id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
22,520 |
2 \times \sqrt{7} \times 4 = \sqrt{7} \times 2 \times 4
|
19,376 |
\dfrac{1}{\left(m + \left(-1\right)\right) m!} = \frac{1}{\left((-1) + m\right)! m*(m + (-1))}
|
28,897 |
\dfrac{36}{44} = 9/11
|
12,489 |
\pi/12 + x\pi/6 = \dfrac{\pi}{12}*(1 + 2x)
|
4,344 |
y + z = 0 \Rightarrow -y = z
|
-3,171 |
\sqrt{4 \cdot 6} + \sqrt{6} = \sqrt{6} + \sqrt{24}
|
21,272 |
\left(f + b\right) \cdot \left(f + b\right) = f^2 + 2\cdot b\cdot f + b \cdot b
|
21,415 |
11 = 2 * 2*2 + 3
|
22,586 |
f_2\times h\times f_1 = \frac{f_2}{h}\times f_1 = f_2\times \frac1h/\left(f_1\right) = \dfrac{f_2}{h\times f_1}
|
-5,570 |
\frac{1}{8\times (-1) + m^2 - m\times 2}\times 23 = \dfrac{(-1) + 4\times m + 8 - m\times 4 + 16}{m^2 - m\times 2 + 8\times (-1)}
|
-23,618 |
0.25 ^ 7 = (1 - 0.75)^7
|
13,400 |
3/6*\frac47 = \frac{2}{7}
|
41,345 |
\frac{1}{12} + \dfrac16 = \frac14
|
-10,544 |
-\frac{8}{3 \cdot q + 5} \cdot \dfrac{1}{12} \cdot 12 = -\frac{96}{60 + 36 \cdot q}
|
22,365 |
\frac{1}{3} + \dfrac{1}{2} = 5/6
|
-22,319 |
12 + m^2 - 8 \cdot m = (6 \cdot (-1) + m) \cdot (2 \cdot \left(-1\right) + m)
|
11,458 |
\dfrac{7 \cdot 6}{10 \cdot 9} = \frac{42}{90} = 7/15
|
26,806 |
(-4)^n/(-4) = (-4)^{n + (-1)} = (-1)^{n + (-1)}*4^{n + (-1)}
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-10,711 |
-\frac{3}{3 + z\cdot 5}\cdot 6/6 = -\dfrac{1}{30\cdot z + 18}\cdot 18
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11,106 |
{10 \choose 2}\times {26 \choose 3}\times 5! = 14040000
|
14,097 |
x_1 \overline{r_1} + ... + \overline{r_n} x_n = r_1 x_1 + ... + x_n r_n
|
33,303 |
\tfrac{1}{ba} = 1/(ab)
|
19,809 |
\frac{1}{x} + 1/x - \tfrac{1}{x \cdot x} = 2/x - \frac{1}{x^2} \lt 2/x
|
-6,697 |
5/100 + 7/10 = 70/100 + \frac{1}{100} 5
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-19,472 |
\frac{7 \cdot 1/4}{5 \cdot 1/2} = \frac{7}{4} \cdot \frac15 2
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23,697 |
\frac{10*85}{100} = 8.5
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-9,472 |
-m \cdot 2 \cdot 3 \cdot 3 \cdot 3 + 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 = -54 \cdot m + 48
|
12,337 |
\frac{1}{f\cdot h} = \dfrac{1}{h\cdot f} \neq 1/(f\cdot h)
|
32,736 |
a^l a^n = a^{l + n}
|
15,663 |
\sin{z} \cdot \cos{z} = \sin{z} \cdot \sin(\frac{1}{2} \cdot \pi - z)
|
15,271 |
1 + 4*e + 9*e^2 + \ldots + l^2*e^{l + (-1)} = e*l^2 - 2*e^2*l
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-15,892 |
