ddrg/math_formulas · Datasets at Hugging Face

id int64 -30,985 55.9k	text stringlengths 5 437k
-1,295	30/15 = 30\cdot \frac{1}{15}/(15\cdot \frac{1}{15}) = 2
-4,782	\frac{-3x + 12}{x^2 - 7x + 10} = -\frac{1}{2\left(-1\right) + x}2 - \tfrac{1}{x + 5(-1)}
26,168	2\cdot y \gt 3 - y\Longrightarrow y > 1
20,608	(m + 1)\cdot (m + (-1)) = m^2 + (-1)
10,117	(b^2 f + bf^2) \cdot 3 = bf \cdot f \cdot 3 + fb^2 \cdot 3
-19,617	\frac{10}{9}\times 7 = \tfrac19\times 70
-1,305	-2/3\cdot (-\frac{3}{4}) = \left((-1)\cdot 2\cdot \frac13\right)/(\frac{1}{3}\cdot (-4))
-24,225	(6 + 2)^2 = 8 \cdot 8 = 8^2 = 64
17,302	0.5 \cdot x = 1.5 \cdot x - x
26,494	-p^2 + d^2 = (p + d) \cdot (d - p)
-9,265	-d^235 + d14 = -57dd + 27*d
-1,333	\frac{1}{3}\cdot 2\cdot (-2/9) = (\left(-1\right)\cdot 2\cdot 1/9)/(3\cdot 1/2)
18,854	\frac{1 + x^2}{(-1) + x^2} = \frac{1}{1 - \tfrac{1}{x} \cdot \tfrac{1}{x}} \cdot (1/x \cdot 1/x + 1)
20,662	2(-1) + 2k = 2*(\left(-1\right) + k)
1,267	-k^3 = -k k*(-k) = -k = -k
9,821	\|e^{x'i}h_2 + e^{iy}h_1\|^2 = h_1^2 + h_1h_2\cos(-x' + y)2 + h_2 h_2
-13,724	\frac{16}{8 + 6 (-1)} = \frac{16}{2} = 16/2 = 8
12,421	r^2\cdot \pi\cdot \pi\cdot x\cdot 2 = 2\cdot \pi \cdot \pi\cdot r^2\cdot x
18,906	d_2\cdot l = (d_2\cdot l)^{d_1} = d_2^{d_1}\cdot l^{d_1}
11,171	\sin(x)\cdot \sin(y) = \sin\left(x\right)\cdot \sin(y)
-21,858	-8/5 + \dfrac{1}{6} \cdot 9 = -\frac{8 \cdot 6}{5 \cdot 6} + \frac{1}{6 \cdot 5} \cdot 45 = -48/30 + 45/30 = -\frac{1}{30} \cdot \left(48 + 45\right) = -\frac{3}{30}
13,797	-4 \cdot 4 + 4 \cdot 26 \cdot 2 = 192
2,290	s + \frac{1}{2}\cdot (2 - s) = 2\cdot s/2 + (2 - s)/2 = \frac12\cdot (s + 2)
14,246	(-1/3 - \dfrac{1}{8} + 1/24 + \frac12) \cdot 2 = 1/6
2,977	\tfrac{1}{(n/4)^{1/2}}(X - \frac12n) = \frac{X*2}{n^{1/2}} - n^{1/2}
-19,666	14/8 = \tfrac1814
26,036	4\cdot q^2\cdot \pi - \pi\cdot q^2 = \pi\cdot q^2\cdot 3
35,210	1 = -x + n \Rightarrow x = (-1) + n
30,416	134 = 11 \cdot 11 + 3^2 + 2^2 = 10^2 + 5^2 + 3^2 = 9^2 + 7^2 + 2^2 = 7^2 + 7^2 + 6^2
24,236	B \backslash G + y = B \cap G + y^\complement = B \cap G^\complement + y
-14,150	\frac{66}{3 + 8} = 66/11 = \frac{1}{11} \cdot 66 = 6
