id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
1,694
|
16^0 \cdot 15 + 16^1 = 31
|
-17,081
|
-1 = -(-1)\cdot t - 6 = t - 6 = t + 6\cdot \left(-1\right)
|
4,712
|
(y + \dfrac{1}{2!}\cdot y^2 + \dfrac{y^3}{3!} + \cdots)^{-1} = \frac{1}{e^y + (-1)}
|
13,670
|
|-1/z + 1/x| = |\frac{1}{xz}(x - z)|
|
10,942
|
\dfrac{cN}{c} = \frac{1}{c}N c
|
-19,063
|
\frac{1}{45}\cdot 31 = A_q/(81\cdot \pi)\cdot 81\cdot \pi = A_q
|
11,188
|
y = \tan^{-1}(z) \Rightarrow \tan(y) = z
|
27,511
|
\sqrt{7 + \sqrt{48}} = \sqrt{\frac12\cdot 8} + \sqrt{6/2}
|
-19,822
|
1.625 = \dfrac{65}{40}
|
33,049
|
88 = 4\cdot (-1) + 2\cdot 27 + 2\cdot 19
|
17,706
|
\frac{1}{z + 0 \cdot (-1)} \cdot (\sin{1/z} \cdot z + 0 \cdot (-1)) = \sin{1/z}
|
3,929
|
x \times 2 \times 3 + 2 = 2 + 6 \times x
|
-1,200
|
\frac{1}{(-1) \times 4 \times 1/7} \times (1/5 \times (-6)) = -\frac{7}{4} \times (-6/5)
|
24,509
|
\tfrac{103}{165} = 1/3 + 1/5 + 1/11
|
-1,717
|
\dfrac{π}{6} - \frac{1}{12}π = π/12
|
3,463
|
(3 + 2*z)/6 = \frac{1}{3}*z + \frac{1}{2}
|
-2,051
|
\pi \cdot 5/6 + \pi \cdot \tfrac{1}{12} \cdot 5 = 5/4 \cdot \pi
|
-536
|
\frac{1}{2}*3*π = \frac{35}{2}*π - 16*π
|
21,404
|
\frac{n\cdot \left(m + (-1)\right)}{n\cdot m + \left(-1\right)} = \frac{1}{(-1) + m\cdot n}\cdot \left(n\cdot m + \left(-1\right) - n + (-1)\right)
|
24,946
|
\dfrac23 \cdot \pi + 0 \cdot (-1) = \frac13 \cdot 2 \cdot \pi
|
4,091
|
\frac{1}{C^4} = (\frac{1}{C})^4
|
-10,392
|
-\frac{180}{y\cdot 20 + 100} = 20/20\cdot (-\tfrac{9}{y + 5})
|
-9,711
|
80\% = 80/100 = \frac{4}{5}
|
-4,998
|
39.5 \cdot 10^2 = 10^{5 - 3} \cdot 39.5
|
17,981
|
\frac{31031}{46656} = -\left(5/6\right)^6 + 1
|
8,089
|
e^1 = (1 + 1/n)^n exp(0) = (1 + 1/n)^n
|
19,985
|
\frac1x = \frac{1}{x \cdot (0 + 1)}
|
12,747
|
6 < X + 3 \cdot (-1) rightarrow X \gt 9
|
17,941
|
5^z = y \implies 5^{2 z} = (5^z)^2 = y^2
|
-18,674
|
0.8931 = 0.9332 - 0.0401
|
6,513
|
(x + 1) * (x + 1) = (x + 1)*(x + 1) = x^2 + 2*x + 1
|
16,467
|
(-1) + \frac{1}{2} = -\frac12
|
9,229
|
\frac{1}{\left(1 - x\right) \cdot \left(1 - x\right)} \cdot \left(1 + x + x^2\right) = \frac{1}{(1 - x)^3} \cdot (x^2 + 1 + x) \cdot \left(-x + 1\right)
|
4,542
|
\frac{y}{x} = \frac{y + 0*(-1)}{x + 0*(-1)}
|
14,356
|
\sin{2\cdot x} = 2\cdot \sin{x}\cdot \cos{x} = 2\cdot \sqrt{1 - \cos^2{x}}\cdot \cos{x}
