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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} |
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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