id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
23,284 |
\frac{a}{b} + c/d = (a\cdot d + b\cdot c)/(b\cdot d) \neq a\cdot d + b\cdot c
|
-9,774 |
-61/100 = 0.01 \cdot (-61)
|
-4,273 |
\tfrac{z}{4} = \frac{z}{4}
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33,093 |
\frac{1}{X\cdot A} = 1/(X\cdot A)
|
25,790 |
0 = 6 + 1^3 - 1^2*2 - 5
|
27,442 |
x+y + xy=10x + y\implies 9x=xy
|
24,941 |
\sin{\dfrac{19}{12}\cdot π} = ((1 + \sqrt{3})\cdot \left(-1\right))/\left(\sqrt{2}\cdot 2\right)
|
31,926 |
107 = 256 + 149 \left(-1\right)
|
28,371 |
\frac{1}{36*\left(\dfrac{1}{36} + \dfrac{895}{7776}\right)} = 216/1111 \approx 0.1944
|
7,799 |
\varnothing = [1, 2] = 2\cdot \left( 1, 1\right)
|
32,796 |
1 - \dfrac{1}{8} = \frac187
|
-15,252 |
\tfrac{(p^4)^4}{\frac{1}{x^5\cdot p^5}} = \frac{p^{16}}{\frac{1}{p^5}\cdot \dfrac{1}{x^5}}
|
21,681 |
E\left[\frac{R_1^2}{R_2^2 + R_1^2}\right] = \dfrac{1}{E\left[R_1^2\right] + E\left[R_2^2\right]}*E\left[R_1^2\right]
|
-4,949 |
0.3 \cdot 10^{4 + 2(-1)} = 0.3 \cdot 10^2
|
20,264 |
\frac92 \cdot 1 = 4.5
|
4,515 |
j + j = 2\cdot j
|
376 |
\dfrac{A}{G} = \tfrac1G \cdot A
|
10,643 |
|b_m\cdot a_m - L\cdot M| = |a_m\cdot b_m - a_m\cdot M + a_m\cdot M - L\cdot M|
|
19,226 |
27 + m^3 = 3^3 + m^3 = \left(m + 3\right) \cdot (m^2 - 3 \cdot m + 9)
|
-23,408 |
\frac15 \times 3 = 4/5 \times \tfrac{1}{4} \times 3
|
39,980 |
\frac{1 + x^2 + y^2}{2} + \alpha x - \beta y = \frac{1}{2} + \frac{x^2 + 2\alpha x + y^2 - 2\beta y}{2}
|
20,421 |
z^3 - y^3 = (z - y) \cdot (y^2 + z^2 + y \cdot z)
|
-13,255 |
\frac{72}{6 + 2} = \frac{72}{8} = \frac18\cdot 72 = 9
|
17,606 |
\frac{u^3 - x^3}{u^2 + x\cdot u + x^2} = u - x
|
26,413 |
153 = \tfrac{17*18}{2}
|
21,664 |
i^2 = ( 0, 1) \cdot \left( 0, 1\right) = [-1, 0] = \overline{-1}
|
16,832 |
t\cdot 10 = 2\cdot 5 t
|
31,442 |
\frac14\cdot (9 + 9 + 10 + 11) = 9.75
|
22,406 |
(v_2 + v_1)\cdot c\cdot T = v_2\cdot T\cdot c + T\cdot c\cdot v_1
|
28,283 |
-i/6 + 1 = \left(6 - i\right)/6
|
-5,091 |
1.83 \cdot 10 = \frac{18.3}{10} \cdot 1 = 1.83 \cdot 10^0
|
5,373 |
\sqrt{u/x} = \sqrt{\frac{1}{u \times x} \times u^2} = \frac{1}{\sqrt{u \times x}} \times u
|
2,287 |
\frac{1}{27}\cdot 4 = -\dfrac{8}{27} + 4/9
|
-3,943 |
\frac{p^2}{p^5} = \dfrac{p}{pp p p p}p = \frac{1}{p^3}
|
-27,368 |
49 = 596 + 547\cdot (-1)
|
-10,595 |
