Need help with these problems:\n\n16. six times times the reciprocal of a number 2 times the reciprocal of 2. Find the number\n\n20. Simplify the complex fraction: 5/3)-(7/x) / (3/10)+(2/x^2)
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Problem 16:\n6 x 1/n(reciprocal of n) = 2 x 1/2(reciprocal of 2)\n\nFirst, a number times it's reciprocal is always 1.\n\n6 x 1/n = 1\n\nSubtract 6.\n\n1/n = -5\n\nMultiply n.\n\n1 = -5n\n\nDivide by -5.\n\nn = 1/-5\n\nTo spgrabia: Think about order of operations. (1/x) must be done first.
431514
First change them to improper fractions to do this multiply the whole number by the denominator so in 3 and 7/8 you would take 3 times 8, once you got that you would add it to the numerator so\n\n3x8=24\n7+24=31\n\nso you have 31/8 for the first fraction\n\nrepeat this step for the second\n2x10=20\n20+9=29\n\nthe second is 29/10\n\nNow you must fine the lowest common denominator for both fractions, which means find a number both 8 and 10 divide into evenly. Both go into 40 evenly, so you want the denominator to be 40 on both fractions, to do this multiply the top and bottom of each so that the denominator is 40 so for the first fraction, 31/8 you would multiply both the top and bottom by 5.\n\n(31/8)x5=155/40\nand the second fraction\n(29/10)x4=116/40\n\nnow you can subtract them\n\n(155/40)-(116/40)=39/40
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Multiply everything by 15 to get rid of the fractions.\n15(6x) -15(1/5) - 15(2x/3) = 15(3)\n90x - 3 - 10x = 45\n80x - 3 = 45 \nAdd 3 to each side and then divide by 80\n80x = 48\nx = 48/80\nx = 3/5\nEDIT: In that case,\n(6x-1)/5 - 2x/3=3\nMultiply everything by 15\n15(6x-1)/5 - 15(2x/3) = 15(3)\n3(6x-1) - 5(2x) = 45\n18x - 3 - 10x = 45\n8x - 3 = 45\n8x = 48\nx = 48/8\nx = 6
315845
a)  1/3^-3 = 3^3  = 27\n\nb)  3/5^-1 = 3*5 = 15\n\nc)  4a^-2b^-3 = 4/(a^2*b^3)\n\nd)  x^-2y^-3/z^-1 = z/(x^2*y^3)\n\ne)  x^6/x^2 = x^3  (I think this is what you wanted to ask, you left out the carets)\n\nf)  x^4y^2z/x^2y^4z^2 = x^2/(y^2*z)
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6/19\n\nif you multiply both sides by 6x, you get\n2x + 3x + 6 = 24x\ntherefore\n6 = 24x - 5x = 19x\ntherefore\n6/19 = x\nor x = 6/19
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Add seven to both sides:\nm/6 = 7 + 2/3\n\nConvert to mixed fraction:\nm/6 = 23/3\n\nMultiply both sides by 6:\nm = 23/3 * 6\nm = 23 * 2\nm = 46
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First one : - ...Correct! Congratulations!\nSecond one : - ...hmm could be wrong\n\n(x - 2)^2 = 3/5\nx - 2 =+-sqrt3/5\nx = 2 +- sqrt3/5\n\nThird one : - hey there is no harm in trying!\n\n(x - 3)^2 = 2\nx - 3 = +-sqrt2\nx = 3 +-sqrt2\n\nBest of luck!!
183962
Well, first you want to isolate the "x".  So, divide out the left side-this gets you 3x/6 + 4/6 = 2/5.  Take 4/6 from each side, so x/2 = 2/5 - 4/6.  You have to make the fractions have the same denominator, so you get x/2 = 12/30-20/30, or x/2 = -8/30.  Now multiply each side by 2, so you get x = -16/30, or x = -8/15.\nplug it back in to check, so (-24/15 + 60/15)/6 is the same as (36/15)/6, which is the same as 6/15, which reduces to 2/5.  O Ho! We got it!  x DOES equal -8/15..  That was fun-I havent done that kind of math for a long time..
