id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-8,598 |
\frac{4}{3} - \frac{1}{10}\cdot 5 = 4\cdot 10/(3\cdot 10) - \dfrac{3}{10\cdot 3}\cdot 5 = 40/30 - \frac{15}{30} = \left(40 + 15\cdot (-1)\right)/30 = \frac{25}{30}
|
2,627 |
\frac{5^1}{6^6} {6 \choose 5} = 30/46656
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20,547 |
1050 = 2^1*3^1*5 * 5*7^1
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-3,647 |
\frac{1}{r^2}\cdot r^4 = \frac{r\cdot r\cdot r\cdot r}{r\cdot r} = r^2
|
20,204 |
a \cdot c = (c^{1/2} \cdot a^{1/2})^2
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-20,230 |
\frac55 \cdot \frac{3}{3 \cdot (-1) - 4 \cdot r} = \dfrac{15}{-20 \cdot r + 15 \cdot (-1)}
|
30,046 |
-(-x^2 + 4) + 4 = x^2
|
-19,399 |
\frac{\frac{2}{9}}{9*\frac12}*1 = 2/9*2/9
|
20,150 |
\sin^2\theta\cos^2\theta = (\sin\theta\cos\theta)^2
|
-2,903 |
2\cdot 13^{\frac{1}{2}} = (3 + 1 + 2\cdot \left(-1\right))\cdot 13^{1 / 2}
|
6,886 |
2^{2^m + 2 \cdot (-1)} + 1 = 4^{2^{m + (-1)} + (-1)} + 1 = 4^{2^{m + \left(-1\right)} + (-1)} + 1^{2^{m + (-1)} + \left(-1\right)}
|
-586 |
\pi\cdot 115/4 - \pi\cdot 28 = 3/4\cdot \pi
|
15,545 |
(5 + 1 + 2 + 3 + 4 + 5)/6 = \dfrac{10}{3}
|
34,864 |
\frac34 = \frac{1}{4} + 1/2
|
4,988 |
1009 = \dfrac12\cdot (1 + 2017)
|
-20,317 |
\dfrac{t + 3}{t + 3}*3/5 = \frac{9 + 3*t}{t*5 + 15}
|
29,884 |
b\cdot i + a = a + i\cdot b
|
-16,695 |
7 = 7 \times 3 \times z + 7 \times 3 = 21 \times z + 21 = 21 \times z + 21
|
43,431 |
1*2*3 + 2*3*4 + 3*4*5 + 4*5*6 = 210 = \frac{840}{4}*1
|
32,074 |
( z^2 + 1, 1 + z) = ( z \cdot z + 1, 1 + z, 2) = \left( z^2 + \left(-1\right), 1 + z, 2\right) = ( 1 + z, 2)
|
5,823 |
Q^2*Q^2*Q^2 = Q^6 = Q^3*Q^3
|
19,767 |
I_2 d*2 = 2dI_2
|
5,173 |
|-\frac{1}{2}\cdot 9 + 5| = |-9/2 + 4|
|
30,444 |
|g_k - h_k| = |h_k - g_k|
|
-3,925 |
\frac{t^3}{t^4}\cdot 8/4 = \frac{8\cdot t^3}{4\cdot t^4}
|
24,203 |
4 \cdot (-\sqrt{2} \cdot 2 + 3) = -\sqrt{2} \cdot 8 + 12
|
40,138 |
6 = 2*3 = \left(1 + \sqrt{-5}\right) \left(1 - \sqrt{-5}\right)
|
9,319 |
\rho_1 + 2 \times \pi \times i = \rho_2 \times 2 - \rho_1 \Rightarrow \rho_2 = \rho_1 + \pi \times i
|
6,748 |
5\cdot \frac{5}{9} = \frac{25}{9}
|
-20,087 |
\frac{1}{28 + 21 z} (35 (-1) + 7 z) = \dfrac{z + 5 (-1)}{3 z + 4}*7/7
|
-20,280 |
(5 \cdot q + 20)/45 = 5/5 \cdot (q + 4)/9