\frac{4}{4 \cdot y + 2 \cdot \left(-1\right)} \cdot 2/2 = \dfrac{8}{4 \cdot (-1) + 8 \cdot y}
|
-22,875 |
\frac{16}{72} = \frac{2 \times 8}{9 \times 8}
|
9,237 |
\sqrt{6 - 2 \cdot \sqrt{5}} = \sqrt{5} + \left(-1\right)
|
19,174 |
2\sqrt{10} + 2 = (1 + \sqrt{10})*2
|
-4,126 |
\frac{11\cdot p^3}{3} = p^3\cdot 11/3
|
15,538 |
-5\cdot l + l\cdot 2\cdot 3 = l
|
-14,026 |
\frac{1}{4 + 6}\cdot 40 = 40/10 = 40/10 = 4
|
24,969 |
z^3 + (\phi + a) \cdot z^2 + z \cdot (\phi \cdot a + h) + \phi \cdot h = (\phi + z) \cdot (z^2 + a \cdot z + h)
|
-15,192 |
\frac{1}{q^{12}*l^8*l^3} = \frac{1}{(l^2*q^3)^4*l^2 * l}
|
6,819 |
\left(0 = x \cdot x + x + 1 \implies x^2 = -x + \left(-1\right)\right) \implies x \cdot x \cdot x = -x \cdot x - x = 1
|
2,021 |
(-1)^y = (e^{i*\pi})^y = \cos\left(\pi*y\right) + i*\sin(\pi*y)
|
34,534 |
1 = -n * n + z^2\Longrightarrow 1 = (z + n) (z - n)
|
27,678 |
\frac{4}{10} = \frac{1}{5}*2
|
12,120 |
s^{k + 2 \cdot \left(-1\right)} \cdot s = s^{k + (-1)}
|
49,701 |
{2 n \choose n} = (\sum_{k=0}^n {n \choose k}) \left({n \choose n} - k\right) = \left(\sum_{k=0}^n {n \choose k}\right)^2
|
24,898 |
\frac{1}{-u + 1} \cdot ((-1) \cdot (u + 1)) = \dfrac{1 + \frac1u}{1 - 1/u}
|
16,262 |
zt = a\Longrightarrow \bar{z} t = \bar{a}
|
41,072 |
\cos(\pi + z) = -\cos{z}
|
13,806 |
\left( t', x'\right)\cdot \left( r, z\right) \coloneqq t'\cdot (-r) + x'\cdot z
|
23,699 |
3^{m + 1} + 1 = 2 \cdot (-1) + (1 + 3^m) \cdot 3
|
-7,758 |
\frac{-8 - 2 \times i}{-i \times 3 + 5} \times \frac{i \times 3 + 5}{3 \times i + 5} = \frac{-i \times 2 - 8}{5 - 3 \times i}
|
8,474 |
3 \cdot y^2 - y \cdot 12 = 12 \cdot \left(-1\right) + \left(y + 2 \cdot (-1)\right)^2 \cdot 3
|
22,130 |
3/20 = \frac{1}{{20 \choose 3}}*{19 \choose 2}*{1 \choose 1}
|
14,971 |
2*y*2 + y*4 = y*8
|
-4,701 |
-\frac{1}{3 + y}*2 - \frac{4}{2 + y} = \frac{16*(-1) - 6*y}{y^2 + y*5 + 6}
|
-24,197 |
8 \cdot 3 + 10 \cdot \tfrac14 \cdot 16 = 8 \cdot 3 + 10 \cdot 4 = 24 + 10 \cdot 4 = 24 + 40 = 64
|
29,470 |
\frac{1}{20}\cdot 16 = 4/5
|
1,659 |
(-1) + \cos^2{z}*2 = \cos{z*2} \Rightarrow \cos^2{z} = \frac12*(\cos{2*z} + 1)
|
-3,329 |
-4^{1/2}\cdot 3^{1/2} + 3^{1/2}\cdot 16^{1/2} = 4\cdot 3^{1/2} - 3^{1/2}\cdot 2
|
-2,278 |
8/13 - \frac{1}{13}\cdot 3 = 5/13
|
14,801 |
2.5 = -(1 - x) + x*3 \Rightarrow x = 7/8
|
1,786 |
\frac{\mathrm{d}}{\mathrm{d}x} e^{x\cdot 3} = e^{x\cdot 3}\cdot 3
|
21,990 |
