instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Evaluate (-86)/(-43)*(-2)/((-4)/(-1)).\n | -1\n | ibivibiv/math_instruct | |
Let m(c) = 2*c - 284 - 50 + 8*c - 56 + 8*c. Calculate m(22).\n | 6\n | ibivibiv/math_instruct | |
Is 1546 not equal to 1546?\n | False\n | ibivibiv/math_instruct | |
What are the prime factors of 869801564?\n | 2, 217450391\n | ibivibiv/math_instruct | |
What is the ten thousands digit of 828425?\n | 2\n | ibivibiv/math_instruct | |
Let h(b) = 164*b - 2828. What is h(16)?\n | -204\n | ibivibiv/math_instruct | |
Solve 2*a = -4*u - 92, 11*a + 4*u - 12 = -59 - 45 for a.\n | 0\n | ibivibiv/math_instruct | |
Simplify (w/(w*w**(-8))*w*w/(w*w*w**(-5)*w))**(-6)*((w/((w*(w/(w*w**6))/w)/w)*w)/w**(-1/4))**0 assuming w is positive.\n | w**(-72)\n | ibivibiv/math_instruct | |
Convert 72159.21 millilitres to litres.\n | 72.15921\n | ibivibiv/math_instruct | |
Suppose -m + 9 = -6. Let s be (-1)/(27/m - 2). Suppose 3*a - s - 1 = 0. What are the prime factors of a?\n | 2\n | ibivibiv/math_instruct | |
Calculate the greatest common divisor of 75953 and 4527.\n | 503\n | ibivibiv/math_instruct | |
Suppose 37*h - 28 = 120. Solve 4*i = -4, h*i = v + 5*i + 6 for v.\n | -5\n | ibivibiv/math_instruct | |
Solve 155*y = 74*y + 75*y + 12 for y.\n | 2\n | ibivibiv/math_instruct | |
What are the prime factors of 27238648?\n | 2, 59, 57709\n | ibivibiv/math_instruct | |
b"What is the hth term of 311, 154, -9, -172, -329, -474, -601?\n" | h**3 - 9*h**2 - 137*h + 456\n | ibivibiv/math_instruct | |
What is 15.12 rounded to the nearest integer?\n | 15\n | ibivibiv/math_instruct | |
How many months are there in 6/5 of a millennium?\n | 14400\n | ibivibiv/math_instruct | |
Is 31393178 a multiple of 83?\n | False\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Why are $S$-arithmetic groups interesting?
Let $K$ be a number field and $S$ a finite set of valuations of $K$, including $\infty$.
Define the $S$-numbers $K_S$ to be the direct product $\prod_{s \in S} K_s$ where $K_s$ d... | Number fields and their associated objects are fundamental structures in the realm of number theory, a branch of pure mathematics concerned with the properties and relationships of numbers, particularly integers. When studying number fields, two crucial definitions are those of $S$-numbers and $S$-integers, which allo... | ibivibiv/math_instruct | |
Suppose -5 = -27*c + 22*c. Let x be 4 - (-2 + c) - (-1)/(-1). Solve 0 = -x*j + u - 14, 2*j - 4*u = -0*u for j.\n | -4\n | ibivibiv/math_instruct | |
Let i = -1 - -9. Let t be (-1)/3*18/i. Let r(m) = 42*m + 843. Let d be r(-20). What is the nearest to 1 in t, d, -2?\n | t\n | ibivibiv/math_instruct | |
Suppose -7*g + 7224 = 14*g. What are the prime factors of g?\n | 2, 43\n | ibivibiv/math_instruct | |
Calculate -4*(-8)/6*321/(-19688).\n | -2/23\n | ibivibiv/math_instruct | |
Calculate the remainder when 249 is divided by 64.\n | 57\n | ibivibiv/math_instruct | |
What is the third root of 15381705 to the nearest integer?\n | 249\n | ibivibiv/math_instruct | |
Let i = 3.84 - -0.16. Put -3, -6, i in descending order.\n | i, -3, -6\n | ibivibiv/math_instruct | |
0/(((-60)/(-8))/5*-2)\n | 0\n | ibivibiv/math_instruct | |
79.35 times -131\n | -10394.85\n | ibivibiv/math_instruct | |
Suppose -13*f - 187 + 252 = 0. Let b(i) be the first derivative of i**3/3 - 2*i**2 - 5*i + 4. Give b(f).\n | 0\n | ibivibiv/math_instruct | |
Simplify ((h**0/h)**(-9)*(h**(-2)/h)/h**(1/4))**(-48) assuming h is positive.\n | h**(-276)\n | ibivibiv/math_instruct | |
Is 589001 prime?\n | False\n | ibivibiv/math_instruct | |
Calculate 6 + 4 + -5 + (-11 - 2).\n | -8\n | ibivibiv/math_instruct | |
What is the thousands digit of 14042?\n | 4\n | ibivibiv/math_instruct | |
Let c be (-60)/6*(-1)/2. Suppose c*v = 56 + 4. Calculate the remainder when v is divided by 7.\n | 5\n | ibivibiv/math_instruct | |
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"# Absolute Values on Q (Part I)
Real numbers, Q, can be constructed from the rational numbers Q={a/b where a,b ϵ the integers Z}. Construction of p-adic numbers, Qp, is done exactly the same way.
