Datasets:
ddrg
/
math_formulas

Dataset card Data Studio Files Community
1
id
int64
-30,985
55.9k
text
stringlengths
5
437k
11,803
\frac{2}{k^4} \cdot k = \frac{2}{k^3}
21,517
1 \times 1 \times 1 \times 4200 \times 5^4 \times 5^2 \times 5 = 328125000
872
5 + 2/3 \times q + 2 \times (-1) = \frac{2}{3} \times q + 3
-26,633
6^2 - y^2 = 36 - y^2
20,533
96 x = 3*2*x*16
2,675
\tan{k} = \frac{\sin{k}}{\cos{k}} = 1/\cot{k}
17,449
\left(1 \leq 0 \Rightarrow 1 = 0, 0 \geq 2\right) \Rightarrow 2 = 0,\dots
16,930
2 \cdot (1 + 1/17) = 35/17 < \tfrac{32}{15}
-4,765
-\frac{3}{y + 2} - \frac{5}{4 + y} = \frac{-y \cdot 8 + 22 (-1)}{y^2 + y \cdot 6 + 8}
17,592
(3^{1 / 2}*2 + 4)^{\dfrac{1}{2}} = 1 + 3^{1 / 2}
-391
\frac{8! \cdot \frac{1}{5! \cdot (8 + 5 \cdot (-1))!}}{10! \cdot \frac{1}{5! \cdot (5 \cdot (-1) + 10)!}} = \frac{8! \cdot \frac{1}{3!}}{\frac{1}{5!} \cdot 10!}
25,145
3^2 + 2^2 - 2\cdot 3 = 7
-18,531
-81/14 = -\frac{81}{14}
28,503
65 = (2^2 + 1^2) (3 \cdot 3 + 2^2) = 8^2 + 1^2 = 4 \cdot 4 + 7 \cdot 7
8,294
\frac{1}{(n + 2) \left(1 + n\right)} = \frac{1}{n + 1} - \frac{1}{n + 2}
-5,270
0.89*10^4 = 10^{3(-1) + 7}*0.89
-1,592
11/12*\pi - 7/6*\pi = -\pi/4
544
x^3 = x \cdot ((-1) + x^2 + 1)
24,221
-11 \cdot 7 + 3 \cdot 26 = 1
-10,503
-\tfrac{27}{6 \cdot k + 3 \cdot (-1)} = -\frac{1}{(-1) + k \cdot 2} \cdot 9 \cdot \frac{1}{3} \cdot 3
14,227
900 = 10^2 \cdot 9
25,142
c/x = \frac{1}{b}*a \Rightarrow x*a = b*c
1,937
(-x + 1)^2\cdot (1 - x^2) = 1 - x^4 + 2\cdot x^3 - 2\cdot x
4,077
(4 + x)\cdot (x \cdot x - 4\cdot x + 16) = x \cdot x \cdot x + 64
-3,964
\dfrac{12\cdot n^2}{21\cdot n^3} = \tfrac{12}{21}\cdot \frac{n \cdot n}{n \cdot n \cdot n}
49,747
7 + 4 + 4 + 4 + 4 + 4 + 4 = 31
17,036
P(x) = P\left(x\right)
14,229
\left(Ax - b\right)^W*(Ax - b) = (x^W A^W - b^W) (Ax - b) = x^W A^W Ax - x^W A^W b - b^W Ax + b^W b
19,697
5 \cdot 1/9/2 = \dfrac{5}{18}
8,572
Qt = tQ
5,093
\left(\frac132^4\right)^{\frac15} = 6^{\frac{4}{5}}/3
8,573
(z + t)^3 = t^2 * t + z * z * z + z^2*t*3 + 3*t^2*z
19,476
X^6 - 2X^3 + 1 = \left(X^3 + (-1)\right)^2 = (X + (-1))^6
-6,175
\frac{3\cdot t}{(t + 2)\cdot (t + 2)} = \frac{t\cdot 3}{t^2 + 4\cdot t + 4}