40,187	23 = 54617663 - 77\cdot 709320
22,445	1 = \|1\| = \|\dfrac1x \times x\| = \|x\| \times \|\frac1x\|
15,705	v \cdot Y = v \Rightarrow \dfrac{v}{Y} = v
5,960	\sin(3t) = 3\sin t - 4\sin^3t
17,614	\cos(z + i\cdot y) = \cos{z}\cdot \cos{i\cdot y} - \sin{z}\cdot \sin{i\cdot y} = \cos{z}\cdot \cosh{y} - i\cdot \sin{z}\cdot \sinh{y}
4,583	\frac{1}{3}\cdot (3 + (-1)) = 2/3
-19,712	\dfrac1528 = 47/(5)
114	\dfrac{\tfrac{1}{12}}{2} \cdot 1 = \frac{1}{24}
-1,730	\pi \cdot 5/6 - \frac{1}{6} \cdot 11 \cdot \pi = -\pi
9,973	x^2 + y^2 + z^2 = 2x \cdot x + 1 = 2xyz + 1
26,964	-8 = 8 \cdot \left(\cos{\pi} + i \cdot \sin{\pi}\right)
1,053	z\cdot y\cdot 2 + z^2 + y^2 = (z + y)^2
314	a^3 + b * b * b + c^2 * c - bca3 = (a + b + c)(-ca + a^2 + b b + c^2 - ab - cb)
10,640	E\left[R_2 \times R_1\right] = E\left[-R_2 \times R_1\right] = E\left[-R_2 \times R_1\right] = -E\left[R_2 \times R_1\right]
-19,735	2/2 = \frac{1}{1\cdot 2}\cdot 2
16,007	-(h + x + f) \cdot 6 = -h \cdot x \cdot 3 + 2 \cdot \left(x + f + h\right) \cdot \left(x + f + h\right) - x \cdot f \cdot 3 - 3 \cdot f \cdot h \Rightarrow 0 = h \cdot x + f \cdot x + f \cdot h
33,576	x\cdot 0.01\cdot y = y\cdot 0.01\cdot x
23,019	(a + c)/b = (-1) + \dfrac1b\left(a + b + c\right)
24,077	1/4 = \frac{1}{36} + 1/9 + 1/9
-2,090	-\pi\cdot 4/3 + \pi/6 = -\pi\cdot 7/6
6,888	\frac{\frac{2}{9}}{1/3}\cdot 1 = \frac{1}{3}\cdot 2
28,575	9 + 9^2 + 9 \cdot (10^2 + \left(-1\right)) = 9 \cdot (1 + 10^2 + (-1) + 9) = 9 \cdot (10 \cdot 10 + 9) = 981
-20,000	\frac{5(-1) - 7z}{5(-1) - 7z} \dfrac{1}{8}9 = \frac{45 (-1) - 63 z}{40 (-1) - 56 z}
18,500	\binom{\left(-1\right) + p}{q + (-1)} p = \binom{p}{q} q
28,748	e + e - b = -b + e\cdot 2
35,040	4!/2 = \frac{24}{2} = 12 = 3*2^2
1,584	k = 316^2 - 3^6\cdot 17 = 316^2 - 3^4\cdot 3^2\cdot 17 = 316 \cdot 316 - 3^4\cdot \left(296^2 - k\right)
658	a^{(-1) + n} + ... + k^{3\cdot \left(-1\right) + n}\cdot a^2 + a\cdot k^{n + 2\cdot (-1)} + k^{(-1) + n} = \dfrac{1}{-k + a}\cdot \left(a^n - k^n\right)
12,609	c + f_2 + f_1 = c + f_2 + f_1
-28,798	150 = \frac{\pi}{1/150 \cdot 2\pi}2