-\frac{1}{10}\cdot 55 = 5\cdot \dfrac{3}{10} - 10\cdot 7/10
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-9,950 |
0.01 (-25) = -25/100 = -0.25
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15,959 |
47^2*7^2*3^2*5 = 2207^2 + 4*(-1)
|
12,119 |
\frac{1}{(1 - 1/2)^2\cdot 2} = 2
|
31,786 |
6 + (t + 3\cdot (-1))/2 + \dfrac{1}{2}\cdot ((-1) + t) = 4 + t
|
-30,381 |
\frac{1}{10000}\cdot 2.077 = 2.077\cdot 0.0001
|
-2,628 |
63^{1 / 2} - 7^{\frac{1}{2}} = -7^{\dfrac{1}{2}} + (9 \cdot 7)^{\frac{1}{2}}
|
-11,086 |
(y + 7\cdot \left(-1\right))^2 + f = (y + 7\cdot (-1))\cdot \left(y + 7\cdot (-1)\right) + f = y^2 - 14\cdot y + 49 + f
|
-4,597 |
6\cdot (-1) + z^2 - z = \left(3\cdot (-1) + z\right)\cdot (z + 2)
|
-7,872 |
\frac{1}{-i - 4}\cdot (-18 - i\cdot 13)\cdot \frac{-4 + i}{-4 + i} = \frac{1}{-i - 4}\cdot (-18 - 13\cdot i)
|
-1,077 |
\frac{2 \cdot 1/7}{8 \cdot \frac15} = \frac27 \cdot \frac58
|
10,014 |
12*(x_1 - x_2) = 8*(z_1 - z_2) \implies 2*(z_1 - z_2) = 3*(x_1 - x_2)
|
-26,498 |
180\cdot x = 9\cdot x\cdot 10\cdot 2
|
-4,715 |
\dfrac{1}{z + 5} \cdot 5 + \frac{2}{z + 1} = \tfrac{1}{5 + z^2 + z \cdot 6} \cdot (7 \cdot z + 15)
|
12,900 |
(\cos\left(Z - B\right) - \cos(B + Z))/2 = \sin{Z} \cdot \sin{B}
|
-2,434 |
4\cdot \sqrt{2} = (3\cdot (-1) + 2 + 5)\cdot \sqrt{2}
|
16,020 |
2 (\cos{x} + (-1)) = 2*(1 - 2 \sin^2{\frac12 x} + (-1)) = 2 (-2 \sin^2{\frac12 x})
|
16,438 |
1/x + 1/2 = 1/x + 1/2
|
1,089 |
4/3 \cdot \pi - 2 \cdot \pi = -\pi \cdot 2/3
|
-26,574 |
162 \cdot (-1) + 2 \cdot z^2 = (81 \cdot (-1) + z^2) \cdot 2
|
3,000 |
\cos\left(Y + G\right) = -\sin{G} \cdot \sin{Y} + \cos{G} \cdot \cos{Y}
|
-6,827 |
8 \times 4 \times 10 = 320
|
-23,000 |
26/39 = \frac{26}{3 \cdot 13} \cdot 1
|
9,500 |
9/36 = \dfrac{1}{6}\cdot 3/6 + 1/6
|
-20,270 |
\frac{(-81) k}{9 + 45 k} = \frac{1}{k*5 + 1}(k*\left(-9\right)) \frac{9}{9}
|
8,927 |
n = 4*k + 2 rightarrow 3*n + 2 = 12*k + 8 = 4*\left(3*k + 2\right)
|
-22,071 |
\dfrac{7}{10} = 14/20
|
18,392 |
(3\cdot n - 5\cdot z)\cdot (z\cdot 7 + 2\cdot n) = 6\cdot n^2 + z\cdot n\cdot 11 - 35\cdot z \cdot z
|
20,337 |
\left(a + a\right)*0 = a*0
|
1,610 |
z \cdot (-d z + c) = c z - d z^2
|
2,541 |
\frac{x + 1}{x + (-1)} = \frac{1}{x + (-1)} \cdot (x + (-1) + 2) = 1 + \dfrac{2}{x + (-1)}
|
5,854 |
\cos(\tfrac{\pi}{3}) = \frac12
|
37 |
4 g h + (h - g)^2 = (h + g)^2
|
3,889 |
\frac{1}{1 + 2p}(4^p + (-1)) = \dfrac{(1 + 2^p) (2^p + (-1))}{2p + 1}
|
-11,604 |
17 - 7i = 15 + 2 - i*7
|
-3,355 |
\sqrt{13}\times \sqrt{25} + \sqrt{13} = \sqrt{13} + \sqrt{13}\times 5
