Aethelwulf 24 Posted December 8, 2012 Report Share Posted December 8, 2012 (edited) I was having some fun with some people on facebook and thought about bringing the idea here. Basically, I was posting some math problems, the idea is of course to solve it. It went like this - Let's see how good your maths is. I have created a problem and solved it myself so I know the answer. simplify terms (involving fractions) and solve for [math]k[/math] [math]\frac{kr}{m} - S + (\frac{5}{ab} - \frac{3}{b^2})= T[/math] values of [math]b, r[/math] and [math]a[/math] are [math]b = 2[/math] [math]r = 20[/math] [math]a = \sqrt{\frac{\frac{4 \cdot 154}{22}}{7}}[/math] I won't lie, some of it might be tricky. Some people particularly had trouble finding the value of [math]a[/math]. Enjoy! Edited December 8, 2012 by Aethelwulf Quote Link to post Share on other sites

sanctus 80,742 Posted December 8, 2012 Report Share Posted December 8, 2012 1 equation 3 unknowns?? Quote Link to post Share on other sites

belovelife 14,227 Posted December 8, 2012 Report Share Posted December 8, 2012 (edited) kr/m - s + 1/2 = t 20k/m = s + t -1/220k=m( s+t-1/2) k= m(s+t-1/2)...... ----------..........20 Edited December 8, 2012 by belovelife Quote Link to post Share on other sites

sanctus 80,742 Posted December 8, 2012 Report Share Posted December 8, 2012 Ok, thought since you gave numbers you wanted some numeric value for k...otherwise I agree completely with belovelife and think it is just basic algebra... Quote Link to post Share on other sites

belovelife 14,227 Posted December 9, 2012 Report Share Posted December 9, 2012 my math is rusty, Quote Link to post Share on other sites

Aethelwulf 24 Posted December 9, 2012 Author Report Share Posted December 9, 2012 kr/m - s + 1/2 = t 20k/m = s + t -1/220k=m( s+t-1/2) k= m(s+t-1/2)...... ----------..........20 Nice try but it is wrong. Quote Link to post Share on other sites

Aethelwulf 24 Posted December 9, 2012 Author Report Share Posted December 9, 2012 (edited) Ok, thought since you gave numbers you wanted some numeric value for k...otherwise I agree completely with belovelife and think it is just basic algebra... There is some basic algebra involved - but I also gave a numerical task. The previous poster was very close, the actual answer is [math]k = Tm+Sm -1[/math] The numbers simplify, so I am not sure where the previous poster got 1/2 from... try it again. Edited December 9, 2012 by Aethelwulf Quote Link to post Share on other sites

sanctus 80,742 Posted December 9, 2012 Report Share Posted December 9, 2012 the sqrt is 2then brackets give 5/4 -3/4=2/4=1/2 Quote Link to post Share on other sites

Aethelwulf 24 Posted December 9, 2012 Author Report Share Posted December 9, 2012 (edited) the sqrt is 2then brackets give 5/4 -3/4=2/4=1/2 That's not right. the value of [math]a[/math] is what gave other people problems as well. Also, that is not how you simplfy what is inside the paranthesis. The way you divide a number by a fraction is like this [math]6 \frac{2}{\frac{4}{8}} = 6\frac{2}{\frac{8}{4}} = \frac{6 \cdot 2 \cdot 8}{4} = 24[/math] So when you divide a number by a fraction, you have to flip the fraction around. So let's go back to our example [math]a = \sqrt{\frac{4 \cdot 154}{\frac{22}{7}}}[/math] swap the fraction round [math]a = \sqrt{\frac{4 \cdot 154}{\frac{7}{22}}}[/math] calculate [math]4 \cdot 154 \cdot 7 / 22 = 196[/math] Take the square root of this and it is 14. Edited December 9, 2012 by Aethelwulf Quote Link to post Share on other sites

Aethelwulf 24 Posted December 9, 2012 Author Report Share Posted December 9, 2012 (edited) How do you simplify what is in the brackets? That's easy It is in paranthesis so you solve this part first [math](\frac{5}{ab} - \frac{3}{b^2}) = \frac{5b - 3a}{ab^2}[/math] now plug in the values. Then simplify by plugging in the value for [math]r[/math] when you get the chance. Edited December 9, 2012 by Aethelwulf Quote Link to post Share on other sites

belovelife 14,227 Posted December 9, 2012 Report Share Posted December 9, 2012 (edited) i think the original problem could have been visually represented different, i thought the same thing as sanctus the original representation of (a) i should say Edited December 9, 2012 by belovelife Quote Link to post Share on other sites

