instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Calculate the least common multiple of 44633742 and 24.\n | 178534968\n | ibivibiv/math_instruct | |
In base 10, what is -36703913 - 0?\n | -36703913\n | ibivibiv/math_instruct | |
Suppose 4*q - 49 = -5*t, 4*t + 4 = 2*q + 2*q. Let d = 516 + -290. Calculate the smallest common multiple of d and q.\n | 678\n | ibivibiv/math_instruct | |
What is 383 to the power of 1/6, to the nearest integer?\n | 3\n | ibivibiv/math_instruct | |
List the prime factors of 21379.\n | 21379\n | ibivibiv/math_instruct | |
Let i be ((-78)/(-4095))/((-1)/5). What is the closest to -2/161 in 0, i, 1/31, 3/5?\n | 0\n | ibivibiv/math_instruct | |
Let c(q) = -4*q - 1. Let r(m) = -3*m - 1. Let i(f) = -f**2 + 7*f - 3. Let w be i(6). Let s be (1 + (-5)/(-3))*3. Suppose -w*a - s = 7. What is a*r(v) + 4*c(v)?\n | -v + 1\n | ibivibiv/math_instruct | |
Express -v**4 + v**2 + 38*v - 147*v**3 + 19*v - 84*v + 29*v in the form p*v**3 + s*v**2 + q*v**4 + u + d*v and give p.\n | -147\n | ibivibiv/math_instruct | |
Let z be (-2)/5 + (-24)/15. Let b = z - 3. Let i = b + 2. Sort -4, i, 5 in increasing order.\n | -4, i, 5\n | ibivibiv/math_instruct | |
Let c(h) = -2*h**3 - 6*h**2 - 2*h + 3. What is the remainder when 169 is divided by c(-4)?\n | 40\n | ibivibiv/math_instruct | |
Let q(t) = 20*t**2 - 114 - t + 113 - 15*t**3 - 17*t**2. Let g(v) = -29*v**3 + 5*v**2 - 2*v - 2. Calculate -3*g(d) + 5*q(d).\n | 12*d**3 + d + 1\n | ibivibiv/math_instruct | |
What is the biggest value in 272, 2/3, -73154?\n | 272\n | ibivibiv/math_instruct | |
Let a = -9 + 4. Suppose 0*w = 5*w - 35. Suppose w*t - 4*t = 0. Put 5, a, t in descending order.\n | 5, t, a\n | ibivibiv/math_instruct | |
Suppose -4*a - 91179 = b, -112*b + 109*b - 5*a = 273551. Let o be ((-34365)/(-10))/((-2)/76). Let p = b - o. Round p to the nearest one thousand.\n | 39000\n | ibivibiv/math_instruct | |
Calculate the remainder when 31005 is divided by 52.\n | 13\n | ibivibiv/math_instruct | |
Suppose 7*m = 4*m. Let g = 1 - m. Let q = 24 - g. Is q composite?\n | False\n | ibivibiv/math_instruct | |
Put 6, 2, -4 in decreasing order.\n | 6, 2, -4\n | ibivibiv/math_instruct | |
Express -3 - 6 + 16 - 9 + 1489*j**2 in the form h + w*j + k*j**2 and give k.\n | 1489\n | ibivibiv/math_instruct | |
Express (150*d - 503 - 302*d + 150*d)*(-d**2 + d**2 + d**2) in the form t*d**3 + b + g*d + r*d**2 and give r.\n | -503\n | ibivibiv/math_instruct | |
What is -387959 divided by -5?\n | 387959/5\n | ibivibiv/math_instruct | |
Is -59869 not equal to -59868?\n | True\n | ibivibiv/math_instruct | |
Let a = -7 - -19. What is the remainder when 496/6 + a/(-18) is divided by 21?\n | 19\n | ibivibiv/math_instruct | |
-2240 divided by -560\n | 4\n | ibivibiv/math_instruct | |
What is the hundreds digit of 808741721?\n | 7\n | ibivibiv/math_instruct | |
Find the second derivative of -8*b**4 - 15*b**3 - b**2 - 55*b + 73 wrt b.\n | -96*b**2 - 90*b - 2\n | ibivibiv/math_instruct | |
Let t = 318 + 435. What is the third derivative of -11*z**2 + t*z**3 - 753*z**3 + 7*z**5 + 6*z**5 wrt z?\n | 780*z**2\n | ibivibiv/math_instruct | |
