id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-7,047 |
1/20 = \dfrac{1}{6}\cdot 3\cdot \frac25/4
|
22,126 |
1 + \frac{1}{1 + m} = \dfrac{m + 2}{m + 1}
|
6,465 |
\frac{1}{99\cdot 999}\cdot (71700 + 71000\cdot (-1) - 717 + 71\cdot (-1)) = \tfrac{1}{99\cdot 999}\cdot (700 + 717\cdot (-1) + 71) \gt 0
|
-11,777 |
\left(3/2\right)^4 = \dfrac{1}{16} \cdot 81
|
-919 |
0 + 4/10 + \frac{4}{100} + 1/1000 + 4/10000 = 4414/10000
|
21,944 |
((-1) + 2^{33}) \cdot (1 + 2^{33}) = 2^{66} + (-1)
|
1,685 |
\cos(\frac{5*\pi}{4}*1) = \cos(\pi*3/4)
|
14,975 |
g\cdot g + a\cdot a + g\cdot 2\cdot a = \left(a + g\right)\cdot \left(a + g\right)
|
40,977 |
\sin\left(\frac{\pi}{6}\right) = \frac{1}{2}
|
-9,188 |
-24 k + 20 = 2 \cdot 2 \cdot 5 - k \cdot 2 \cdot 2 \cdot 2 \cdot 3
|
20,388 |
2\times \cos{\alpha}\times \sin{\alpha} = \sin{2\times \alpha}
|
609 |
m - m^2 = m \implies m = 0
|
-10,605 |
\tfrac{16}{12 + 16\cdot r} = \frac{4}{4}\cdot \frac{4}{3 + r\cdot 4}
|
-2,146 |
4/3 \pi - \frac{7}{4} \pi = -\pi \frac{1}{12} 5
|
28,041 |
\tan^{-1}{-\dfrac{1}{\sqrt{3}}} = -\frac{\pi}{6}
|
-27,491 |
2 \cdot b \cdot b \cdot 2 \cdot 2 = b^2 \cdot 8
|
-23,424 |
1 - 2/7 = \frac57
|
-18,249 |
\dfrac{q \cdot \left(1 + q\right)}{\left(1 + q\right) \cdot (q + 1)} = \frac{q + q^2}{q^2 + q \cdot 2 + 1}
|
-10,296 |
\dfrac{4}{4} \cdot \dfrac{8}{10 \cdot (-1) + l \cdot 5} = \frac{32}{40 \cdot (-1) + l \cdot 20}
|
-29,374 |
-g^2 + h^2 = (h + g)\cdot \left(h - g\right)
|
26,154 |
x^{2 \cdot k} \cdot (2 \cdot k + 1) = \frac{\partial}{\partial x} x^{k \cdot 2 + 1}
|
-5,737 |
\frac{4}{3y + 9(-1)} = \frac{1}{3(3(-1) + y)}4
|
2,200 |
(\sqrt{2} + \sqrt{3})\times \sqrt{6}\times 2 = (2\times \sqrt{3} + \sqrt{2}\times 3)\times 2
|
-20,931 |
\frac{7*k + 7*(-1)}{28*\left(-1\right) + k*7} = 7/7*\frac{1}{4*(-1) + k}*\left(k + (-1)\right)
|
49,492 |
4 \Rightarrow 5
|
-10,144 |
-0.49 = -5/10 = -\dfrac{1}{100}49
|
5,724 |
3q^2 = 9t^2 rightarrow 3t^2 = q^2
|
25,906 |
x \geq 3 \times x + 2 \times (-1) \implies 1 \geq x
|
5,972 |
10!/12! = \frac{1}{12\cdot 11\cdot 10!}\cdot 10! = \frac{1}{132}
|
21,977 |
g_2*(b + g_1) = g_2*b + g_2*g_1
|
26,768 |
1 = \left(-2\right)*0 + 4*\frac{1}{2*2}
|
13,857 |
1 + m \cdot m - 2 \cdot m = (m + (-1))^2
|
10,404 |