Aethelwulf 24 Posted December 9, 2012 Author Report Share Posted December 9, 2012 i think the original problem could have been visually represented different, i thought the same thing as sanctus the original representation of (a) i should say You both wouldn't have needed to think anything if it had been calculated right. The rule for dividing whole numbers by fractions is well-known. http://www.cimt.plymouth.ac.uk/resources/help/miscon5.pdf An example from this site is [math]3/1/4[/math] The answer they give is 12. Use the rule I gave, remember to swap the fraction about [math]3/4/1[/math] is [math]3 \cdot 4/1 = 12[/math] It is perfectly consistent and nothing wrong with any kind of representation. I did warn you it could be tricky. Quote Link to post Share on other sites

Aethelwulf 24 Posted December 9, 2012 Author Report Share Posted December 9, 2012 (edited) So what is your answer? you should end up with [math]kr + \frac{36}{56} = m(T + S)[/math] right? Plug in the value for [math]r[/math] you should end up with [math]k + \frac{56}{56} = m(T + S)[/math] (I noticed in the answer I gave I forgot to plug in the value of 1 (I'll change it now), so what you have for you final answer is [math]k = m(T + S) -1[/math] Edited December 9, 2012 by Aethelwulf Quote Link to post Share on other sites

Aethelwulf 24 Posted December 9, 2012 Author Report Share Posted December 9, 2012 I'll write up a calculus problem later but I need to dash for now. Quote Link to post Share on other sites

sanctus 80,742 Posted December 10, 2012 Report Share Posted December 10, 2012 wulf: I do not agree. You say that [math]\frac{x}{\frac{y}{z}}\equiv \frac{x}{\frac{z}{y}}[/math]. You should see right away that this is wrong. What you want to say I guess is [math]\frac{x}{\frac{y}{z}}\equiv \frac{x}{1}\cdot{\frac{z}{y}}[/math], so you have the swapping around you mean. In general you have the rule [math]\frac{\frac{x}{k}}{\frac{y}{z}}\equiv \frac{x}{k}\cdot \frac{z}{y}[/math]. Applying this to your a (squared): x=4*154=616, k=22, y=7, z=1 hence it follows: [math]\frac{616}{22}\cdot \frac{1}{7}=28\cdot\frac{1}{7}=4 [/math]. Hence a=2. But re-reading through your posts, you are not coherent on where you put the main fraction!! And this changes everything, as written in the opening post you have:[math]a^2=\frac{\frac{4\cdot 154}{22}}{7}[/math] and then belovelife and I are right. Where you say that we are wrong you actually develop:[math]\frac{4\cdot 154}{\frac{22}{7}}[/math] which is different and leads to a =14 as you say. So it is your typo in OP that started all this discussion ;-) Quote Link to post Share on other sites

Aethelwulf 24 Posted December 10, 2012 Author Report Share Posted December 10, 2012 (edited) How where you right? You are still doing it wrong. Belovelife has calculated 4*154 then divides that by 22 and then by 7 - that does indeed give you 4 but that isn't the correct operation for dividing whole numbers by fractions. Let us for a moment, say we where doing it the other way around, say we where dividing a fraction by a whole number, that is still not what you get. Dividing a fraction by a whole number, let's say we had 2/5/4 = 2/ 5 *4 = 2/20 = 1/10 So in my example 616/22/7 = 616/ 22*7 = 616/154 = 308/77 If you even tried both dividing a whole number by a fraction and a fraction by a whole number, one would be able to work out which one was probably intended. Edited December 11, 2012 by Aethelwulf Quote Link to post Share on other sites

CraigD 398,736 Posted December 11, 2012 Report Share Posted December 11, 2012 (edited) you should end up with [math]kr + \frac{36}{56} = m(T + S)[/math] right?I don't think so. Starting with post #1's [math]\frac{kr}{m} - S + (\frac{5}{ab} - \frac{3}{b^2})= T[/math] I get [math]k = \frac{m(T +S -\frac{5}{ab} +\frac{3}{b^2} )}{r} [/math] Substituting the givens [imath]a=14, b=2, r=20[/imath] and simplifying, that's [math]k = \frac{m(7T +7S +4)}{40}[/math] Evaluating the original equation with sample values for the m, T, S, and k calculated with my result checks out. Using your doesn't. I think you've erred, Aetherwolf. Edited December 12, 2012 by CraigD Replaces incorrect given a=2 with correct a=14 Quote Link to post Share on other sites

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