4,136	\left((6\times 2^{1/2})^2 + 4 \times 4\right)^{1/2} = (72 + 16)^{1/2} = 88^{1/2}
-12,335	5\cdot \sqrt{7} = \sqrt{175}
32,443	2^4*3^4 = 1296
6,846	1/2 = 1/2\frac{1}{2} + \frac12\dfrac{1}{2}
40,194	3 + 2(-\dfrac{4}{3}) = 1/3
21,851	3b - b = 60 rightarrow 30 = b
1,791	c + 2 = 3 + c + (-1)
24,230	C_{2 + n} = C_{n + 1} + C_n \implies C_{n + 1} = -C_n + C_{2 + n}
2,030	\tfrac{1}{1 + x}(x^2 + 2x + 2) = x + 1 + \frac{1}{1 + x}
32,272	5 \cdot 5 - \left\lceil{\tfrac16 \cdot 5}\right\rceil + 5 \cdot (-1) = 19
-7,626	\dfrac{1}{-i + 2}\cdot (i\cdot 13 - 1)\cdot \frac{1}{i + 2}\cdot (2 + i) = \frac{1}{-i + 2}\cdot (13\cdot i - 1)
-23,143	-\tfrac{1}{3}4\cdot 3/2 = -2
8,985	1/(UT) = \frac{1}{TU}
-26,139	10 \cdot (e^{14} + (-1)) = e^{14} \cdot 10 - 10 e^0
21,272	(c + b)^2 = c^2 + b c\cdot 2 + b^2
23,568	(3^{2^9} + \left(-1\right)) \left(3^{2^9} + 1\right) = 3^{2^{10}} + (-1)
-7,396	\dfrac{1/9\cdot 4}{5} = 4/45
-621	\frac{\pi}{3} = \frac{25}{3}\cdot \pi - \pi\cdot 8
5,846	-24 = h \times 32 \implies h = -3/4
34,763	163\cdot (-1) + 42^2 = 40^2 + 1^2
7,820	a^2 - b^2 = \left(b + a\right)*\left(-b + a\right)
7,949	\sin(x) \cos(x) \cdot 2 = \sin\left(2 x\right)
4,238	z = 4 - x^2 - y^2\Longrightarrow 0 = x^2 + y^2 + z + 4*(-1)
8,956	4 \cdot (4^j + (-1)) = 4^{j + 1} + 4(-1) = 4^{j + 1} + 3(-1) + (-1)
8,569	2z = z + 1 - 1 - z
29,115	f + yx*3 = 0 \Rightarrow -f/\left(3x\right) = y
-2,199	\tfrac{2}{13} = 6/13 - \frac{4}{13}
-4,476	\frac{1}{10 + x^2 - 7 \cdot x} \cdot \left(33 - 9 \cdot x\right) = -\frac{5}{x + 2 \cdot \left(-1\right)} - \dfrac{1}{x + 5 \cdot (-1)} \cdot 4
8,437	\cos{\frac18 \cdot \pi} = (2^{1/2} + 2)^{1/2}/2
4,365	\frac{1}{7}6 = 6/7
8,064	π/2 = π/10 + π\cdot 2/5
-434	3/2\pi = -6\pi + \pi*15/2
30,087	w^T\cdot q = w^T\cdot q
12,818	3 \cdot \dfrac{930}{2} \cdot 1 = 1395
-15,170	\dfrac{n^4}{p^9\cdot \frac{1}{n^3}} = \dfrac{1}{\frac{1}{\dfrac{1}{p^9}\cdot n^2 \cdot n}\cdot \dfrac{1}{n^4}}
29,890	\frac{z + \left(-1\right)}{(z + (-1))^2} = \frac{1}{(-1) + z}
26,303	1 = (\sqrt{15} + 4)^{\tfrac{1}{3}}\cdot \left(4 - \sqrt{15}\right)^{1/3}
-1,548	5/8 = \dfrac{1}{8}\cdot 5
-25,371	\tan{y} = \frac{1}{\cos{y}}*\sin{y}

