Datasets:
ddrg
/
math_formulas

Dataset card Data Studio Files Community
1
id
int64
-30,985
55.9k
text
stringlengths
5
437k
-6,188
\frac{2}{\left(2 + s\right)\cdot 2} = \tfrac{2}{2\cdot s + 4}
-15,225
\frac{b^{15}}{b^4 \cdot j^4} = \frac{b^{15}}{j^4} \cdot \frac{1}{b^4} = \frac{1}{j^4} \cdot b^{15 + 4 \cdot (-1)} = \frac{b^{11}}{j^4}
2,718
\frac{1/6}{6 - i} \cdot (6 - i) = 1/6
-26,447
\left(g\cdot 16/4 + x\cdot 20/4\right)\cdot 4 = 4\cdot (x\cdot 5 + 4\cdot g)
9,454
(b + a)^2 = 4*b*a + (a - b) * (a - b)
28,438
k \cdot (1 + p) = (p + 1) \cdot x \Rightarrow x \cdot p + x = p \cdot k + k
1,458
n + 1 = 2^n - \left(n + (-1)\right)\cdot 2^{n + 2\cdot \left(-1\right)} + \frac{1}{2!}\cdot (n + 3\cdot (-1))\cdot (n + 2\cdot (-1))\cdot 2^{n + 4\cdot (-1)} - ...
-13,329
\frac{35}{8 + 3 \cdot (-1)} = 35/5 = \frac{35}{5} = 7
29,713
\frac{1}{(k + (-1))!}\cdot n + \frac{1}{(k + (-1))!}\cdot m = \frac{1}{(k + \left(-1\right))!}\cdot (n + m)
-20,234
\frac{1}{-y \cdot 8 + 18} \cdot (10 \cdot \left(-1\right) + y \cdot 10) = 2/2 \cdot \frac{5 \cdot (-1) + 5 \cdot y}{9 - 4 \cdot y}
11,809
\left(0 = 6*\left(-1\right) + y + 2*(-1) + y*3 \Rightarrow -8 = y*4\right) \Rightarrow -2 = y
-6,988
\frac{6}{10}\cdot 5/9 = 1/3
25,382
b + x + d + x = d + x + b + x
11,453
(V + 1) \cdot (V^2 - V + 2) = (V + 1) \cdot (V^2 - V + 1) + V + 1 = V^3 + 1 + V + 1 = 6 + V
-25,223
x^{n + \left(-1\right)}\cdot n = d/dx x^n
-950
\frac95 = \frac{9}{5}
24,871
x + \left(-1\right) + x + 1 = x\cdot 2
4,768
2^{n + \left(-1\right)}\cdot 2^{n + \left(-1\right)}\cdot 4^n = 2^{2\cdot (n + (-1))}\cdot 4^n = 4^{n + (-1)}\cdot 4^n = 4^{2\cdot n + (-1)}
29,462
2 t + \beta = 2 (\beta/2 + t)
27,361
\left(x \cdot y\right)^g = x^g \cdot y^g = \frac{1}{x \cdot y} = \frac{1}{y \cdot x} = (y \cdot x)^g
25,992
\frac{1}{1 - \frac{9}{10}} + \left(-1\right) = 10 + (-1) = 9
24,249
q^2 = 2^2 + 5 = 9 \Rightarrow 3 = q
-20,419
\frac{1}{10*z + 100*\left(-1\right)}*(90*(-1) + 9*z) = 9/10*\frac{1}{10*(-1) + z}*(z + 10*\left(-1\right))
-20,512
\frac{1}{q + 6*\left(-1\right)}*(q + 1)*10/10 = \frac{1}{q*10 + 60*(-1)}*(10 + q*10)
37,659
\dfrac{1}{60}4 = \frac{1}{15}
19,366
1 \lt |R| \Rightarrow 1 > \frac{1}{|R|}
17,246