|
25,007 |
vA = Av
|
-4,782 |
\dfrac{12 - 3 \cdot y}{y^2 - 7 \cdot y + 10} = -\tfrac{2}{y + 2 \cdot (-1)} - \dfrac{1}{y + 5 \cdot (-1)}
|
21,099 |
\left(2\cdot B\right)^2 = 2^2\cdot B \cdot B = 4\cdot B^2
|
10,322 |
-h = h + g\cdot g = h\cdot g
|
5,687 |
-x*4 = -Y * Y*3 + Y^3 \Rightarrow Y^3 - 3*Y^2 + Y*4 - 5*x = 4*Y - x*9
|
4,745 |
z^{1/3} = p + i\cdot q\Longrightarrow z = (q\cdot i + p) \cdot (q\cdot i + p) \cdot (q\cdot i + p)
|
-6,593 |
\frac{1}{3\cdot p + 21\cdot (-1)} = \frac{1}{3\cdot (p + 7\cdot (-1))}
|
35,507 |
\frac{4}{\sqrt{3}} = 4*\sqrt{3}/3 \approx 6.928/3
|
7,552 |
\frac{b}{c} \Rightarrow b/c
|
25,160 |
1 - \cos{t} = 2*\sin^2{t/2} \leq \dfrac{1}{2}*t * t
|
8,644 |
2\sin\left(π\right) \cos(0) = 0
|
-18,981 |
\frac{1}{40}\cdot 37 = D_t/(64\cdot \pi)\cdot 64\cdot \pi = D_t
|
45,987 |
1 = (\left(-1\right)^2)^{\frac13}
|
-3,657 |
\frac{j^4}{j^3} = \frac{j^4}{j\cdot j\cdot j}\cdot 1 = j
|
7,361 |
2\cdot z + 2\cdot x = x + x + z + z
|
-20,916 |
\frac22 \cdot (-\dfrac{1}{5 \cdot x + 5 \cdot (-1)} \cdot 4) = -\frac{8}{10 \cdot x + 10 \cdot \left(-1\right)}
|
-596 |
\tfrac{2}{3}*\pi = 92/3*\pi - \pi*30
|
3,743 |
\frac{3}{1} \times \frac{1}{4} = \frac{3}{4}
|
-10,359 |
\frac{1}{3 \cdot y + 6} \cdot (6 \cdot (-1) + 3 \cdot y) \cdot \frac55 = \frac{1}{30 + 15 \cdot y} \cdot (15 \cdot y + 30 \cdot (-1))
|
-3,076 |
(4 + 2 \cdot (-1)) \cdot 2^{\frac{1}{2}} = 2 \cdot 2^{1 / 2}
|
11,302 |
2 \cdot \cos{n} \cdot \sin{n} = \sin{n \cdot 2}
|
5,724 |
p^2 \cdot 3 = s^2 \cdot 9 \Rightarrow s \cdot s \cdot 3 = p^2
|
16,685 |
\frac12*\left(\sqrt{5} + 3\right) = ((\sqrt{5} + 1)/2)^2
|
-7,279 |
\dfrac{3}{7} \cdot \frac34 = 9/28
|
31,733 |
\cos(2 \cdot z) = \cos^2(z) - \sin^2(z) = 1 - 2 \cdot \sin^2(z)
|
-20,772 |
\dfrac{1}{3 \times \left(-1\right) + x} \times (x + 3 \times (-1)) \times (-8/5) = \frac{1}{15 \times (-1) + x \times 5} \times (24 - x \times 8)
|
21,051 |
\frac{dp}{dq} = \tfrac{4 \cdot p^2}{4 \cdot p \cdot q} = \frac1q \cdot p
|
24,675 |
(-z^2\cdot 2) \cdot (-z^2\cdot 2) \cdot (-z^2\cdot 2) + (z \cdot z \cdot z\cdot 3) \cdot (z \cdot z \cdot z\cdot 3) = z^6
|
13,595 |
-\sin{d}\cdot \cos{g} + \sin{g}\cdot \cos{d} = \sin(g - d)
|
-10,783 |
50 = -75 q + 75 + 12 (-1) = -75 q + 63
|
20,039 |
(Z_2 + Z_1) \cdot (Z_2 - Z_1) = -Z_1^2 + Z_2^2
|
-19,068 |
7/20 = \frac{A_r}{16 \cdot \pi} \cdot 16 \cdot \pi = A_r
|
-20,841 |
-\frac{1}{9 + z} \cdot 4/4 = -\frac{1}{4 \cdot z + 36} \cdot 4
|
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