-1,295

30/15 = 30\cdot \frac{1}{15}/(15\cdot \frac{1}{15}) = 2

-4,782

\frac{-3x + 12}{x^2 - 7x + 10} = -\frac{1}{2\left(-1\right) + x}2 - \tfrac{1}{x + 5(-1)}

26,168

2\cdot y \gt 3 - y\Longrightarrow y > 1

20,608

(m + 1)\cdot (m + (-1)) = m^2 + (-1)

10,117

(b^2 f + bf^2) \cdot 3 = bf \cdot f \cdot 3 + fb^2 \cdot 3

-19,617

\frac{10}{9}\times 7 = \tfrac19\times 70

-1,305

-2/3\cdot (-\frac{3}{4}) = \left((-1)\cdot 2\cdot \frac13\right)/(\frac{1}{3}\cdot (-4))

-24,225

(6 + 2)^2 = 8 \cdot 8 = 8^2 = 64

17,302

0.5 \cdot x = 1.5 \cdot x - x

26,494

-p^2 + d^2 = (p + d) \cdot (d - p)

-9,265

-d^2*35 + d*14 = -5*7*d*d + 2*7*d

-1,333

\frac{1}{3}\cdot 2\cdot (-2/9) = (\left(-1\right)\cdot 2\cdot 1/9)/(3\cdot 1/2)

18,854

\frac{1 + x^2}{(-1) + x^2} = \frac{1}{1 - \tfrac{1}{x} \cdot \tfrac{1}{x}} \cdot (1/x \cdot 1/x + 1)

20,662

2*(-1) + 2*k = 2*(\left(-1\right) + k)

1,267

-k^3 = -k k*(-k) = -k = -k

9,821

|e^{x'*i}*h_2 + e^{i*y}*h_1|^2 = h_1^2 + h_1*h_2*\cos(-x' + y)*2 + h_2 * h_2

-13,724

\frac{16}{8 + 6 (-1)} = \frac{16}{2} = 16/2 = 8

12,421

r^2\cdot \pi\cdot \pi\cdot x\cdot 2 = 2\cdot \pi \cdot \pi\cdot r^2\cdot x

18,906

d_2\cdot l = (d_2\cdot l)^{d_1} = d_2^{d_1}\cdot l^{d_1}

11,171

\sin(x)\cdot \sin(y) = \sin\left(x\right)\cdot \sin(y)

-21,858

-8/5 + \dfrac{1}{6} \cdot 9 = -\frac{8 \cdot 6}{5 \cdot 6} + \frac{1}{6 \cdot 5} \cdot 45 = -48/30 + 45/30 = -\frac{1}{30} \cdot \left(48 + 45\right) = -\frac{3}{30}

13,797

-4 \cdot 4 + 4 \cdot 26 \cdot 2 = 192

2,290

s + \frac{1}{2}\cdot (2 - s) = 2\cdot s/2 + (2 - s)/2 = \frac12\cdot (s + 2)

14,246

(-1/3 - \dfrac{1}{8} + 1/24 + \frac12) \cdot 2 = 1/6

2,977

\tfrac{1}{(n/4)^{1/2}}*(X - \frac12*n) = \frac{X*2}{n^{1/2}} - n^{1/2}

-19,666

14/8 = \tfrac1814

26,036

4\cdot q^2\cdot \pi - \pi\cdot q^2 = \pi\cdot q^2\cdot 3

35,210

1 = -x + n \Rightarrow x = (-1) + n

30,416

134 = 11 \cdot 11 + 3^2 + 2^2 = 10^2 + 5^2 + 3^2 = 9^2 + 7^2 + 2^2 = 7^2 + 7^2 + 6^2

