id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-1,952 |
\pi*37/12 - 2 \pi = \pi*13/12
|
44,463 |
0.6 = 0.024*25
|
-6,629 |
9/9 \cdot \frac{4}{(7 + z) \left(z + 1\right)} = \frac{36}{9(z + 1) (7 + z)}
|
28,588 |
108.25 = (-1)*6.75 + 115
|
14,199 |
\left(x + (-1)\right)! = \frac{x!}{x}
|
4,751 |
|-z + y\cdot 2| = |z - 2\cdot y|
|
-1,290 |
-\frac{28}{42} = \dfrac{\left(-28\right)*\frac{1}{14}}{42*\frac{1}{14}} = -2/3
|
29,309 |
k*x = k*x
|
13,779 |
Y Y Y = Y J = J Y
|
-588 |
(e^{\dfrac{\pi*i}{12}*1})^{16} = e^{16*\frac{\pi*i}{12}}
|
-18,314 |
\dfrac{3 \cdot (-1) + n^2 - 2 \cdot n}{n^2 - 6 \cdot n + 7 \cdot (-1)} = \frac{(n + 3 \cdot (-1)) \cdot \left(n + 1\right)}{(n + 1) \cdot (n + 7 \cdot \left(-1\right))}
|
16,296 |
2^{n + l + (-1)} = 2^{n - l + 1} \cdot 4^{l + (-1)}
|
29,442 |
p - q + 2q = -(-q - p)
|
24,728 |
2 = \binom{2}{1}\cdot \binom{1}{1}
|
19,530 |
d + g = v \cdot z \Rightarrow \frac1z \cdot (d + g) = v
|
-23,720 |
12/35 = \frac{4}{5}*\frac{3}{7}
|
1,433 |
5/7 \frac68*1/(9*10)*24*3 = 3/7
|
2,282 |
3\times (1 + x^2) - (x^2 + (-1))\times 3 = -2\times (x\times 2 + 3\times (-1)) + 4\times x
|
10,156 |
6^3 = 5^3 + 3 * 3 * 3 + 4 * 4 * 4
|
14,516 |
7191 = 10000 + 2809 (-1)
|
7,502 |
8 \cdot \frac{1}{27}/(\frac13) = \frac89
|
9,185 |
9!/(3!*3!*3!*3!) = 280
|
-2,586 |
-\sqrt{6} + \sqrt{6}\cdot \sqrt{4} = 2\cdot \sqrt{6} - \sqrt{6}
|
23,150 |
6 = 7\cdot 0 + 3\cdot 2
|
1,075 |
\binom{s}{q} = s/q \cdot \binom{(-1) + s}{q + (-1)}
|
2,522 |
(33 + 33 + 11)/55 = (3 + 3 + 1)/5 = \dfrac75
|
31,339 |
8\times 221^3\times 442^{257} = 442^{260}
|
-7,096 |
\frac15 = \frac{2}{5} \cdot 3/6
|
26,420 |
e_1 \times k_1 \times e_2 \times k_2 = e_1 \times e_2 \times k_1 \times k_2 = e_1 \times e_2 \times k_1 \times k_2
|
20,859 |
Z^g = Z^p \Rightarrow Z^{\frac{g}{p}} = Z
|
2,303 |
\dfrac{\left(n!\right)!}{n!} = (n! + (-1))!
|
23,093 |
312500 = 5^3*5^3*{6 \choose 3}
|
28,157 |
1 = 1/y + y rightarrow 1 = y^7 + \frac{1}{y^7}
|
21,043 |
\dfrac{1}{x^3} = \dfrac1x - \dfrac{3}{x^2} = \frac{10}{x} + 3 \cdot (-1)
|
-6,821 |
10 \cdot 11 \cdot 9 = 990
|
7,942 |
x\cdot l = 88 \Rightarrow \frac{1}{l}\cdot 88 = x
|
-547 |
\left(e^{5*i*π/4}\right)^{14} = e^{14*i*π*5/4}
|
36,773 |
1 - \dfrac{50}{81} = \tfrac{31}{81}
|
-4,031 |
\frac{12 \cdot 10}{12 \cdot 3} \cdot \tfrac{r^5}{r^4} = \frac{r^5}{r^4} \cdot \frac{1}{36} \cdot 120
|
5,243 |
\cot((π\cdot (-1))/4) = \cot(\frac{π}{4}\cdot 3)
|
-151 |
{5 \choose 3} = \tfrac{5!}{3! \cdot (5 + 3 \cdot \left(-1\right))!}
|
2,567 |
r^4 + 2\cdot (-1) = r^4 + 4 = r^4 + 4\cdot r \cdot r + 4 - r^2 = r^2 + 2 - r^2 = (r^2 + 2 - r)\cdot (r^2 + 2 + r)
|
-22,254 |
x^2 + 13 x + 36 = (x + 4) \left(x + 9\right)
|
38,353 |
\left(1 + 1\right) \cdot \left(1 + 1\right) - 1^2 = 1 + 2
|
21,072 |
\left(3\cdot (-1) + z\right)\cdot (2\cdot (-1) + z) = 6 + z^2 - z\cdot 5
|
5,269 |
U + x = U + x + k - n rightarrow U + x + k = U + x + n
|
63 |
|l^l| = 1 > |l|
|
27,423 |
