How do you solve #6/a=3/8#?

2 Answers
Anjali G
Jan 3, 2017

#frac{6}{a}=3/8#

Multiply each side by #a#:
#6=3/8a#

Isolate #a# by multiplying each side by the reciprocal of #3/8#:
#6*(8/3)=a#

#a=16#

smendyka
Jan 3, 2017

Multiply each side of the equation by the lowest common denominator to eliminate the fractions and then solve for #a#. See full solution process below.

Explanation:

First, multiply each side of the equation by the lowest common denominator (in this case #color(red)(8)color(blue)(a)#)to eliminate the fractions and keep the equation balanced:

#6/color(blue)(a) xx color(red)(8)color(blue)(a) = 3/color(red)(8) xx color(red)(8)color(blue)(a)#

#6/cancel(color(blue)(a)) xx color(red)(8)cancel(color(blue)(a)) = 3/cancel(color(red)(8)) xx cancel(color(red)(8))color(blue)(a)#

#6 xx color(red)(8) = 3color(blue)(a)#

#48 = 3color(blue)(a)#

We can now divide each side of the equation by #color(red)(3)# to solve for #a# and keep the equation balanced:

#48/color(red)(3) = (3color(blue)(a))/color(red)(3)#

#16 = (color(red)(cancel(color(black)(3)))color(blue)(a))/cancel(color(red)(3))#

#16 = a#

or

#a = 16#

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