Solve -9*w + 59 + 4 = 0 for w.\n | 7\n | ibivibiv/math_instruct | |
3 (base 10) to base 5\n | 3\n | ibivibiv/math_instruct | |
How many minutes are there between 5:53 PM and 2:06 AM?\n | 493\n | ibivibiv/math_instruct | |
Factor -98*d**2/19 + 54780*d/19 + 1118/19.\n | -2*(d - 559)*(49*d + 1)/19\n | ibivibiv/math_instruct | |
Does 21 divide 408964?\n | False\n | ibivibiv/math_instruct | |
Expand (-3*f + 10*f + f)*(-2079*f + 2079*f - 38*f**3).\n | -304*f**4\n | ibivibiv/math_instruct | |
Simplify ((l*l*l/(l*l*l*(l*l**(-2)*l*l)/l)*l)/(l*l**(-11)/l*l))/(l**(-16)*l*l*l**(1/13)) assuming l is positive.\n | l**(324/13)\n | ibivibiv/math_instruct | |
Let k = 11 - 5. Suppose 0 = 23*j - 137 + 45. Suppose -k - 30 = -j*u. Solve -l + u = 3*f - 1, 0 = 3*l - 5*f + 26 for l.\n | -2\n | ibivibiv/math_instruct | |
Simplify (((sqrt(2) - (sqrt(2)*-2 - sqrt(2))*1)*-6*-5 - (6*sqrt(200) - (4 + sqrt(50)*1)))*-2)**2.\n | 2080*sqrt(2) + 33864\n | ibivibiv/math_instruct | |
Is 885806152 a multiple of 631?\n | False\n | ibivibiv/math_instruct | |
How many kilograms are there in 3524.916g?\n | 3.524916\n | ibivibiv/math_instruct | |
Round -43270 to the nearest 10000.\n | -40000\n | ibivibiv/math_instruct | |
Let l = -0.04 - 0.36. Let d = 3255 - 3252. What is the fourth biggest value in l, d, -2/9, 1?\n | l\n | ibivibiv/math_instruct | |
What is the second derivative of 534957*n**5 - 2*n**3 - 1490053*n wrt n?\n | 10699140*n**3 - 12*n\n | ibivibiv/math_instruct | |
Let q(f) = f**2 + 8*f + 19. Let m be q(-6). Let y be m/(-2)*(-4)/14*4. Calculate the greatest common divisor of 80 and y.\n | 4\n | ibivibiv/math_instruct | |
-2 divided by -15\n | 2/15\n | ibivibiv/math_instruct | |
What is 1336817 to the power of 1/3, to the nearest integer?\n | 110\n | ibivibiv/math_instruct | |
Simplify ((2*sqrt(170) + sqrt(170))*6 - sqrt(170))/(6*(sqrt(10)*1 + sqrt(10))).\n | 17*sqrt(17)/12\n | ibivibiv/math_instruct | |
Let m(o) be the second derivative of 0*o**2 + 16*o + 0 + 0*o**4 + 0*o**5 + 17/6*o**3 - 19/30*o**6. What is the second derivative of m(c) wrt c?\n | -228*c**2\n | ibivibiv/math_instruct | |
Collect the terms in -2*f + 0*f + 17*f**2 - 18*f**2 + 4*f - 69*f**3.\n | -69*f**3 - f**2 + 2*f\n | ibivibiv/math_instruct | |
Solve 0 = 13*c + 3 - 16 for c.\n | 1\n | ibivibiv/math_instruct | |
Which is the second smallest value? (a) 126 (b) -0.2 (c) -4 (d) -1130\n | c\n | ibivibiv/math_instruct | |
Suppose d = x - 1278, 2*d + 1275 = -17*x + 18*x. What is the remainder when x is divided by 37?\n | 23\n | ibivibiv/math_instruct | |
What are the prime factors of 148329969?\n | 3, 49443323\n | ibivibiv/math_instruct | |
Let w = 718 - 715. Put w, -38, -2, 1 in decreasing order.\n | w, 1, -2, -38\n | ibivibiv/math_instruct | |
Let z = -0.103 + -84.897. Let m = z + 85.3. Is -1.3 >= m?\n | False\n | ibivibiv/math_instruct | |
Suppose 0 = -32*o + 26*o + 6924. Let y = o - 819. List the prime factors of y.\n | 5, 67\n | ibivibiv/math_instruct | |
Which is bigger: -0.04 or 4?\n | 4\n | ibivibiv/math_instruct | |
Put -62, 11928, -3 in increasing order.\n | -62, -3, 11928\n | ibivibiv/math_instruct | |