1/(\sqrt{3.4}) = \tfrac{1}{\sqrt{4 - 0.6}} = \frac{1}{2 \cdot \sqrt{1 - 0.15}}
-4,510
\frac{y + 9}{y^2 + 6y + 5} = \dfrac{2}{1 + y} - \frac{1}{y + 5}
18,545
16 = \dfrac{1}{3!}\times 4!\times 4
-5,779
\frac{3y}{(y + 5) (6 + y)} = \frac{3y}{y * y + y*11 + 30}
19,108
\dfrac{1}{12} = \dfrac{1}{2*6}
29,664
3\cdot (-1) + (n + 1)\cdot 2 = (-1) + 2\cdot n
27,036
\frac{3}{49}*\frac{4}{50} = 6/1225
-14,979
410 = 79 + 75 + 81 + 80 + 95
21,049
\frac{1}{(1 + x)^{1/2} \cdot (1 + x)^{1/2}} = \frac{1}{x + 1}
20,894
\tfrac{y}{s} = \sin{U}\Longrightarrow y = s*\sin{U}
-20,559
\frac{45}{y \cdot (-10)} \cdot y = -\frac{9}{2} \cdot \frac{1}{(-5) \cdot y} \cdot ((-5) \cdot y)
31,313
\cos{x} = \cos(2 \cdot \pi + x)
405
(1 + t \cdot t)^2 - 2t \cdot t = t^4 + 1
7,409
\delta + 3(-1) + 4\delta = 10 + \delta*5 + 13 \left(-1\right)
20,987
97 + 32\cdot \left(-1\right) = 65
-18,773
x = \frac{x\cdot 3}{3}1
36,851
M \cdot y = M \cdot y
28,731
y \cdot z^2 = y \cdot z^2
-20,875
\dfrac{1}{\left(-28\right) \cdot j} \cdot (7 \cdot j + 7 \cdot (-1)) = \frac{7}{7} \cdot \dfrac{(-1) + j}{j \cdot (-4)}
24,471
e^H e^A = e^{H + A}
-6,556
\frac{3}{27 + y^2 - y*12} = \dfrac{3}{(3 (-1) + y) (9 (-1) + y)}
-5,621
\frac{1}{10 + x\cdot 2}5 = \frac{5}{2(x + 5)}
12,733
900 = 360 \times (-1) + 1260
6,935
( 17, t + \left(-1\right)) = 1\Longrightarrow t
1,881
\frac{dy}{dt}\cdot z = \frac{dz}{dt}\cdot y
17,932
x\cdot f'\cdot f + f^2 = c\cdot f' \implies f + f'\cdot x - f'\cdot \frac{c}{f} = 0
-4,753
(z + 3)*(z + 5) = z^2 + z*8 + 15
5,993
-z_0 + z = (-z_0^{1/2} + z^{1/2})\cdot (z^{1/2} + z_0^{1/2})
-2,583
\sqrt{3}*\sqrt{25} + \sqrt{3}*\sqrt{9} = \sqrt{3}*5 + 3*\sqrt{3}
13,260
z^{216} + \left(-1\right) = \left(-1\right) + (z^6)^{36}
12,160
\frac{1}{5^4} \cdot 648 = \dfrac{1}{625} \cdot 648 > 1
-679
e^{\pi*i/12*12} = (e^{i*\pi/12})^{12}
25,746
-(v + x) = \dots = -v - x
10,398
a^{b + x} = a^x\cdot a^b
25,424
(x - c*I)^n*v = (x - c*I)^{n + (-1)}*\left(x*v - c*v\right) = (x - c*I)^{n + \left(-1\right)}*x*v - (x - c*I)^{n + (-1)}*c*v
11,522
(z + 2)\cdot (z^2 - 2\cdot z + 4) - 2\cdot 5 = 2\cdot (-1) + z^3
24,944
\ln(9^{15}) = 30\cdot \ln\left(3\right) = 14.31
-18,339