25,724
det\left(H\right)^\alpha\times det\left(H\right) = det\left(H\right)^{\alpha + 1}
-18,259
\tfrac{p\cdot \left(p + 7\right)}{(p + 9(-1)) (7 + p)} = \frac{1}{p^2 - p\cdot 2 + 63 (-1)}(7p + p^2)
46,942
995 = 5\cdot 199
-26,560
96 - 6z^2 = 6*(16 - z^2) = 6(4 + z) (4 - z)
15,517
2*5 + 3 (-1) = 7
-19,749
2 = \dfrac84
39,590
\sin\left(2 \cdot \pi + z\right) = \sin(z)
15,029
\frac{1}{((-1) + x) \cdot ((-1) + x) + 4} = \frac{1}{5 + x^2 - x\cdot 2}
28,900
3^{m + 1} + \left(-1\right) = 3 \cdot 3^m + \left(-1\right) = 2 \cdot 3^m + 3^m + (-1)
121
0 \neq (-1) + c, 0 = (-1) + c^2 \Rightarrow c + 1 = 0
-30,497
3 = \frac{3}{2}\cdot 2^2 + Z = 6 + Z
6,382
3^{45} = 3*3^{44} = 3(3^2)^{22} = 3(10 + (-1))^{22} = 3(1 + 10 (-1))^{22}
-10,147
-\frac12 (-\frac{1}{25}16) = ((-1) (-16))/(2*25) = 16/50 = 8/25
-2,443
13^{\frac{1}{2}} \cdot 25^{\tfrac{1}{2}} + 13^{1 / 2} = 13^{1 / 2} + 5 \cdot 13^{\frac{1}{2}}
-9,099
127.3\% = \dfrac{1}{100} \cdot 127.3
-20,433
-6/1 \dfrac{3l + 8}{8 + l*3} = \dfrac{-18 l + 48 \left(-1\right)}{3l + 8}
-11,798
\frac{1}{81}4 = (\frac{1}{9}2)^2
31,727
{1 + 52 \choose 12 + 0 + 1} = {53 \choose 13}
15,724
0 = ]D, E_{ij}[ = D \cdot E_{ij} - E_{ij} \cdot D
10,712
( y' + y, x' + z) = ( z, y) + \left( x', y'\right)
5,572
(z_2 + z_1)^2 = z_1 * z_1 + z_2^2 + z_1 z_2*2!
1,470
(2^{7\%} \times 5)^2 = \left(128\% \times 5\right)^2 = 3^2 = 9
-11,970
1/2 = \frac{s}{8 \times \pi} \times 8 \times \pi = s
23,155
3 - z = 0 \Rightarrow 3 = z
-1,676
\frac32 \pi + \pi/4 = 7/4 \pi
32,954
\cos^2{\alpha} - \sin^2{\alpha} = \cos{\alpha \cdot 2}
-16,546
\sqrt{8}\cdot 9 = \sqrt{4\cdot 2}\cdot 9
20,257
(2 + x \cdot x + x\cdot 2)\cdot (x^2 - x\cdot 2 + 2) = x^4 + 4
-13,643
\dfrac{ 27 }{ (5 - 2) } = \dfrac{ 27 }{ (3) } = \dfrac{ 27 }{ 3 } = 9
31,979
\frac{1}{6} = \frac{1}{36}*6
-20,465
\frac{z\cdot 2}{-18\cdot z + 2\cdot (-1)} = \frac{z}{-9\cdot z + (-1)}\cdot 2/2
28,092
\frac{1}{8} = (\frac{1}{2})^4 + (1/2)^4
-26,386
\frac{z^{l_2}}{z^{l_1}} = z^{-l_1 + l_2}
13,804
\frac{1}{1! \times \left(1 + \left(-1\right)\right)!} \times 1! \times \frac{1}{10^1} \times (10 + (-1))^{1 + (-1)} = 1/10
20,521
