Datasets:
ddrg
/
math_formulas

Dataset card Data Studio Files Community
1
id
int64
-30,985
55.9k
text
stringlengths
5
437k
47,370
600 = 2\cdot (100 + 100 + 100)
-11,466
12 - 8 \cdot i = 12 + 0 \cdot (-1) - i \cdot 8
-20,523
(45 - 40\times j)/((-50)\times j) = \dfrac{1}{5}\times 5\times (9 - 8\times j)/\left(j\times (-10)\right)
23,780
1 + x + x^2 + \dots = \frac{1}{-x + 1}
33,200
2\cdot 7 = \left(1 + \left(-13\right)^{1 / 2}\right)\cdot (-(-13)^{1 / 2} + 1)
3,737
\left(d_2 * d_2 + d_1^2 + d_1*d_2\right)*(-d_2 + d_1) = -d_2^3 + d_1 * d_1 * d_1
4,771
\varphi = \frac12(1 + \sqrt{5}) = 1 + \frac{1}{\varphi}
4,335
(2 \cdot (-1) + 2^n)/2 + \left(2^n + 2 \cdot (-1)\right)/2 = 2^n + 2 \cdot \left(-1\right)
34,896
24 = \left(-1\right) + \frac14 \cdot 100
5,874
x^2 + 4 = x^2 - (-1)\cdot 4 = x^2 - i^2\cdot 2^2 = x^2 - \left(2\cdot i\right)^2 = (x - 2\cdot i)\cdot (x + 2\cdot i)
542
\|x + y\|^2 = |1 + i|^2\cdot \|x\|^2 = 2\cdot \|x\| \cdot \|x\| = \|x\|^2 + \|y\|^2
5,804
\sqrt{(y + 3)\cdot (2 + y)} = \sqrt{y^2 + y\cdot 5 + 6}
-15,171
\frac{1}{(r^5 x)^2 \frac{1}{r^{16}}} = \frac{r^{16}}{r^{10} x^2}
41,216
1^2 + 9 \cdot 9 = 82
31,902
e^I = 2 \Rightarrow e = 2^{\dfrac1I}
10,648
\left(x = \frac{x\cdot 2 + 1}{2 + x} \Rightarrow 1 = x^2\right) \Rightarrow x = 1
43,042
h = 4 + h + 4\cdot (-1)
-27,342
\tan\left(-\pi + \theta\right) = \tan{\theta}
-9,188
-i*2*2*2*3 + 2*2*5 = -24*i + 20
31,082
1 + \frac{1}{\frac{1}{1 + \frac13\cdot 2} + 1} = 1 + \dfrac{1}{1 + 1/(5\cdot 1/3)}
6,136
y^h\cdot y^d = y^{d + h}
23,776
28/126 + \frac{30}{126} = \dfrac{58}{126}
16,117
\frac{2}{1/3} \cdot 1/3 \cdot 40 = 2 \cdot 40 = 80
6,062
y^2 - 4 \cdot y = \left(2 \cdot (-1) + y\right)^2 + 4 \cdot \left(-1\right)
-2,452
-\sqrt{9} \cdot \sqrt{5} + \sqrt{5} \cdot \sqrt{25} = \sqrt{5} \cdot 5 - \sqrt{5} \cdot 3
19,638
0.6 = \frac{1}{3} \cdot \left(0.7 + 0.5 + 0.6\right)
27,762
37 = 37\times 3\times 5 - 37\times 2\times 7
29,994
2 \pi = \pi*2
22,200
b \cdot a \cdot x = a \cdot x \cdot b
10,294
\frac{(-1)^{1 + k}}{2^{1 + k}} = (-\frac{1}{2})^{k + 1}
-4,882
7*10^{3 + 4} = 10^7*7.0
17,636
e^x = 5 - x^2 + x*2\Longrightarrow x * x - 2*x + e^x = 5
21,729
(k + 1) \cdot (k + 1) \cdot (k + 1) = \left(k + 1\right)\cdot (1 + k)\cdot (k + 1)