Let’s now consider absolut... | Now let's delve into the world of absolute values on Q, starting with the definition of an absolute value itself. Simply stated, an absolute value is a function that maps real numbers to non-negative numbers while adhering to certain conditions. These conditions include:
1. The absolute value of zero must be zero, i.... | ibivibiv/math_instruct | |
What is the second derivative of -354*f**3*r**2 - 2*f**3*r - 3*f**2 - 2443*f*r**2 - 1314*f*r + f - 35*r**2 - 21*r - 43 wrt r?\n | -708*f**3 - 4886*f - 70\n | ibivibiv/math_instruct | |
Suppose 2*u + 4*n - 22 = 0, u = -u + 4*n - 2. Suppose 23 = 2*t + 4*y - y, -u*y + 29 = 2*t. Calculate the lowest common multiple of 1 and t.\n | 7\n | ibivibiv/math_instruct | |
Let j(m) = -m**2 + 18*m - 46. Let y be j(14). Suppose -5*h + 5*d + 0*d - y = 0, -3*d = -h - 6. Solve 15 = 5*v - h*v for v.\n | 3\n | ibivibiv/math_instruct | |
Calculate prob of picking 1 c and 2 a when three letters picked without replacement from {b: 1, e: 5, c: 3, a: 4}.\n | 9/143\n | ibivibiv/math_instruct | |
Expand (y - 2*y + 5*y)*((74 + 1 - 12)*(-3 + 2 + 2) - 23 + 6 - 2).\n | 176*y\n | ibivibiv/math_instruct | |
Sort -1, 3, -40, -4, 0 in descending order.\n | 3, 0, -1, -4, -40\n | ibivibiv/math_instruct | |
Round 7097000 to the nearest 1000000.\n | 7000000\n | ibivibiv/math_instruct | |
Let r(w) = w**3 - 5*w**2 - 6*w - 3. Suppose 6*c = 5*c - 4. Let l be (c/(-6))/((-8)/(-60)). Suppose 5*g = 3*t + 24, -l*g = -g - 5*t - 14. Calculate r(g).\n | -3\n | ibivibiv/math_instruct | |
Suppose -88*o = -86*o - 1530. Is o a multiple of 45?\n | True\n | ibivibiv/math_instruct | |
b"What is the cth term of -809, -804, -795, -782, -765?\n" | 2*c**2 - c - 810\n | ibivibiv/math_instruct | |
Solve 49 = 5*u - 4*c, 4*u + 52*c + 282 = -0*u - 2*u for u.\n | 5\n | ibivibiv/math_instruct | |
What is -0.00875047 rounded to 3 decimal places?\n | -0.009\n | ibivibiv/math_instruct | |
Collect the terms in 72 - 72 - 3*b - 6*b - 21*b.\n | -30*b\n | ibivibiv/math_instruct | |
What is the third derivative of 9907341*m**3 + 1723360*m**2 - 3*m wrt m?\n | 59444046\n | ibivibiv/math_instruct | |
What is the derivative of -108*j**3 + 298 wrt j?\n | -324*j**2\n | ibivibiv/math_instruct | |
What is the nearest to 78 in 0.1, 4, -1/4, 7.06?\n | 7.06\n | ibivibiv/math_instruct | |
Suppose 0 = -6*q + 4*q - 3*s - 35, -q = -3*s + 4. Is (-1)/(q/65) - -1*11896 a composite number?\n | True\n | ibivibiv/math_instruct | |
What is the thousands digit of 3154?\n | 3\n | ibivibiv/math_instruct | |