|
36,752 |
2(x - k) = -(1 + 2k) + 2x + 1
|
25,619 |
c/g \cdot g = c \cdot g \cdot \frac{1}{c \cdot g} \cdot c
|
8,376 |
-s + (-1) = x\Longrightarrow s + x = -1
|
38,634 |
Y = Y\times \pi/\pi
|
4,980 |
\tfrac{1}{2} \cdot (1 - \cos(2 \cdot z)) = \sin^2(z)
|
-4,901 |
\frac{1}{10}\cdot 3.8 = 3.8/10
|
30,367 |
2 = 198 \cdot \left(-21\right) + 288 \cdot (-14) + 16 \cdot 512
|
4,309 |
\frac{1}{2} \cdot (n + (-1)) + \frac{1}{2} \cdot \left(n + 5 \cdot (-1)\right) + 3 = n
|
-24,650 |
\frac{11}{20} = -3/10 + \frac14 + \dfrac{1}{5}3
|
15,353 |
(-1) + \dfrac{2}{\cos(2\cdot z) + 1} = \tan^2(z)
|
-1,884 |
3/2*\pi - \pi*\frac{7}{4} = -\pi/4
|
14,026 |
5^2 \cdot 5^k = 5^{k + 2}
|
7,225 |
\sin{\frac{1}{5}\cdot 2\cdot \pi} = -\sin{\frac{8}{5}\cdot \pi}
|
12,445 |
5/6*(1 - p) + 1/6 = p \Rightarrow 6/11 = p
|
4,291 |
(-1) * (-1) * (-1) = \left(-1\right)^{\frac62} = (\left(-1\right)^6)^{1/2} = 1^{\frac{1}{2}} = 1
|
35,620 |
\left(f = f*2 \implies f + f = f\right) \implies f = 0
|
23,286 |
\cos{l \cdot y} \cdot \left(1 + i \cdot \tan{l \cdot y}\right) = e^{i \cdot l \cdot y} = (e^{i \cdot y})^l
|
14,917 |
\left(-1\right) + 120 = 7\cdot 17
|
18,458 |
\psi\cdot 0 + \psi\cdot 0 = \psi\cdot 0
|
24,217 |
\frac{\tan{z\cdot 2}}{\tan{2 z} + 1} = 1 - \tan{z} + \tan^2{z} - \tan^3{z} + \ldots
|
-15,828 |
-55/10 = 8/10 - 7 \cdot 9/10
|
-16,026 |
\frac{46}{10} = \frac{1}{10} \cdot 7 \cdot 10 - 8 \cdot 3/10
|
34,041 |
\frac{d}{dx} x \cdot x = x \cdot 2
|
29,105 |
F*a = a*F
|
25,072 |
a\cdot y = y\cdot a
|
35,539 |
\sin(g + b) = \cos(b)*\sin(g) + \cos(g)*\sin(b)
|
-18,250 |
\frac{1}{-z\cdot 7 + z z} (7 (-1) + z^2 - z\cdot 6) = \frac{1}{\left(z + 7 (-1)\right) z} (7 (-1) + z) \left(1 + z\right)
|
4,797 |
z = \frac{z}{(-1) + e^z} \left(e^z + (-1)\right)
|
-26,667 |
(x\cdot 3 + 2\cdot (-1))\cdot (5\cdot x + 2) = 15\cdot x^2 - 4\cdot x + 4\cdot (-1)
|
-28,794 |
\frac{2*\pi}{\pi*2*1/365}*1 = 365
|
28,972 |
Q^{n + 1} = Q^n*Q
|
-1,449 |
\dfrac{3}{4} \cdot (-2/1) = \frac{\tfrac{1}{4} \cdot 3}{\left(-1\right) \cdot 1/2}
|
-10,286 |
-\frac{80}{40 \cdot (-1) + 20 \cdot m} = 20/20 \cdot \left(-\frac{1}{2 \cdot (-1) + m} \cdot 4\right)
|
-10,620 |
\dfrac{20 + 20*q}{q*20 + 5*(-1)} = \dfrac{4*q + 4}{(-1) + q*4}*5/5
|
17,287 |
\sqrt{10}\cdot 4/9 - 10/9 = \left(-10 + 4\cdot \sqrt{10}\right)/9