24,236

B \backslash G + y = B \cap G + y^\complement = B \cap G^\complement + y

-14,150

\frac{66}{3 + 8} = 66/11 = \frac{1}{11} \cdot 66 = 6

40,187

23 = 54617663 - 77\cdot 709320

22,445

1 = |1| = |\dfrac1x \times x| = |x| \times |\frac1x|

15,705

v \cdot Y = v \Rightarrow \dfrac{v}{Y} = v

5,960

\sin(3t) = 3\sin t - 4\sin^3t

17,614

\cos(z + i\cdot y) = \cos{z}\cdot \cos{i\cdot y} - \sin{z}\cdot \sin{i\cdot y} = \cos{z}\cdot \cosh{y} - i\cdot \sin{z}\cdot \sinh{y}

4,583

\frac{1}{3}\cdot (3 + (-1)) = 2/3

-19,712

\dfrac15*28 = 4*7/(5)

114

\dfrac{\tfrac{1}{12}}{2} \cdot 1 = \frac{1}{24}

-1,730

\pi \cdot 5/6 - \frac{1}{6} \cdot 11 \cdot \pi = -\pi

9,973

x^2 + y^2 + z^2 = 2x \cdot x + 1 = 2xyz + 1

26,964

-8 = 8 \cdot \left(\cos{\pi} + i \cdot \sin{\pi}\right)

1,053

z\cdot y\cdot 2 + z^2 + y^2 = (z + y)^2

314

a^3 + b * b * b + c^2 * c - b*c*a*3 = (a + b + c)*(-c*a + a^2 + b * b + c^2 - a*b - c*b)

10,640

E\left[R_2 \times R_1\right] = E\left[-R_2 \times R_1\right] = E\left[-R_2 \times R_1\right] = -E\left[R_2 \times R_1\right]

-19,735

2/2 = \frac{1}{1\cdot 2}\cdot 2

16,007

-(h + x + f) \cdot 6 = -h \cdot x \cdot 3 + 2 \cdot \left(x + f + h\right) \cdot \left(x + f + h\right) - x \cdot f \cdot 3 - 3 \cdot f \cdot h \Rightarrow 0 = h \cdot x + f \cdot x + f \cdot h

33,576

x\cdot 0.01\cdot y = y\cdot 0.01\cdot x

23,019

(a + c)/b = (-1) + \dfrac1b\left(a + b + c\right)

24,077

1/4 = \frac{1}{36} + 1/9 + 1/9

-2,090

-\pi\cdot 4/3 + \pi/6 = -\pi\cdot 7/6

6,888

\frac{\frac{2}{9}}{1/3}\cdot 1 = \frac{1}{3}\cdot 2

28,575

9 + 9^2 + 9 \cdot (10^2 + \left(-1\right)) = 9 \cdot (1 + 10^2 + (-1) + 9) = 9 \cdot (10 \cdot 10 + 9) = 981

-20,000

\frac{5(-1) - 7z}{5(-1) - 7z} \dfrac{1}{8}9 = \frac{45 (-1) - 63 z}{40 (-1) - 56 z}

18,500

\binom{\left(-1\right) + p}{q + (-1)} p = \binom{p}{q} q

28,748

e + e - b = -b + e\cdot 2

35,040

4!/2 = \frac{24}{2} = 12 = 3*2^2

1,584

k = 316^2 - 3^6\cdot 17 = 316^2 - 3^4\cdot 3^2\cdot 17 = 316 \cdot 316 - 3^4\cdot \left(296^2 - k\right)

658

a^{(-1) + n} + ... + k^{3\cdot \left(-1\right) + n}\cdot a^2 + a\cdot k^{n + 2\cdot (-1)} + k^{(-1) + n} = \dfrac{1}{-k + a}\cdot \left(a^n - k^n\right)