11,320
(\left(-1\right) + u)*(u + 1) = u^2 + (-1)
36,752
-(1 + k\cdot 2) + n\cdot 2 + 1 = 2(n - k)
-612
\pi\cdot 119/6 - 18 \pi = \pi \frac{1}{6} 11
-500
\frac{1}{4}\pi = \frac{17}{4} \pi - 4\pi
-7,785
\frac{8 - i*2}{i - 4} = \frac{8 - i*2}{i - 4} \frac{-i - 4}{-4 - i}
-22,966
90/63 = \frac{10\cdot 9}{7\cdot 9}
36,283
6 = 2*3 = \left(1 + \left(-5\right)^{1/2}\right)*\left(1 - (-5)^{1/2}\right)
22,770
3 \cdot 3 + 3\cdot \left(-1\right) + (-1) = 9 + 3\cdot (-1) + (-1) = 0
11,860
\frac{C}{p + \left(-1\right)} + \frac{H}{p + 1} = \dfrac{1}{(p + 1)\cdot (p + (-1))} rightarrow 1 = (C + H)\cdot p + C - H
37,939
3^{1/4} = 3^{1/4}
2,642
128 = 256/2
-14,125
\frac{1}{10 + 9\cdot \left(-1\right)}\cdot 2 = 2/1 = \frac21 = 2
16,821
5^{1 / 2}\cdot 15/5 = 5^{1 / 2}\cdot 3
40,752
\left\{2, 6\right\} = \left\{2, 6\right\}
-13,019
8/11 = \frac{1}{22} 16
24,144
2^{k + 5 \cdot \left(-1\right)} = 2 \cdot 2^{6 \cdot (-1) + k}
843
2\cdot H_2 \geq 3\cdot H_1 \implies H_1 \leq H_2\cdot 2/3
-30,213
\frac{5! \cdot \frac{1}{(5 + 4 \cdot \left(-1\right))! \cdot 4!}}{7! \cdot \frac{1}{\left(7 + 4 \cdot (-1)\right)! \cdot 4!}} = \frac{5! \cdot \dfrac{1}{1!}}{7! \cdot 1/3!}
18,357
73 = \left(19 - 12 \sqrt{2}\right) (19 + 12 \sqrt{2})
-20,134
\frac{x \cdot (-18)}{90 \cdot \left(-1\right) + 9 \cdot x} = \dfrac{\left(-2\right) \cdot x}{x + 10 \cdot (-1)} \cdot 9/9
26,780
(\omega + (-1)) \cdot (\omega^4 + \omega \cdot \omega \cdot \omega + \omega^2 + \omega + 1) = (-1) + \omega^5
-11,645
-3 + 5 - 8 \cdot i = -8 \cdot i + 2
-20,888
(18 \cdot (-1) + 81 \cdot q)/(-36) = \frac{1}{-4} \cdot (9 \cdot q + 2 \cdot (-1)) \cdot 9/9
5,871
z\cdot x/y = x/(y\cdot 1/z)
9,142
(-1) + 2^{2 \cdot n} = (2^n + 1) \cdot (2^n + (-1))
42,834
\sec(x) = \sec\left(-x\right)
8,068
\cos(2 \cdot F) = 1 - 2 \cdot \sin^2(F) = 2 \cdot \cos^2(F) + (-1)
33,842
\delta + x = 0 \Rightarrow -\delta = x
-2,671
11^{1 / 2} + (16\cdot 11)^{\frac{1}{2}} = 176^{\frac{1}{2}} + 11^{1 / 2}
-15,529
\tfrac{1}{\frac{1}{\frac{1}{d^4} \cdot r^8} \cdot r} = \frac{1}{r \cdot \frac{d^4}{r^8}}
22,653
2 - 10^4 = 2 + 10000 (-1) = -9998 = -9.998*10^3 = -10/1000 = -10^4
8,751
0 = A^2 \times x \Rightarrow 0 = x \times A
-18,335