Express -u - 2 - 318*u**4 + 315*u**4 + 2*u + (0*u + 0*u - 2*u**2)*(2*u**2 + 4*u**2 + 0*u**2) as c*u**2 + n*u**3 + h*u**4 + t*u + r and give t.\n | 1\n | ibivibiv/math_instruct | |
(2*(-1)/(-6))/(2/(-6))\n | -1\n | ibivibiv/math_instruct | |
Let l = -4.019 + 0.019. What is the closest to 1.4 in l, -0.1, 0.3?\n | 0.3\n | ibivibiv/math_instruct | |
Let w(f) = f**3 + 13*f**2 + 21*f - 6. Let j be w(-11). Solve j = -y + 2*y for y.\n | 5\n | ibivibiv/math_instruct | |
Let k = 0.8055893 + 0.1141487. Let q = k + -0.92. Round q to five decimal places.\n | -0.00026\n | ibivibiv/math_instruct | |
What is the product of 13 and -4728848?\n | -61475024\n | ibivibiv/math_instruct | |
What is the ten millions digit of 40516599?\n | 4\n | ibivibiv/math_instruct | |
What are the prime factors of 936?\n | 2, 3, 13\n | ibivibiv/math_instruct | |
What is the value of 41/((-8405)/(-287))*-3?\n | -21/5\n | ibivibiv/math_instruct | |
Solve -x**2/7 - 16*x/7 - 15/7 = 0.\n | -15, -1\n | ibivibiv/math_instruct | |
How many minutes are there between 10:11 AM and 8:34 PM?\n | 623\n | ibivibiv/math_instruct | |
Calculate the lowest common multiple of 8 and 128.\n | 128\n | ibivibiv/math_instruct | |
Suppose -4*c = -c. Suppose -92 + 94 = z + d, -5*z - 2*d + 10 = 0. Solve -z*w = t + 2, c = 3*w + 9 for t.\n | 4\n | ibivibiv/math_instruct | |
Total of -50279.8734 and 22.6.\n | -50257.2734\n | ibivibiv/math_instruct | |
Let c be 6706*3/101442 - 0. Let b = -5/583 - c. Let w = -268 - -269. Are w and b equal?\n | False\n | ibivibiv/math_instruct | |
Collect the terms in 3*p**2 + 13364*p - 13364*p.\n | 3*p**2\n | ibivibiv/math_instruct | |
Rearrange 0*i - 96 - 6*i + 89 + i + 303 to the form s + c*i and give s.\n | 296\n | ibivibiv/math_instruct | |
Let p(b) be the second derivative of -50*b**3/3 - 3*b**2 - 13*b. Let x be p(-1). Let j = -60 + x. What is the remainder when j is divided by 19?\n | 15\n | ibivibiv/math_instruct | |
Collect the terms in -88*t**2 + 153*t**2 - 95*t**2.\n | -30*t**2\n | ibivibiv/math_instruct | |
Expand (-7*z**2 + 2*z**2 - 27879*z + 28096*z)*(-2 + 1 - 1)*(0*z - z - z).\n | -20*z**3 + 868*z**2\n | ibivibiv/math_instruct | |
Suppose 2*v**4/21 - 82*v**3/21 + 92*v**2/3 + 1984*v/7 - 14592/7 = 0. Calculate v.\n | -8, 6, 19, 24\n | ibivibiv/math_instruct | |
Simplify -1 + (-5*(6*sqrt(204)*-3)/(1*sqrt(1200)))**2.\n | 1376\n | ibivibiv/math_instruct | |
Let h be (-580)/(-80)*94*2. Suppose 3*l = 4*l - h. Is l a prime number?\n | False\n | ibivibiv/math_instruct | |
Let t be ((-14)/546)/(3/(-18)). Which is the third smallest value? (a) -11 (b) t (c) -17\n | b\n | ibivibiv/math_instruct | |