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Add them... 8+7+7+5+3+2+2= 34 and divided by 7\nYyou have 34/7=\nYou know 4x7= 28 so you need 6 more to reach 34\nso you have 4 and 6/7
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2*root(5/7) - 3*root(7/5)\n\nFirst we notice we can distribute the root throughout the fractions, and rewrite our equation\n\n2*(root5 / root7) - 3*(root7 / root5)\n\nTo get rid of the radical denominators, we can multiply through by the denominators. So we multiply through by root5*root7\n\n2*root5*root7*(root5/root7) - 3*root5*root7*(root7/root5)\n\nWe see that the denominators cancel with their respective partners, and the numerators are squared. Thus the roots all dissapear and we are left with:\n\n2*5 - 3*7\n= 10 - 21\n= -11
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In order to solve, you need a common denominator:\n2(sqrt(3/5)) - 5(sqrt (5/3))\n2(sqrt 3/sqrt 5) - 5 (sqrt 5/sqrt 3)\n2(sqrt3/sqrt3)(sqrt 3/sqrt 5) - 5(sqrt 5/sqrt 5)(sqrt 5/sqrt 3)\n2(3/sqrt 15) - 5(5/sqrt 15)\n6/sqrt 15 - 25/sqrt 15\n-19/sqrt 15
506147
It looks like you are trying to solve a literal equation, which is an equation with more than one variable, and you have to solve for a specified variable.  You can use the SAME rules to solve this kind of equation as you do with regular equations (those with numbers).  For example, if you had 8=2(b)(9), you would divide by 2 and then again by 9 (which is like dividing by 18).  \n\nIf your problem is a=(1/2)bc^2, then you would divide by 1/2 and then again by c^2.  Remember that to divide by a fraction, you multiply by the reciprocal.
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1) 1, 2, 3 and 6\n2) 1, 2, 2m\n3) 1\n4) 1, 3\n\n5) 5/9 (55/99) > (45/99) 5/11\n6) 2/3 (8/12) < (9/12) 3/4\n7) 4/5 (32/40) < (35/40) 7/8\n8) 1/3 (4/12) = (4/12) 4/12
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(4/x^5) / (8/x^2)\n\nTo divide a fraction, you multiply by the reciprocal.\n\n(4/x^5) * (x^2/8)\n\nThen the 4 crosses out and the 8 becomes a 2 because 8 / 4 = 2\n\n(1/x^5) * (x^2/2)\n\nThen x^5 becomes x^3 and the x^2 is crossed out because x^5 / x^2 = x^3\n\nSo\n(1/x^3) * (1/2)\n\nThen we will put multiply the two together and get\n1/(2x^3)
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Ok it is very simple.\nFirst, subtract the five. This leaves you with -x/2 + x/3 = -4. \nWork on the left side first.  \nFind a common denominator, in this case it would be 6.  \nMultiply the -x/2  by 3 to get a 6 on bottom. Your new fraction should be -3x/6. \nMultiply the x/3 by 2 to get a 6 on bottom. Your new fraction should be 2x/6. \nYou should have: \n-3x/6  +  2x/6  = -4\nNOW, add your fractions together. \n-x/6 = -4\nTo get rid of the 6 on bottom, you have to multiply BOTH sides by 6. \n(6) -x/6 = (6) -4\nYou should get:\n-x = -24\nDivide both sides by -1, to get X alone.\nx=24
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4) 5/2 b/c:\n1) 84 = -(-42x+21)    cross multiply\n2) 84 = 42x-21           distribute the negative.\n3) 84 + 21= 42x -21+21     add 21 to each side\n4) 105 = 42x\n5) x = 2.5 or 5/2                divide each side by 42
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I will try to explain step by step....\n\nA) x-2/3 + x+3/4=5/6\nFirst you would place like terms together;\nx+x-2/3+3/4=5/6\nThen try to make all the denominators equal.  Do this by thinking of what the denominators can all go into.  In this case, they can all go into 12 using whole numbers.  Since multiplying by 1 doesn't change the value, you can do that by multiplying the top and bottom of each fraction by the same number.  \n  So the -2/3 would all be multiplied times 4/4 giving you -8/12.  The 3/4 would all be multiplied times 3/3 giving you 9/12.  The 5/6 would all be multiplied times 2/2, giving you 10/12.\n\nThe equation would now look like;\nx+x-8/12+9/12=10/12\n\nYou then combine like terms;\nx+x=2x\n-8/12+9/12= 1/12\nSo your equation is now;\n2x+1/12=10/12\n\nSubtract 1/12 from both sides;\n2x=9/12\n\nAnd divide by 2;\nx=4.5/12 or 9/24\n\n9/24=3/8\n\nSo, the answer to A would be x=3/8\n\nAs for B...I'm not to good at word problems, sorry :)\n\n\nAnd NS in line 3 of your work, it should be -8/12 because -2*4= -8 not 8