(\frac{1}{2} \cdot (1 + 5^{\frac{1}{2}}))^2 = \frac12 \cdot (3 + 5^{1 / 2})
|
20,015 |
(d,\infty) = (d, \infty)
|
1,660 |
e^z = \frac12 \times \frac{\mathrm{d}}{\mathrm{d}z} (e^z)^2
|
16,083 |
\frac1l + 1 = \frac{1}{l} \cdot \left(l + 1\right)
|
-6,998 |
2/7 = 3/6\cdot \dfrac47
|
21,099 |
(2\cdot A)^2 = 2^2\cdot A \cdot A = 4\cdot A^2
|
32,376 |
\binom{7}{3}*\binom{4}{2}*2! = 7!/(3!*4!)*4!/(2!*2!)*2! = 7!/\left(3!*2!\right)
|
22,825 |
a\cdot \left(1 + a\right) = 9 \Rightarrow a^2 + a = 9
|
-11,642 |
-6 + 2 \cdot i = 2 \cdot i + 0 + 6 \cdot (-1)
|
-13,049 |
9 \left(-1\right) + 25 = 16
|
14,066 |
\frac{1}{1 - x} \cdot (-x \cdot x \cdot x + 1) = x^2 + 1 + x
|
24,614 |
\{D,G\} \Rightarrow D \cap G = D
|
21,600 |
(a + b) \cdot (a + b)^{s + (-1)} = (a + b)^s
|
28,951 |
2 = x \implies x \in ]2,3]
|
27,450 |
\left(-y + 2 = y n \Rightarrow 2 = (n + 1) y\right) \Rightarrow y = \frac{2}{n + 1}
|
19,454 |
x^n = (0 (-1) + x)^n
|
303 |
\frac{x^2 + 1}{x^2 + 3} = \frac{x^2 + 3 + 2(-1)}{x^2 + 3} = 1 - \frac{1}{x^2 + 3}2
|
-20,019 |
\frac{80\cdot (-1) + 8\cdot p}{56\cdot p + 72} = \tfrac{p + 10\cdot (-1)}{7\cdot p + 9}\cdot 8/8
|
16,837 |
b \times v + d \times v = (d + b) \times v
|
-9,561 |
75\% = 75/100 = \frac14 \cdot 3
|
13,064 |
\frac{\partial}{\partial x} (e\cdot x) = x\cdot \frac{\mathrm{d}e}{\mathrm{d}x} + e\cdot \frac{\mathrm{d}x}{\mathrm{d}x}
|
157 |
\mathbb{Var}[x_C - x_Z] = \mathbb{Var}[x_C] + \mathbb{Var}[-x_Z] = \mathbb{Var}[x_C] + \mathbb{Var}[x_Z]
|
6,670 |
\frac{x + (-1)}{x + 3 \cdot \left(-1\right)} = 1 + \frac{1}{x + 3 \cdot (-1)} \cdot 2
|
6,302 |
3*n + \left(-1\right) = 0 \implies n = 1/3
|
9,475 |
\frac{1}{\frac{a}{x} - \frac{b}{x}} = \frac{x}{a - b}
|
5,463 |
\frac{1}{d*\chi} = \frac{1}{d*\chi}
|
-1,417 |
(\frac{1}{2} (-1))/(1/3 \left(-1\right)) = -\frac12 (-\frac31)
|
22,389 |
2*\delta*x + \delta^2 = (\delta + x)^2 - x * x
|
-9,632 |
0.01 \cdot (-10) = -10/100 = -\dfrac{1}{10}
|
-29,572 |
-\tfrac{10}{z} + 3*z^2/z = (10*\left(-1\right) + z^2*3)/z
|
-11,526 |
-2 + i = i + 0 + 2\cdot (-1)
|
-23,023 |
48/120 = \frac{24*2}{5*24}
|
1,105 |
37 = 5*5 + 3*4
|
4,816 |
2*-I*(-h) = 2*I*h
|
19,888 |
\dfrac{4}{32} = 1/8
|
12,251 |
3 + q \neq 0 \Rightarrow q \neq -3
|
-7,882 |