\frac{n^2 - 4 \cdot n + 60 \cdot (-1)}{6 \cdot n + n \cdot n} = \dfrac{1}{n \cdot \left(n + 6\right)} \cdot \left(n + 6\right) \cdot (n + 10 \cdot (-1))
16,343
51200 = 8^3 \times 10 \times 10
-19,020
29/40 = \tfrac{1}{25\cdot \pi}\cdot A_s\cdot 25\cdot \pi = A_s
44,052
52 = 8 \cdot \left(-1\right) + 60
672
(2*\pi*m)^{1/2}*\frac{e^m}{m^m}*\dfrac{m^m}{e^m} = \left(\pi*m*2\right)^{1/2}
39,271
100800 = 5 \cdot 4 \cdot 5 \cdot 4 \cdot \binom{10}{5}
11,116
5^3 = 4*19 + 7^2
25,859
\left(y^2\right)^b = (1/y)^b = y^{b + \left(-1\right)}
28,582
2^{\frac{1}{2}}*3 = 18^{1 / 2}
12,892
\frac{1}{\sigma} = 1 \implies \frac{1}{\sigma}
15,855
-\frac{1}{Y + (-1)} = \frac{1}{-Y + 1}
4,414
2\cdot Y + 2\cdot \frac{\mathrm{d}Y}{\mathrm{d}z}\cdot z = \frac{\partial}{\partial z} (Y\cdot z\cdot 2)
-27,012
\sum_{n=1}^\infty \frac{1}{n \cdot 6^n} \cdot (1 + 5)^n \cdot (n + 2) = \sum_{n=1}^\infty \frac{6^n}{n \cdot 6^n} \cdot (n + 2) = \sum_{n=1}^\infty \frac1n \cdot (n + 2)
15,087
e_1 x + ye_2 + ze_3 = ze_3 + xe_1 + e_2 y
7,232
\frac{1}{x + (-1)} \cdot (x \cdot 6 + 9 \cdot (-1)) = \frac{6 - 9/x}{1 - 1/x}
16,048
6 = d^3 + b^2 \cdot b = d^3 - (-b)^3
6,406
1 = (m + 1)!/m! = \dfrac{1}{m!} \cdot (m + 1) \cdot (m + 1 + (-1)) \cdot (m + 1 + 2 \cdot (-1))!
19,710
65 = 8 * 8 + 1 * 1
14,931
X \cdot V = Y\Longrightarrow \frac{\mathrm{d}Y}{\mathrm{d}X} = X \cdot \frac{\mathrm{d}V}{\mathrm{d}X} + V
13,621
y = \cos^{-1}{\frac{z}{\alpha}} \Rightarrow z/\alpha = \cos{y}
19,283
\,a-b = a+(-1)b\,]
19,401
z + z\cdot \frac13\cdot 4 = z\cdot 7/3
24,064
\frac{3}{2} = \frac{1}{2} \cdot (2 + 1) = 1
21,082
\tfrac{1}{d + X} = \tfrac{1}{-X^2 + d^2} \times (d - X)
24,487
8 + 2(-1) = 6 = 3\cdot 2
5,440
((33 + 43*(-1))^2 + (7 + 0*(-1))^2 + (33 + 21*(-1))^2 + (29*(-1) + 33) * (29*(-1) + 33))/4 = 77.25
3,789
(a - b)^2 = a^2 + b \cdot b - 2 \cdot a \cdot b = (a + b)^2 - 4 \cdot a \cdot b
2,165
1/(S*T) = 1/\left(S*T\right)
17,972
\frac1y\times (x + y\times z) = x/y + z + 0\times y
15,445
(4 + z^2)^2 = 16 + z^4 + z^2*8
11,226
(x + z) \times (x + z) = z \times z + x^2 + 2 \times x \times z
31,442
9.75 = \frac14*(9 + 9 + 10 + 11)
12,787
d * d = (d + 6)*(12 + d)\Longrightarrow d = -4
-25,900
0.6 = 9/15
8,162
(c*I - A)*X = C\Longrightarrow \frac{C}{c*I - A} = X