Datasets:
ddrg
/
math_formulas

Dataset card Data Studio Files Community
1
id
int64
-30,985
55.9k
text
stringlengths
5
437k
-24,888
1/18 = q/(6*\pi)*6*\pi = q
28,919
\frac{1}{x\cdot (-1/x + 1)} = \frac{1}{x + \left(-1\right)}
22,696
((\dfrac{2}{3})^{70} + 1) \cdot 3^{70} = 3^{70} + 2^{70}
15,970
-b\cdot \left(-c\right) = c\cdot b
15,878
(l^2 + \tfrac{l}{2}) \cdot (l^2 + \tfrac{l}{2}) = l^4 + l^2 \cdot l + \tfrac14\cdot l^2 \lt l^4 + l \cdot l \cdot l + l^2 + l + 1
9,717
F \times x + x = x \times (F + 1)
608
\frac{1}{n^{1/2}} = n^{-\frac{1}{2}}
4,656
300 = \dfrac{3}{10}*(6*\left(-1\right) + 1006)
26,238
-4/1024 + 1 = \dfrac{255}{256}
28,432
By + I = \left(1 + y\right) (-(I - B) \tfrac{y}{1 + y} + I)
3,575
y \cdot x \cdot x = x^6 \cdot y = x \cdot x \cdot y
32,723
-b^2 + a * a = (a - b) (a + b)
12,955
x^4 + 16\cdot (-1) = \left(2 + x\right)\cdot (4 + x^2)\cdot (x + 2\cdot (-1))
1,443
(a + d)/d = 1 + a/d
-5,244
24.0/1000 = \tfrac{1}{1000} 24
4,002
\left(\dfrac23\right)^2 \left(1/3\right)^3 = \dfrac{4}{243}
3,050
(-1)^{1 / 2} = \frac{2^{\frac{1}{4}}}{2^{\frac14}} \cdot (-1)^{1 / 2}
2,765
m\cdot (v + u) = u\cdot m + m\cdot v
21,050
\tfrac{1}{Y*\omega} = \frac{1}{\omega*Y}
-3,855
\frac{7}{2 \cdot q} = 7 \cdot \frac{1}{2}/q
36,087
1 = 17 + 4 \cdot (-4)
-16,468
5 \times \sqrt{4 \times 5} = \sqrt{20} \times 5
-24,261
\frac{126}{9 + 5} = \frac{126}{14} = \frac{126}{14} = 9
20,413
2 + (2 \cdot (-1) + z)^2 = 6 + z^2 - z \cdot 4
33,995
194906228517 = \left(3\cdot 7\cdot 11\cdot 13\right)^2\cdot 21613
7,289
3*(n + 1) + \left(-1\right) = 2 + 3*n
-22,797
90/40 = 9*10/(4*10)
34,049
1/9 = \frac{1}{36}4
-20,311
5/5\cdot \dfrac17\cdot (k + 4) = (20 + 5\cdot k)/35
20,378
48^2 + 4^2 + 48^2 = 34 * 34*4
16,808
\frac{1}{x + 1}\cdot (x^3 + 4\cdot x^2 + 5\cdot x + 2) = (1 + x)\cdot (2 + x)
30,969
1 + \tan^2\left(y\right) = \frac{1}{\cos^2(y)}\cdot (\cos^2(y) + \sin^2(y)) = \sec^2(y)
30,838
e^{-z} = \tfrac{1}{e^z} \neq e^{\frac1z}
46,759
\sin 0 = \sin \pi
449
e^z = (e^{\frac{z}{2}})^2 \geq (\dfrac{e}{2} \cdot z)^2
15,574
d_2^2 + d_1 \cdot d_1 + 2 \cdot d_1 \cdot d_2 = (d_1 + d_2)^2
-5,703
\dfrac{3}{2(n - 1)} \times \dfrac{5(n + 2)}{5(n + 2)} = \dfrac{15(n + 2)}{10(n - 1)(n + 2)}
19,357
\tfrac{1}{a}\cdot (1 - u + a\cdot u) = \frac1a\cdot (1 + (-1 + a)\cdot u) = \dfrac1a\cdot \left(1 - \left(1 - a\right)\cdot u\right)
38,972
\lim_{z \to 3} \tfrac{\frac{1}{3} - 1/z}{z + 3(-1)} = \lim_{z \to 3} \frac{1}{z^2} = \lim_{z \to 3} \frac{1}{z^2}
20,799
9^2 * 9 = 8^3 + 1^3 + 6^3
29,500
\frac{1 + 3^{\dfrac{1}{2}}}{(-1) + 3^{1 / 2}} = 2 + 3^{1 / 2}
2,268
0 = e \cdot e\cdot 0\cdot e^3
44,659
{11 \choose 4} = 11!/(4!\cdot 7!) = 330
-3,052
(1 + 4 + 5) \cdot 10^{1 / 2} = 10^{1 / 2} \cdot 10
-19,996
12/2 = \dfrac22\cdot 6/1
31,627
r \cdot z_1^2/(z_2) = \dfrac{(r \cdot z_1)^2}{z_2 \cdot r}
24,857
\cos{y\cdot 2} = \left(-1\right) + 2\cdot \cos^2{y}
-15,171
\frac{1}{\frac{1}{p^{16}} \cdot (x \cdot p^5)^2} = \frac{p^{16}}{p^{10} \cdot x^2}
47,713
210 = 6\cdot 35
-1,247
\frac{30}{35} = 30\cdot \frac{1}{5}/(35\cdot \frac{1}{5}) = 6/7
423
\dfrac{1}{B - d} \cdot (-d + x) + \left(-1\right) = \frac{1}{-d + B} \cdot \left(-B + x\right)
-5,940