12,609

c + f_2 + f_1 = c + f_2 + f_1

-28,798

150 = \frac{\pi}{1/150 \cdot 2\pi}2

4,136

\left((6\times 2^{1/2})^2 + 4 \times 4\right)^{1/2} = (72 + 16)^{1/2} = 88^{1/2}

-12,335

5\cdot \sqrt{7} = \sqrt{175}

32,443

2^4*3^4 = 1296

6,846

1/2 = 1/2*\frac{1}{2} + \frac12*\dfrac{1}{2}

40,194

3 + 2(-\dfrac{4}{3}) = 1/3

21,851

3b - b = 60 rightarrow 30 = b

1,791

c + 2 = 3 + c + (-1)

24,230

C_{2 + n} = C_{n + 1} + C_n \implies C_{n + 1} = -C_n + C_{2 + n}

2,030

\tfrac{1}{1 + x}(x^2 + 2x + 2) = x + 1 + \frac{1}{1 + x}

32,272

5 \cdot 5 - \left\lceil{\tfrac16 \cdot 5}\right\rceil + 5 \cdot (-1) = 19

-7,626

\dfrac{1}{-i + 2}\cdot (i\cdot 13 - 1)\cdot \frac{1}{i + 2}\cdot (2 + i) = \frac{1}{-i + 2}\cdot (13\cdot i - 1)

-23,143

-\tfrac{1}{3}4\cdot 3/2 = -2

8,985

1/(UT) = \frac{1}{TU}

-26,139

10 \cdot (e^{14} + (-1)) = e^{14} \cdot 10 - 10 e^0

21,272

(c + b)^2 = c^2 + b c\cdot 2 + b^2

23,568

(3^{2^9} + \left(-1\right)) \left(3^{2^9} + 1\right) = 3^{2^{10}} + (-1)

-7,396

\dfrac{1/9\cdot 4}{5} = 4/45

-621

\frac{\pi}{3} = \frac{25}{3}\cdot \pi - \pi\cdot 8

5,846

-24 = h \times 32 \implies h = -3/4

34,763

163\cdot (-1) + 42^2 = 40^2 + 1^2

7,820

a^2 - b^2 = \left(b + a\right)*\left(-b + a\right)

7,949

\sin(x) \cos(x) \cdot 2 = \sin\left(2 x\right)

4,238

z = 4 - x^2 - y^2\Longrightarrow 0 = x^2 + y^2 + z + 4*(-1)

8,956

4 \cdot (4^j + (-1)) = 4^{j + 1} + 4(-1) = 4^{j + 1} + 3(-1) + (-1)

8,569

2z = z + 1 - 1 - z

29,115

f + yx*3 = 0 \Rightarrow -f/\left(3x\right) = y

-2,199

\tfrac{2}{13} = 6/13 - \frac{4}{13}

-4,476

\frac{1}{10 + x^2 - 7 \cdot x} \cdot \left(33 - 9 \cdot x\right) = -\frac{5}{x + 2 \cdot \left(-1\right)} - \dfrac{1}{x + 5 \cdot (-1)} \cdot 4

8,437

\cos{\frac18 \cdot \pi} = (2^{1/2} + 2)^{1/2}/2

4,365

\frac{1}{7}6 = 6/7

8,064

π/2 = π/10 + π\cdot 2/5

-434

3/2*\pi = -6*\pi + \pi*15/2

30,087

w^T\cdot q = w^T\cdot q

12,818

3 \cdot \dfrac{930}{2} \cdot 1 = 1395

-15,170

\dfrac{n^4}{p^9\cdot \frac{1}{n^3}} = \dfrac{1}{\frac{1}{\dfrac{1}{p^9}\cdot n^2 \cdot n}\cdot \dfrac{1}{n^4}}

29,890

\frac{z + \left(-1\right)}{(z + (-1))^2} = \frac{1}{(-1) + z}

26,303

1 = (\sqrt{15} + 4)^{\tfrac{1}{3}}\cdot \left(4 - \sqrt{15}\right)^{1/3}

-1,548

5/8 = \dfrac{1}{8}\cdot 5

-25,371

\tan{y} = \frac{1}{\cos{y}}*\sin{y}