|
27,236
|
\frac{3\pi}4 - \frac{\pi}4 = \frac{2\pi}4
|
600
|
z \cdot t \cdot s = t \cdot z \cdot s
|
-3,819
|
c^5/c = cc c c c/c = c^4
|
-25,530
|
\frac{d}{dt} (3t^2 + t) = 2\cdot 3t + 1 = 6t + 1
|
2,465
|
1 + x*\ln(a) + \ln(a)^2*x^2/2 + x^3*\ln(a)^3*\ldots/6 = a^x
|
9,537
|
\sin(-b + a) = \sin{a} \cos{b} - \sin{b} \cos{a}
|
-5,560
|
\frac{(8*(-1) + n)*3}{(n + 9)*(n + 8*(-1))*6} - \dfrac{(n + 9)*10}{6*(n + 9)*(8*(-1) + n)} - \frac{12}{6*(n + 8*\left(-1\right))*(9 + n)} = \dfrac{1}{6*(n + 8*\left(-1\right))*\left(n + 9\right)}*(12*\left(-1\right) + \left(n + 8*\left(-1\right)\right)*3 - 10*\left(9 + n\right))
|
40,945
|
{4 \choose 2} \cdot {9 \choose 1} = 54
|
8,087
|
-s = -q*p\Longrightarrow s = p*q
|
-4,396
|
\frac47 \cdot q \cdot q \cdot q = q^3 \cdot \frac47
|
34,550
|
\sec(\operatorname{atan}\left(z\right)) = \left(z^2 + 1\right)^{1/2}
|
37,525
|
1 = 1*...
|
-24,656
|
\dfrac{5}{6\cdot 5}\cdot 1 = 5/30
|
53,076
|
-\int_{-\pi/2}^{\pi/2}\frac{d\theta}{a-\sin\theta}=-\int_{0}^{\pi/2}\frac{2a\,d\theta}{a^2-\sin^2\theta}=-\int_{0}^{\pi/2}\frac{2a\,d\theta}{a^2-\cos^2\theta}
|
-1,445
|
\frac{5 / 2}{\frac17 \cdot 6} \cdot 1 = \frac16 \cdot 7 \cdot 5/2
|
1,140
|
(l + 1)^2 = (l + (-1))^2 + 4\cdot l
|
7,984
|
0 = \frac{1}{2} + \tfrac{1}{2} \cdot (-1)
|
13,267
|
(a+0)^2 = a^2 = a^2 + 2(0) + 0^2
|
260
|
\sin{Z} = \sin(\pi - Z)
|
17,980
|
\cos(-x + 2\cdot \pi) = \cos{x}
|
29,685
|
1 = \left(1 + 0\right)^{\tfrac12}
|
-10,216
|
0.01 (-92) = -92/100 = -\tfrac{23}{25}
|
-12,744
|
11 = 6 \cdot (-1) + 17
|
-20,601
|
-7/5 \frac{6s + \left(-1\right)}{(-1) + s*6} = \frac{-s*42 + 7}{30 s + 5\left(-1\right)}
|
15,020
|
4^{\frac{1}{3}}\cdot 6 = 3\cdot 32^{\frac{1}{3}}
|
-9,454
|
-7*5 - 3*5 n = 35 \left(-1\right) - 15 n
|
-3,397
|
-\sqrt{13} + \sqrt{9 \cdot 13} = -\sqrt{13} + \sqrt{117}
|
24,251
|
3*(2^1 + 1) = 9
|
24,425
|
2\cdot (1 + x)\cdot \left(x + (-1)\right) = x^2\cdot 2 + 2\cdot (-1)
|
18,290
|
\left(7500 - 60 \cdot 20 - 80 \cdot 60\right)/30 = \frac{1}{30} \cdot 1500 = 50
|
-3,347
|
3 \times \sqrt{6} + \sqrt{6} \times 5 = \sqrt{25} \times \sqrt{6} + \sqrt{6} \times \sqrt{9}
|
-13,465
|
-\frac{4}{7 + 9(-1)} = -4/(-2) = -\frac{4}{-2} = 2
|
-6,698
|
\frac{70}{100} + 8/100 = \dfrac{1}{10} \cdot 7 + \frac{8}{100}
|
38,091
|
x^{135} = (x^2 \cdot x)^{45}
|
29,591
|
