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# 'simple' Algebraic manipulation.

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If m/n = 15, p/n = 3, and p/q = 1/10. find m/q

How should I do this?

Jul 9, 2021

#1
+121084
+3

m/n  = 15

p/n =    3

This implies  that    m =  5p

And

p/q   = 1/10     impiies  that  q  =  10 p

So

m / q    =    5p  / [ 10 p ]    =   1/2

EDIT .....

Jul 9, 2021
edited by CPhill  Jul 9, 2021
#2
+137
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THANK YOU!!!!!!!'

I am stuck on this step: why will p/q = 1/10 imply  q = (1/10) p?

i'll try to figure it out now. p/q = 1/10. so 10q = p. so q = p/10 which is (1/10) p FIGURED IT OUT

Wait... it's p/q =1/10. so it is 10p = q???? so then p = (1/10) q

HighSchoolDx  Jul 9, 2021
edited by HighSchoolDx  Jul 9, 2021
edited by HighSchoolDx  Jul 9, 2021
#3
+121084
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Slight mistake.....check my edit  !!!!!

CPhill  Jul 9, 2021
#4
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YOO NOW i get it! Thank you for the edit CPHILL :)

Jul 9, 2021
#5
+2322
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Another way you could do this is to assume that q = 1.

If q = 1, and p/q = 1/10, p = 1/10.

If p = 1/10, and p/n = 3, n = 1/30.

If n = 1/30, and m/n = 15, m = 1/2.

CPhill's way is very smart by using substitution. :))

=^._.^=

Jul 9, 2021
#6
+137
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YOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

THIS IS BIG BRAIN TIME! ANOTHER WAY OF GETTING> THE SAME ANSWER

HighSchoolDx  Jul 9, 2021
#7
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Yours works OK , too, catmg   !!!!

CPhill  Jul 9, 2021
#8
+137
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BIG BRAINS

Jul 9, 2021
#9
+35290
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m/  *    n/p   * p/q      =   15  * 1/3 * 1/10                   See how things 'cancel out' and you are left with  m/q  ?

m/q = 1/2

Jul 9, 2021
#10
+121084
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I think I like EP's  simple solution the  best.....no fuss.....no muss  !!!!!

CPhill  Jul 9, 2021
#11
+137
+1

THANK
THATS ONE ELEGANT SOLUTION!

HighSchoolDx  Jul 9, 2021
edited by HighSchoolDx  Jul 9, 2021