\frac{1}{4 + 2\cdot d}\cdot 5 = \frac{1}{2\cdot (d + 2)}\cdot 5
-7,743
\left(24 - 32\times i - 18\times i + 24\times (-1)\right)/25 = \left(0 - 50\times i\right)/25 = -2\times i
10,516
7^4 - 7^3 + 7^2 + 7 \cdot (-1) + 1 = 2101 = 11 \cdot 191
12,325
3*x * x + x*4 + 1 = -x^2 + (2*x + 1) * (2*x + 1)
-4,459
(2\cdot (-1) + y)\cdot (5 + y) = y \cdot y + 3\cdot y + 10\cdot (-1)
3,585
n + 1 = 2(1 + n)/2
-14,225
\frac{24}{5 + 1} = \dfrac{24}{6} = \frac{1}{6}\cdot 24 = 4
9,326
(d^{x + g} - d^x)/g = \dfrac1g \cdot (d^x \cdot d^g - d^x) = d^x \cdot \left(d^g + \left(-1\right)\right)/g
3,138
e \geq 2\times (2 - k + e) \implies e \leq 4\times (-1) + 2\times k
7,586
\frac{1}{6} \cdot (30 - 0.2 - 0.5 + \left(-1\right) + 4 \cdot (-1)) = 4.05
11,541
haC \bar{f_y} = \bar{f_y} aC h
27,017
\frac{1}{M}*a*d/c = \frac{a*\tfrac{1}{M}}{c*\frac1d}
23,487
2^g + 3^b = (1 + 1)^g + (1 + 2)^b \leq 1 + g + 1 + b*2
34,337
b + 3 \cdot b \cdot b/24 = \tfrac{b^2}{8} + b
-1,404
-5/3*4/5 = ((-5)*1/3)/(5*\frac{1}{4})
-19,422
9*\dfrac17/(2*1/5) = 9/7*5/2
106
e^y = \sum_{n=0}^\infty \frac{y^n}{n!} = 1 + y + \sum_{n=2}^\infty y^n/n!
3,913
\dfrac12 \cdot 3 \cdot x = k + \dfrac23 \implies \frac23 \cdot k + (2/3) \cdot (2/3) = x
15,398
\sin\left(4\cdot π/3\right) = -\sin(π/3)
13,829
-(t - a/2)^2 + a^2/4 = a*t - t * t
10,305
\left(a\times c = a + c \Rightarrow -c + a\times c - a = 0\right) \Rightarrow (\left(-1\right) + c)\times (a + \left(-1\right)) = 1
-11,449
-8\cdot d - 4\cdot i = -4\cdot (-5\cdot d - k) = 20\cdot d + 4\cdot k
17,385
12*(3z^2 + 4z + 4(-1)) = 36 z * z + 48 z + 48 (-1) = (6z + 4)^2 + 64 (-1)
32,010
12 \cdot 23 \cdot 34 \cdot \dotsm \cdot n \cdot \left((-1) + n\right) = 1234 \cdot \dotsm \cdot n
-22,374
(r + 6\cdot (-1))\cdot (r + (-1)) = r^2 - 7\cdot r + 6
3,671
(a^{p/q}*a^{t/s})^{q*s} = a^{p*s}*a^{t*q} = a^{p*s + t*q}
-500
\tfrac{17}{4} \pi - 4\pi = \frac{\pi}{4}
2,722
\sqrt{3}/2 = \cos{\dfrac{4*\pi}{24}}
26,630
2\cdot 3 + 5\cdot (-1) = 1
14,061
\sin(t\times 2) = 2\times \sin(t)\times \cos(t)
-1,864
-\frac{11}{6} \pi + \pi/12 = -\pi \frac{7}{4}
24,240
(y + z) (y + z) = z^2 + z y*2 + y^2
33,248
(-1)^{6/2} = (-1) \cdot (-1)^2
27,889
\mathbb{E}[S + x] = \mathbb{E}[x] + \mathbb{E}[S]
10,916
\frac{1989}{867} = 51\cdot 39/(51\cdot 17) = \frac{39}{17}
46,229
19 \cdot 4 = 76 = 7 \cdot 10 + 6
-2,740
-6^{1/2} \cdot 2 + 5 \cdot 6^{1/2} = -6^{1/2} \cdot 4^{1/2} + 6^{1/2} \cdot 25^{1/2}
32,840
-\frac83 = -\frac13*8
31,999
\frac{k}{q}\cdot k\cdot q = k^2 = \frac1q\cdot k^3
-20,415
-\frac{1}{5 \cdot q + 35} \cdot 45 = \dfrac15 \cdot 5 \cdot \left(-\frac{9}{7 + q}\right)
8,051
3 \lt (-1) - x \cdot 3 \Rightarrow 4 < -3 \cdot x
6,504
\frac{(2 + (-1) + 2)!}{(2 + (-1))!\cdot 2!} = \frac{1}{1!\cdot 2!}\cdot 3! = \frac{1}{1\cdot 2}\cdot 6 = 3
-25,584
\frac{1}{t^2}*3 = \frac{\mathrm{d}}{\mathrm{d}t} \left(-\frac{1}{t}*3\right)
-20,854
\frac{1}{x + 10\cdot (-1)}\cdot (40\cdot (-1) + 4\cdot x) = \frac{x + 10\cdot (-1)}{x + 10\cdot (-1)}\cdot 4/1
28,976
3\cdot (-2) + 7 = 1
-20,527
-\frac{7}{6} \cdot (-\frac{8}{-8}) = 56/(-48)
5,613
\frac{1}{l}l! = (l + (-1))!
17,574
6(-1) + y^2 - y = 0 \implies 3 = y
-27,759
d/dx (2*\tan(x)) = 2*d/dx \tan(x) = 2*\sec^2(x)