\frac{2}{13} = \frac{1}{117}\cdot 18
|
10,959 |
C\cdot \epsilon = C\cdot \epsilon
|
15,272 |
0 = b_4 - b_1 \cdot 2 - \left(b_1 \cdot 2 - b_2\right)/5 \cdot 3 rightarrow b_4 \cdot 5 - b_1 \cdot 16 + b_2 \cdot 3 = 0
|
7,419 |
\lim_{l \to ∞}\left(\dfrac{1}{l} + l\right) = \lim_{l \to ∞} l
|
-22,354 |
t^2 - t\cdot 5 + 4 = (4\cdot (-1) + t)\cdot (t + (-1))
|
-3,259 |
5^{1/2}\cdot (2 + 4 + 5) = 11\cdot 5^{1/2}
|
-26,582 |
16 - 49*x^2 = (4 - x*7)*(7*x + 4)
|
37,854 |
\frac19 = \frac{1}{10} + \dfrac{1}{100} + \frac{1}{1000} + \dots
|
13,088 |
1^{3/2} = (1^3)^{\frac{1}{2}} = 1^{1/2} = 1
|
-2,147 |
-19/12\cdot \pi + 7/6\cdot \pi = -\dfrac{5}{12}\cdot \pi
|
6,612 |
w_3\cdot c + h\cdot w_1 + x\cdot w_2 = w_1\cdot (h - x + c - c) + (x - c)\cdot (w_2 + w_1) + (w_1 + w_2 + w_3)\cdot c
|
28,250 |
239\cdot 4649 = 1111111
|
21,297 |
\frac{4}{144} + 1/12 = \frac19
|
-30,326 |
(-1) + 7 = 6
|
-18,583 |
r + 1 = 5\times (3\times r + 10) = 15\times r + 50
|
5,091 |
-z/\left(z\cdot 2\right) + \dfrac{1}{2\cdot z}\cdot 6 = \tfrac{1}{z}\cdot 3 - \frac12
|
-3,204 |
25^{\frac{1}{2}}*2^{\dfrac{1}{2}} + 2^{\tfrac{1}{2}}*9^{\frac{1}{2}} = 3*2^{1 / 2} + 2^{\frac{1}{2}}*5
|
-5,291 |
7.8 \cdot 10^{7 + 4 \cdot (-1)} = 7.8 \cdot 10^2 \cdot 10
|
13,389 |
\dfrac1l \cdot (l + 1) = 1 + \frac1l
|
9,372 |
\dfrac12\cdot \left(35\cdot \left(-1\right) - 7\right) = -21
|
-7,818 |
\tfrac{1}{4 + 3 \cdot i} \cdot (3 \cdot i + 4) \cdot \frac{-10 \cdot i + 5}{4 - 3 \cdot i} = \frac{1}{-i \cdot 3 + 4} \cdot (-i \cdot 10 + 5)
|
2,869 |
|Z| = v \implies Z Z = |Z| |Z| = v v = v^2
|
27,724 |
c\cdot g = c^Y\cdot g = g^Y\cdot c
|
2,303 |
\frac{(l!)!}{l!} = (l! + (-1))!
|
18,693 |
( x', y') + ( n, y'') + ( x, k) = ( x' + n, y' + y'') + ( x, k)
|
46,120 |
84\cdot 90 = 84\cdot \left(100 + 10\cdot (-1)\right) = 8400 + 840\cdot \left(-1\right) = 7560
|
-10,630 |
\frac15 \cdot 5 \cdot \frac{5}{3 \cdot r} = \dfrac{25}{15 \cdot r}
|
26,426 |
-\dfrac{1}{2} = 1/2 + (-1)
|
-2,014 |
\dfrac{1}{12}11 \pi = -\pi/6 + \pi \dfrac{13}{12}
|
3,080 |
E\left[Q_{i \cdot i}\right] = E\left[Q_{i \cdot i}\right]
|
38,309 |
81 = \left(-2\right) \cdot 5 \cdot 4 + \binom{3}{2} \cdot 4 \cdot \binom{5}{2} + 1
|
-5,623 |
\tfrac{1}{3\cdot (x + 4\cdot (-1))}\cdot 5 = \frac{5}{3\cdot x + 12\cdot (-1)}
|
2,348 |
\frac{1}{X^2} + X^2 = (X + 1/X)^2 + 2 \cdot (-1)
|
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