u_v \cdot x = u_w \Rightarrow \frac{u_w}{x} = u_v
|
-19,430 |
7/3 \cdot \frac{7}{2} = \dfrac{1/2}{\frac{1}{7} \cdot 3} \cdot 7
|
52,406 |
1000000007 = 7 + 10^9
|
35,307 |
3*(e + a) = e*3 + a*3
|
14,464 |
(q + 1)^2 = q^2 + 2 \cdot q + 1 = q \cdot q + 1
|
24,787 |
-\sin(2*z) = -2*\cos(z)*\sin(z)
|
27,415 |
z^5 + (-1) = \left(1 + z^4 + z^3 + z^2 + z\right)\cdot ((-1) + z)
|
154 |
-E[R] = E[-R]
|
11,175 |
w = \frac{1}{z + 4(-1)}(3(-1) + z) \Rightarrow \tfrac{4w + 3(-1)}{(-1) + w} = z
|
38,568 |
x x = 2^2\Longrightarrow x = 2
|
36,798 |
-4/15 = -\tfrac{4}{15}
|
5,738 |
\sqrt{2} = \tfrac{4\cdot \cos{\pi/12}}{-\tan{\frac{\pi}{12}} + 3}
|
25,195 |
(1 + m)*(1 + m)! + (1 + m)! = (m + 1)!*(1 + m + 1)
|
-3,502 |
\frac{7}{10} = 0.7
|
3,581 |
\cos{h}*\sin{e} + \sin{h}*\cos{e} = \sin\left(h + e\right)
|
17,819 |
3 - 2f_2 = f_2 + b + f_1 - 2f_2 = -f_2 + b + f_1
|
8,123 |
(k \cdot k)^3 = k^6
|
113 |
3945636 = 4\cdot (1!\cdot \binom{9}{1} + \binom{9}{2}\cdot 2! + \dotsm + \binom{9}{9}\cdot 9!)
|
48,293 |
x^{x^{(-1) + 1}} = x
|
16,391 |
\frac{\theta}{4 + \theta} = \frac{\theta}{4 + i + \theta - i}
|
-18,607 |
-20/11 = -\dfrac{1}{11}*20
|
11,711 |
-\mathbb{E}(V) = \mathbb{E}(-V)
|
24,897 |
g*d*x = g*x*d
|
11,403 |
e^x = 1 + x + \frac{1}{2!}\times x^2 + \frac{1}{3!}\times x^3 + \dots > \frac16\times x^3
|
-22,831 |
\dfrac{72}{16} = 9\cdot 8/(2\cdot 8)
|
51,289 |
\left\lfloor{\frac13*6}\right\rfloor = 2
|
28,409 |
y + x + x + y = x + y + x + y
|
-23,244 |
\dfrac{1}{3} = \frac421/6
|
8,792 |
1.0000006^2 = (1 + \frac{6}{10^7}) \cdot (1 + \frac{6}{10^7}) = (1 + \frac{3}{5 \cdot 10^6})^2
|
1,791 |
2 + a = a + (-1) + 3
|
12,315 |
g_2 + g_1 = -2\Longrightarrow -g_1 + g_2 = -8
|
-20,288 |
4/4 \cdot (-\frac{8}{3}) = -\frac{1}{12} \cdot 32
|
24,830 |
z*7 - z*4 = z*3
|
47,553 |
2^{31} = 1298 + 734182\cdot 2925
|
26,349 |
A = A \cup \left(B \cap B^c\right) = (A \cap B) \cup (A \cap B^c)
|
10,054 |
\pi/3 - \pi = \frac{1}{3}\times (\pi\times (-2))
|
7,129 |
\sqrt{S_n} = F_n \Rightarrow F_n \cdot F_n = S_n
|
20,662 |
2\times (n + (-1)) = n\times 2 + 2\times (-1)
|
21,816 |
y \cdot 99 = 13\Longrightarrow y = \frac{13}{99}
|
26,612 |
x = c^2 \Rightarrow c = \sqrt{x}
|
21,590 |
a + x = (a + x)^2 = a^2 + a \times x + x \times a + x^2 = a + a \times x + x \times a + x
|
1,859 |
-7.5 = -17/6 - 14/3
|
-7,355 |
4/14\cdot 5/13 = \frac{10}{91}
|
-15,964 |
-9/10 \cdot 8 + \frac{10}{10} = -62/10
|
375 |
y + 144 = 11\cdot (9 + y) \Rightarrow 99 + 11\cdot y = y + 144
|
4,318 |
2\cdot \sin{1} = 1.683\cdot \dots > \frac85
|
27,944 |
\frac{\omega^2\cdot 5^{1/3}}{5^{1/3} \omega} = \omega
|
23,490 |
a\cdot z = b \implies z = b/a
|
-22,073 |
\frac{4}{24} = \frac{1}{6}
|
14,183 |
3 = \tfrac{1}{-1/3 + 1} \times 2
|
43,512 |
\frac{1}{3}*6 = 2
|
3,965 |
\frac{x}{x + 30}\cdot 0.4 = \tfrac{3}{10} \implies 90 = x
|
26,467 |
10 10 + 23 \left(-1\right) = 77
|
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