c + d = h - c - d
|
10,035 |
2! \binom{5}{2} = \frac{3! \binom{5}{2}}{3}1
|
-7,712 |
\left(104 - 28*i + 78*i + 21\right)/25 = \dfrac{1}{25}*(125 + 50*i) = 5 + 2*i
|
-1,697 |
\pi \cdot \dfrac{1}{12} \cdot 17 + \pi \cdot \frac{1}{6} \cdot 5 = 9/4 \cdot \pi
|
11,262 |
x^3 = 8x^2 - 20^x + 16 + \dotsm
|
21,753 |
2 = (3^2 + 0^2 + 0^2 + 1^2 + 1^2 + 1^2)/6
|
6,551 |
734 = 34 + 500 + 334 + 200 + 167 (-1) + 100 (-1) + 67 (-1)
|
-17,505 |
3 = 78 + 75\cdot \left(-1\right)
|
17,416 |
121 \cdot 121 \cdot 121 = 49^3 + 84^3 + 102^3
|
4,036 |
A/X \cdot x = X \cdot x \cdot \frac1X/X \cdot A
|
17,177 |
1 + x\cdot 2 \leq e^x \implies e^{x + 1} \gt e^x + e^x \gt x \cdot x + 2\cdot x + 1 = (x + 1)^2
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9,830 |
(\mathbb{P}(Z_1) + \mathbb{P}(Z_2))^2 = \mathbb{P}(Z_1)^2 + 2\mathbb{P}(Z_1) \mathbb{P}(Z_2) + \mathbb{P}(Z_2)^2 = 1 \Rightarrow 0.9 = \mathbb{P}(Z_1)^2 + \mathbb{P}(Z_2)^2
|
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