Which is the closest to 3/5? (a) 1/11 (b) -0.4 (c) -2.6 (d) 0.2 (e) 2/7\n | e\n | ibivibiv/math_instruct | |
What is the tens digit of 23248?\n | 4\n | ibivibiv/math_instruct | |
Let w(h) = -65*h. Let q be 1*(-3)/((-12)/(-4)). Is w(q) a composite number?\n | True\n | ibivibiv/math_instruct | |
Let j(u) be the third derivative of -u**10/7560 - u**9/2520 - u**8/3360 - u**4/4 + 2*u**2. Let l(y) be the second derivative of j(y). Factor l(c).\n | -2*c**3*(c + 1)*(2*c + 1)\n | ibivibiv/math_instruct | |
Let c(g) be the second derivative of -85*g**3/6 + 44*g**2 - 2*g - 27. What is the derivative of c(x) wrt x?\n | -85\n | ibivibiv/math_instruct | |
Calculate the remainder when 4937 is divided by 1222.\n | 49\n | ibivibiv/math_instruct | |
How many minutes are there between 8:24 PM and 5:33 AM?\n | 549\n | ibivibiv/math_instruct | |
Evaluate 7 + -7 + 58 - ((-2 - 4) + 3 + -2).\n | 63\n | ibivibiv/math_instruct | |
How many minutes are there between 11:09 AM and 1:09 PM?\n | 120\n | ibivibiv/math_instruct | |
Suppose -9*b + 15*b - 24 = 0. Solve -m = -b*m, -i + 4*m = -2 for i.\n | 2\n | ibivibiv/math_instruct | |
(((-35)/(-15))/(8/18))/(42/(-112))\n | -14\n | ibivibiv/math_instruct | |
Convert 522 (base 6) to base 10.\n | 194\n | ibivibiv/math_instruct | |
Solve -18*l + 17*m + 11*m - 27*m + 229 = 0, m + 11 - 3 = l for l.\n | 13\n | ibivibiv/math_instruct | |
Convert -12011 (base 13) to base 9.\n | -50202\n | ibivibiv/math_instruct | |
896/140 - (-2 - -8)\n | 2/5\n | ibivibiv/math_instruct | |
Suppose 2*g = -3*z + 1, -4*z = -0*z + 4. Suppose -3*m + 9 = -6. Suppose 6 = m*h + 1. What is the remainder when g is divided by h?\n | 0\n | ibivibiv/math_instruct | |
Four letters picked without replacement from {z: 2, a: 5, i: 1, f: 6, l: 3}. What is prob of picking 1 a, 1 z, 1 f, and 1 l?\n | 9/119\n | ibivibiv/math_instruct | |
Let s be 4/10 + (-5)/25*62. Let b = -16 - s. Let v(h) = -h**3 - 4*h**2 - h + 1. What is v(b)?\n | 5\n | ibivibiv/math_instruct | |
What is the result of the following expression?
(-1.9839 % 35.7536) / (79.0993 % -23.3022) | -2.3934 | ibivibiv/math_instruct | |
Let j = -2/23 - -31/92. Let x be ((-4)/16)/(1/(-4)). Let m be 5/4 - x/4. Is m != j?\n | True\n | ibivibiv/math_instruct | |
Find the first derivative of -8*c*j**2 - 3390272*c*j + 95697973*j**2 wrt c.\n | -8*j**2 - 3390272*j\n | ibivibiv/math_instruct | |
Calculate prob of sequence kk when two letters picked without replacement from okokdokadddkoak.\n | 2/21\n | ibivibiv/math_instruct | |
Convert -4504c (base 13) to base 11.\n | -86153\n | ibivibiv/math_instruct |
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