(72 + 52\cdot i - 18\cdot i + 13)/17 = \dfrac{1}{17}\cdot (85 + 34\cdot i) = 5 + 2\cdot i
|
25,787 |
(-d + c) \cdot (c^2 + d \cdot c + d \cdot d) = c^3 - d^3
|
-29,581 |
\frac{\text{d}}{\text{d}x} (-x\cdot 10 + x^4 - x^2\cdot 4) = 10\cdot (-1) + 4\cdot x^3 - 8\cdot x
|
-7,912 |
\tfrac{1}{13}\cdot (14 + 34\cdot i - 21\cdot i + 51) = \tfrac{1}{13}\cdot (65 + 13\cdot i) = 5 + i
|
-14,535 |
\frac{10}{4 + 2*(-1)} = 10/2 = \dfrac{10}{2} = 5
|
-24,558 |
\frac{1}{2 + 6}\cdot 32 = 32/8 = \frac{32}{8} = 4
|
4,344 |
x + z = 0 \implies z = -x
|
29,046 |
\frac{0.3}{0.3\times 0.6}\times 0.3\times 0.6 = 0.3
|
32,665 |
-{2 + k \choose 3} + {k + 3 \choose 3} = {2 + k \choose 2}
|
36,774 |
310 = 31/2 \cdot (2 \cdot a_1 + 30 \cdot d) = 31 \cdot \left(a_1 + 15 \cdot d\right)
|
15,421 |
m + 1 = m + \left(-1\right) + 2 = ... = \frac{m}{2} + 1 + m/2
|
-20,220 |
\frac55*\frac{1}{-6*x + 9}*(x*(-5)) = \frac{x*(-25)}{45 - 30*x}
|
24,806 |
(5 - 1.8) x + (9 - 3.7) x + (9 - 3.7) x = 3.2 x + 5.3 x + 5.3 x = 13.8 x
|
-2,949 |
4 \cdot \sqrt{11} = \sqrt{11} \cdot \left(3 + (-1) + 2\right)
|
216 |
d \cdot d = 1 \neq d
|
-19,405 |
3/4*5/2 = 3*5/(4*2) = \dfrac{15}{8}
|
-6,590 |
\tfrac{1}{\left(a + 4(-1)\right) (5\left(-1\right) + a)}2a = \frac{2a}{20 + a^2 - a*9}
|
-5,413 |
1.4 \times 10^0 = 10^{-2 - -2} \times 1.4
|
-4,353 |
\frac{r^4\cdot 60}{r^2\cdot 42}\cdot 1 = \frac{r^4}{r^2}\cdot \dfrac{60}{42}
|
31,193 |
(c + h) \cdot (-c + h) = h^2 - c^2
|
-12,016 |
\frac{1}{3} = \frac{p}{4 \cdot \pi} \cdot 4 \cdot \pi = p
|
9,566 |
\tfrac{2\cdot x}{\sqrt{x^2 + 1} + x + \left(-1\right)} = \dfrac{1}{\sqrt{1 + x^2} + x + \left(-1\right)}\cdot ((-1) + x \cdot x + 1 - x^2 + x\cdot 2)
|
34,378 |
((-1) + n) (\left(n + \left(-1\right)\right)! + \left(n + 2(-1)\right)!) = n!
|
4,805 |
1^2 + 1^2 + 2^2 + 3^2 + 3 \cdot 3 = 24
|
30,004 |
\cos{y \cdot y} = \cos{y^2}
|
-21,609 |
\sin\left(-\pi\cdot 5/6\right) = -0.5
|
-6,015 |
\dfrac{2}{3*s + 30} = \frac{2}{3*\left(10 + s\right)}
|
-22,884 |
104 = 2 \cdot 2 \cdot 2 \cdot 13
|
6,681 |
\cos(i\times z) = (e^{-z} + e^z)/2 = \cosh(z)
|
43,387 |
(1 + 2)\cdot (1 + 2) = 9
|
20,127 |
11 \times (-1) - 2 \times 5 \times (-1) = -1
|
1,780 |
2xb + z\cdot 2 = 4 \Rightarrow z = -bx + 2
|
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