Convert -858476 (base 11) to base 4.\n | -11033022130\n | ibivibiv/math_instruct | |
Let z(g) = -13*g + 246. Let k(l) = 15*l - 245. Let m(x) = -3*k(x) - 4*z(x). Let q be m(36). Put 4, -2, -6, q in decreasing order.\n | 4, q, -2, -6\n | ibivibiv/math_instruct | |
Rearrange (-2*u**2 + 0*u**2 - 5*u**2)*(-12 + 12 + 19*u + (-5*u + 3*u + 0*u)*(1 - 3 + 3)) to j*u + b*u**2 + l + k*u**3 and give k.\n | -119\n | ibivibiv/math_instruct | |
Solve 5*t = -5*l + 40, -3*t + 18 - 6 = -l for t.\n | 5\n | ibivibiv/math_instruct | |
In base 8, what is 25546 - -23?\n | 25571\n | ibivibiv/math_instruct | |
What is the closest to -1 in -1/6, 0.4, 7.8, -1/4?\n | -1/4\n | ibivibiv/math_instruct | |
Let v = 1613 - 1141. Suppose v = 9*f - f. Does 17 divide f?\n | False\n | ibivibiv/math_instruct | |
Let t be 2*2/4 + -1. Suppose -g - y - 1 + 6 = t, 2*g - 13 = -3*y. Differentiate -x**2 - 3 + 0*x**2 + g with respect to x.\n | -2*x\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Ordering Principle
## Theorem
Let $S$ be a set.
Then there exists a total ordering on $S$.
## Proof 1
From the Well-Ordering Theorem, $S$ has a well-ordering.
The result follows from Well-Ordering is Total Ordering.
... | The field of set theory is fundamental to modern mathematics, providing a framework for organizing and studying abstract objects and their properties. At its core, set theory seeks to answer questions about collections of objects, called sets, and how they can be ordered and compared. Two important principles in this ... | ibivibiv/math_instruct | |
Suppose 3*j = 3*c + 108, 2*c - 37 = 4*c + 5*j. Let h be -12 - -12 - (2 - 86). Let g = c + h. Is g a multiple of 14?\n | False\n | ibivibiv/math_instruct | |
Simplify (k*k*k/(k*k**(-2/7))*k*k*k*(k*k**(-6))/k*k)/(k*k**0*k)**(4/5) assuming k is positive.\n | k**(-46/35)\n | ibivibiv/math_instruct | |
((-9)/(-25))/9*-4*1\n | -4/25\n | ibivibiv/math_instruct | |
What is the fifth smallest value in 0.4, -2, -4/7, 232, -0.5?\n | 232\n | ibivibiv/math_instruct | |
Work out -770 * -0.7.\n | 539\n | ibivibiv/math_instruct | |
Factor f**4/5 - f**3/5 - 2*f**2 - 8*f/5.\n | f*(f - 4)*(f + 1)*(f + 2)/5\n | ibivibiv/math_instruct | |
Let r be (-34 - 5)*3/21. Let h = 163/28 + r. Which is the second biggest value? (a) h (b) -1 (c) 0.2 (d) 0.1\n | c\n | ibivibiv/math_instruct | |
What are the prime factors of 409?\n | 409\n | ibivibiv/math_instruct | |
Let b(c) = 4*c**2 + 4*c + 4. Suppose t + t - 4 = 0. Let d(f) = -5*f - 5*f**t + 2 - 4 + 0*f - 3. Suppose 5*r - 1 + 16 = 0. Calculate r*d(o) - 4*b(o).\n | -o**2 - o - 1\n | ibivibiv/math_instruct | |
Solve 0 = -85*t - 9559 + 12364 for t.\n | 33\n | ibivibiv/math_instruct | |
Expand (54*i + 14*i - 13*i)*(-i - 2 + 0 + 5*i).\n | 220*i**2 - 110*i\n | ibivibiv/math_instruct | |
Let d(z) = 3*z - 25. Let b be d(-5). Let m = b + 36. Put m, -5, -1, -3 in descending order.\n | -1, -3, m, -5\n | ibivibiv/math_instruct | |
Is 72019 composite?\n | False\n | ibivibiv/math_instruct | |
What is prob of picking 1 u, 1 d, and 2 g when four letters picked without replacement from gpigggdgiiud?\n | 4/99\n | ibivibiv/math_instruct | |