\dfrac{s^2 + 12*s + 20}{s^2 + 10*s} = \dfrac{1}{(s + 10)*s}*(s + 2)*(s + 10)
-16,610
2 \sqrt{16} \sqrt{7} = 2*4 \sqrt{7} = 8 \sqrt{7}
19,491
-(b - e) \cdot 3 = (e + a + b) \cdot (b - e) rightarrow e + a + b = -3
6,426
\left(5 + 3\right)^3 - 5^3 - 3^3 = 3*3*5*\left(3 + 5\right) = 18*20 = l^2 + \left(-1\right) = (l + (-1))*\left(l + 1\right)
5,339
\tfrac17 28 = (1 + 2 + 3 + 4 + 5 + 6 + 7)/7
-4,915
\dfrac{1}{10}\cdot 0.74 = 0.74/10
-11,550
-24\cdot i - 8 + 16 = 8 - i\cdot 24
11,006
2 = \sin^2{C} + \sin^2{A} + \sin^2{B} rightarrow 2 = -(\cos^2{B} - \sin^2{C}) + 1 - \cos^2{A} + 1
16,950
\tfrac{1}{37} \cdot 34 \cdot 35/38 \cdot \frac{37}{40} \cdot 36/39 \cdot 33/36 = 1309/1976
6,667
z*2 = 2\left(2(-1) + z\right) + 4
6,799
\left(0 = x^3 + 6 x + 20 (-1) \implies \left(x + 2 (-1)\right) (9 + (x + 1)^2) = 0\right) \implies 2 = x
19,851
0 = c_0 + c_1 \implies c_0 = -c_1
-20,899
\frac{1}{9} \cdot 1 = \dfrac{-7 \cdot x + 1}{-x \cdot 63 + 9}
5,914
(-1/2 + z)^2 + \frac{3}{4} = z \cdot z - z + 1
-20,193
-18/3 = -\dfrac61 \cdot 3/3
14,551
1/7 + 1/7 + \frac17 = \frac{3}{7}
20,362
x h l \frac{1}{q}/q = \frac{l h x}{q q}
9,458
\sin(y) = \frac{y}{1 + \frac{y^2}{2\cdot 3 - y^2 + \dots}}
-4,214
x\frac{8}{7} = 8x/7
-18,955
\dfrac35 = \tau_q/(25\cdot \pi)\cdot 25\cdot \pi = \tau_q
3,897
1 = \frac{\frac12}{\frac12}
42,172
\frac{1}{0 \cdot 0 + 0^2}(1 + 0 + 0(-1)) = 1/0 = \infty
7,256
\alpha^2 + \alpha + 2(-1) = 0 \implies \alpha = 1\text{ or }-2
-19,630
\frac{1}{2}\times 3/2 = 1/(2\times 2/3)
29,553
(1 + y)!*y! = (y + 1)*y!^2
12,965
\dfrac12 \times (-\cos{2 \times \theta} + 1) = \sin^2{\theta}
2,008
\frac{1}{C^2} = 1/C * 1/C
-1,871
7/12\cdot \pi = 23/12\cdot \pi - \pi\cdot 4/3
51,596
(-1)p=-p\in S
31,336
\frac{1}{2}(1 + (-1)) = 0/2 = 0
5,336
e^{\frac{30}{4}\cdot \pi\cdot i} = e^{\frac{15}{2}\cdot \pi\cdot i} = e^{8\cdot \pi\cdot i - \pi\cdot i/2} = e^{((-1)\cdot i\cdot \pi)/2}
-24,665
\frac{2 \times 3}{7 \times 3} = \dfrac{6}{21}
-20,362
\frac{7}{-q*63 + 14} = \frac{7*\frac17}{-q*9 + 2}
-22,804
54/72 = \frac{18}{4 \cdot 18} \cdot 3
22,639
f!\cdot (1 + \frac{g!}{f!}) = f! + \dfrac{g!}{f!}\cdot f!
29,866
C \cdot z = z \cdot C
26,763
12^{\frac{1}{3}} \cdot 12^{\frac{1}{3}}/2 = 18^{\tfrac13}