4\cdot \binom{3}{2} = 12
|
16,012
|
(\frac{2}{\dfrac{1}{13} \cdot 5 + 1})^{\tfrac{1}{2}} = 13^{1 / 2}/3
|
11,100
|
\left(0 \leq z\Longrightarrow r = |r|\right)\Longrightarrow \int\limits_0^z r\,dr = z\times z/2
|
-626
|
-π \cdot 4 + 65/12 \cdot π = \frac{17}{12} \cdot π
|
-2,926
|
\left(2*\left(-1\right) + 3\right)*\sqrt{6} = \sqrt{6}
|
22,895
|
63\% \cdot y = 90\% \cdot 70\% \cdot y
|
4,789
|
\lim_{n \to \infty} z^{\lim_{n \to \infty} y} = \lim_{n \to \infty} z^y
|
-10,663
|
12/12 \cdot \frac{1}{g \cdot g}2 = \frac{24}{12 g \cdot g}
|
-4,807
|
10^5*28.5 = 28.5*10^{1 + 4}
|
23,124
|
C + \frac14\cdot x^3 + \frac{x}{4}\cdot x^2 = \frac{x^3}{2} + C
|
3,438
|
p^u = p^w \Rightarrow p^{u - w} = 1
|
-22,730
|
\dfrac{40}{90} = \dfrac{10}{9\cdot 10}\cdot 4
|
42,672
|
( 1, 0) \left( 0, 1\right) = ( 2, 0) ( 0, 1) = 0
|
26,543
|
a^n \cdot x = a \cdot \dots \cdot a \cdot a \cdot x = a \cdot \dots \cdot a \cdot x \cdot a = a \cdot \dots \cdot x \cdot a \cdot a = \dots = x \cdot a^n
|
24,578
|
\frac{1}{x} = \tfrac{1}{x^{1/2} x^{\frac{1}{2}}}
|
-3,423
|
6\sqrt{10} = (5 + 2 + (-1)) \sqrt{10}
|
31,840
|
1/(l\cdot k)\cdot k\cdot l = \frac{l}{k}\cdot k\cdot \frac{1}{l}
|
-580
|
\pi \cdot 80/3 - 26 \cdot \pi = \tfrac{1}{3} \cdot 2 \cdot \pi
|
-12,681
|
82 + 37 (-1) = 45
|
-12,367
|
80^{1/2} = 5^{1/2} \cdot 4
|
-9,237
|
-72 \cdot p + 24 = -2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot p + 2 \cdot 2 \cdot 2 \cdot 3
|
34,798
|
{1 + b \choose c + 1} = {b \choose c} + {b \choose 1 + c}
|
30,723
|
\left(2 - z = 1.75 - 0.5\cdot z \Rightarrow 0.5\cdot z = 0.25\right) \Rightarrow z = 0.5
|
18,467
|
\dfrac{2}{3}*\left(1 - 6*d^2\right) = 0 \Rightarrow 1/(\sqrt{6}) = d
|
29,766
|
\frac{\partial}{\partial f} (u_1 \cdot u_2) = \frac{\partial}{\partial f} (u_1 \cdot u_2)
|
-20,404
|
\frac18\times 1 = \frac{9\times \left(-1\right) - 9\times z}{-z\times 72 + 72\times (-1)}
|
1,518
|
1 + h^3 = (1 + h)\cdot (1 - h + h^2) = (1 + h)\cdot 3^{1/2}\cdot h
|
10,145
|
\frac{1}{1 + (1 + \frac{1 - m}{m \cdot 2}) \cdot 2} = \frac{m}{2 \cdot m + 1}
|
32,789
|
n \cdot v + v = (1 + n) \cdot v
|
10,287
|
x/x = 1 \Rightarrow x = 1/(\frac1x)
|
7,151
|
(1 + A + ... + A^5)^8 = (\frac{1}{1 - A}*(1 - A^6))^8 = \frac{(1 - A^6)^8}{\left(1 - A\right)^8}
|
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