Let f = -12643 + 24042. Is f a composite number?\n | False\n | ibivibiv/math_instruct | |
Let y(n) be the third derivative of n**5/12 + 3*n**2. Let a be y(-2). What is the greatest common divisor of 220 and a?\n | 20\n | ibivibiv/math_instruct | |
Let k(a) = -9*a - 2. Let n be 3*(-6)/2*6/(-9). Let f(l) be the third derivative of 1/6*l**3 + l**2 + 0 + 5/24*l**4 + 0*l. Determine n*k(h) + 11*f(h).\n | h - 1\n | ibivibiv/math_instruct | |
What is -16467 plus -3?\n | -16470\n | ibivibiv/math_instruct | |
Let z(g) = -g**3 - 2*g**2 + 11*g + 6. Let h be z(-5). Suppose 0 = -h*d - 66560 + 189670. Is d prime?\n | False\n | ibivibiv/math_instruct | |
Calculate the greatest common factor of 36 and 44.\n | 4\n | ibivibiv/math_instruct | |
Let f(r) be the second derivative of -r**4/12 - 8*r**3/3 + r**2/2 + 3*r. Is f(-8) composite?\n | True\n | ibivibiv/math_instruct | |
Which is bigger: 0 or 3/17972734?\n | 3/17972734\n | ibivibiv/math_instruct | |
Simplify (6*(sqrt(77)/(sqrt(7)*-5) + 2) + -1)*-6.\n | -66 + 36*sqrt(11)/5\n | ibivibiv/math_instruct | |
What is 13/65*24 + 12/10?\n | 6\n | ibivibiv/math_instruct | |
Let m(x) = -151351*x**2 - 352*x + 15. Let w be m(-5). Round w to the nearest 1000000.\n | -4000000\n | ibivibiv/math_instruct | |
Let r = -33/14 - -45/28. Which is the nearest to 9? (a) -2/3 (b) -4/3 (c) r\n | a\n | ibivibiv/math_instruct | |
What is the thousands digit of 12457948?\n | 7\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# On a special kind of graph connectig n point to n points.
I don't know anything about graph theory and I was wondering about something :
If you draw two parallel rows of n points in $\mathbb R^4$ and link each point with ... | The concept you are describing involves graph theory, specifically a type of graph known as a complete bipartite graph, along with some elements of geometry and topology. Lets break down these concepts step by step to provide a thorough understanding.
1. **Graph Theory:** A graph is a collection of objects called ver... | ibivibiv/math_instruct | |
Let m = 581.04 - 32.84. Let j = m - 641. Let i = j + 93. What is the closest to 7 in i, 0, 4?\n | 4\n | ibivibiv/math_instruct | |
Differentiate 5022288*g + 6286726.\n | 5022288\n | ibivibiv/math_instruct | |
Which is the biggest value? (a) -4 (b) -1/3 (c) 0 (d) -1/4 (e) -0.1\n | c\n | ibivibiv/math_instruct | |
Express -2*p**4 + 18*p**2 + 4*p**2 + 27*p**2 + (1319*p**2 + 64*p**3 - 1319*p**2)*(2*p + 3*p - 7*p) as x*p**2 + k*p**3 + s*p**4 + y*p + a and give s.\n | -130\n | ibivibiv/math_instruct | |
Find the second derivative of 1236091*s**3*x - 15*s**2 + 985*s*x - s - 331*x - 2 wrt s.\n | 7416546*s*x - 30\n | ibivibiv/math_instruct | |
Which is the biggest value? (a) -1/23 (b) 731 (c) 1 (d) 2/11 (e) -0.5 (f) -0.4 (g) 1/4\n | b\n | ibivibiv/math_instruct | |
What is the fourth smallest value in -2/3, -1/31, 2/9, 4/3, 3?\n | 4/3\n | ibivibiv/math_instruct | |
Calculate the greatest common factor of 2219 and 14899.\n | 317\n | ibivibiv/math_instruct |
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