|
27,244 |
z_2 + z_1 = 100 rightarrow z_1 = 100 - z_2
|
36,542 |
63 = 4 + 100 + 25 \cdot (-1) + 16 \cdot (-1)
|
12,225 |
2*x + \frac{1}{16}*(1 - 2*x - \frac{15*x}{16} - 1/16) = 2*x + 15/256 - 47*x/256 = 465*x/256 + \frac{15}{256}
|
29,521 |
4 \cdot a = (a + 1 + x)^2 = a \cdot a + 2 \cdot (1 + x) \cdot a + (1 + x)^2
|
12,672 |
\binom{31 + 11 + \left(-1\right)}{31} = \binom{41}{31} = \binom{41}{10}
|
11,827 |
-2^{1/2}\cdot 7 + 3 + 2^{1/2}\cdot 8 = 3 + 2^{1/2}
|
18,942 |
\sin{\pi/4} - \sin{\frac{(-1) \pi}{4}} = \sqrt{2}
|
31,613 |
1/(b\times c) = 1/(b\times c)
|
-11,467 |
-20 + i*12 = 0 + 20*\left(-1\right) + 12*i
|
-12,755 |
7\times (-1) + 28 = 21
|
-15,874 |
\frac{1}{10}\cdot 5 = 7\cdot 5/10 - 6\cdot 5/10
|
47,368 |
p^2 - p + 1 = p^2 - 2\cdot \frac12\cdot p + \dfrac14 + 1 - \dfrac{1}{4} = (p - \frac{1}{2}) \cdot (p - \frac{1}{2}) + \frac{3}{4}
|
7,818 |
(e + g) \cdot x = x \cdot e + g \cdot x
|
27,982 |
e^x = \lim_{n \to \infty} \left(1 + x/n\right)^n = \lim_{n \to \infty} (1 - \frac1n\cdot x)^{-n}
|
33,723 |
2*\left(-1\right) + 0 = -2
|
7,309 |
3\cdot \left(-1\right) + 2^3 = 5
|
31,373 |
\dfrac12\cdot 20 = 10
|
17,209 |
\frac{1}{0^2 + 1}\cdot 0 = 0
|
-7,123 |
\dfrac{1}{30} = \frac{1}{10}*4*\tfrac39*\frac{1}{8}*2
|
39,481 |
(-3)^4 = ((-1)*3)^4 = \left(-1\right)^4*3^4 = 81 = 81
|
9,052 |
2 \cdot \left(q \cdot 3 + 1\right) = 6 \cdot q + 2
|
14,512 |
c\cdot (a\cdot b + b\cdot a) = c\cdot \left(a\cdot b + a\cdot b\right)
|
1,234 |
\alpha,\beta,\alpha \leq \beta \implies \beta = \alpha*\beta
|
22,006 |
{y \choose n} = {n + y - n + 1 + \left(-1\right) \choose n}
|
5,956 |
(-y + x)\cdot (x^1 + x^0\cdot y + \dots + x\cdot y^0 + y^1) = x^2 - y \cdot y
|
40,125 |
l^2 = l\cdot l = l + (l + (-1))\cdot l
|
6,295 |
105 \cdot 105^2 + (-104)^3 = 181 \cdot 181
|
-4,464 |
20*(-1) + x^2 - x = (x + 4)*(x + 5*(-1))
|
-9,346 |
50*(-1) + k*10 = k*2*5 - 2*5*5
|
11,541 |
\bar{c_x} \cdot D \cdot e \cdot d = d \cdot D \cdot e \cdot \bar{c_x}
|
-3,951 |
\frac{f^5 \cdot 44}{f^5 \cdot 55} = \frac{44}{55} \cdot \frac{1}{f^5} \cdot f^5
|
10,842 |
x^3*2 + 6x + 12 = (x^3 + 3x + 6)*2
|
24,223 |
e^{i \cdot s \cdot X} \cdot E = E \cdot e^{X \cdot s \cdot i}
|
16,123 |
2/775 = \frac{2}{25} \cdot \dfrac{1}{31}
|
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