How do you solve the rational equation #2/a = 4#?

Question

Eva Adamson · Accepted Answer

#a=1/2#

#color(Red)("This is the system behind the shortcuts. The short cuts are very much faster")# #color(green)("Jim has used the shortcut method but understanding")##color(green)("what I have shown you will help with harder maths.")#

Given: #2/a=4#

Multiply both sides by a giving:

#axx2/a=axx4#

To make sure that initially you do not get in a muddle write this as:

#color(brown)(a/1)xxcolor(blue)(2/a)=axx4#

By the laws of mathematics you can do this next bit:

#color(blue)(color(brown)(a)/axx2/(color(brown)(1))=4a#

See the way I have swapped the bottom numbers of the fractions around!

But #a/a" is the same as 1 giving"#

#1xx2/1=4a#

And #2/1# is the same as just #2#

so we end up with:

#2=4a#

Now if I do the same sort of thing with multiply both sides by #1/4# I end up with:

#2/4=a#

so #a=1/2#

Eli Assouline · Answer

# a = 1/2# the first step in solving this equation is to 'cross multiply' hence : 4a = 2 now divide both sides by 4 :# (cancel(4) a)/cancel(4) = 2/4 = 1/2#

Ethan Adkins · Answer

undefined To solve the rational equation 2/a = 4, you can cross-multiply and solve for a. Multiply both sides of the equation by a to eliminate the denominator. This gives you 2 = 4a. Divide both sides of the equation by 4 to isolate the variable a. The solution is a = 1/2.