\frac{1}{1 + x} = \dfrac{1}{1 + x} (1 + x - x - x^2 + x^2 + x^3 - x^3) = 1 - x + x^2 - \dfrac{x^3}{1 + x}
-6,134
\frac{2}{(10\cdot (-1) + r)\cdot (r + 2\cdot \left(-1\right))} = \frac{2}{20 + r \cdot r - 12\cdot r}
-19,156
2/5 = A_s/\left(100*\pi\right)*100*\pi = A_s
-3,418
99^{\dfrac{1}{2}} - 11^{\frac{1}{2}} = \left(9\cdot 11\right)^{1 / 2} - 11^{1 / 2}
4,277
\tfrac{5^{25} + (-1) + 75*(-1)}{2 + (-1)} = 5^{25} + 76*(-1) \gt \frac{1}{4}*(5^{25} + 101*(-1))
-30,875
4\cdot \left(-1\right) + 28 = 24
-22,177
12 \left(-1\right) + y^2 - y = \left(4(-1) + y\right) (3 + y)
47,234
699 = 3 \cdot 233
2,964
\sin\left(x + z\right) = \sin{x}*\cos{z} + \sin{z}*\cos{x}
-23,721
\frac{3}{7}*3/4 = 9/28
-20,811
\frac{s\cdot 5 + 30}{(-45)\cdot s} = \frac{1}{s\cdot (-9)}\cdot (s + 6)\cdot \frac15\cdot 5
16,382
c^{l_1}\cdot c^{l_2} = c^{l_1 + l_2}
17,755
1 = a\times 2 \Rightarrow a = 1/2
17,586
-83520\cdot T^3 = \left(360\cdot (-1) - 98280 + 15120\right)\cdot T^3
31,951
x h = \tfrac12 (-h^2 + (h + x)^2 - x x)
24,058
0 = \tfrac{1}{4}(2x + 5) \Rightarrow -5/2 = x
-4,621
\frac{8 \cdot y + (-1)}{y^2 - y + 2 \cdot (-1)} = \frac{1}{y + 2 \cdot (-1)} \cdot 5 + \frac{3}{y + 1}
1,652
2 + \left(-1\right) + 1 = 3 + 0 \cdot (-1) \Rightarrow 2 = 3
-24,358
\dfrac{30}{3 + 2} = 30/5 = \frac15\cdot 30 = 6
14,562
\sin\left(-y + \pi/2\right) = \cos\left(y\right)
4,889
\frac{d}{dt} \left(i*b\right) = \frac{di}{dt}*b + i*\frac{db}{dt} = 0*b + i*\frac{db}{dt}
-26,592
16*\left(-1\right) + z^2*25 = (4*\left(-1\right) + 5*z)*(5*z + 4)
-2,015
-\frac{1}{12}*5*\pi + \frac{23}{12}*\pi = 3/2*\pi
23,847
q^{b^h} = q^{b^h}
8,250
\tanh(z) = \tanh(x) \implies x = z
-12,106
\frac{1}{72} \cdot 25 = \dfrac{p}{12 \cdot \pi} \cdot 12 \cdot \pi = p
14,661
\sin^2(r) = x\Longrightarrow \cos(2\cdot r) = 1 - 2\cdot \sin^2(r) = 1 - 2\cdot x
21,615
\left(1 - y + y^2\right)^{3 n} (1 + y)^{3 n} = ((1 - y + y^2) (1 + y))^{3 n} = \left(1 + y^3\right)^{3 n}
-22,327
g^2 - g \cdot 14 + 45 = (5 \cdot (-1) + g) \cdot (g + 9 \cdot (-1))
16,765
x d - x + d = 1 + \left((-1) + d\right) \left(x + 1\right)
-19,714
3*5/(8) = \frac{15}{8}
30,692
a + 6d = a + d\cdot \left(7 + (-1)\right)