How do you solve #2/3 = 2/9m#?

2 Answers
Johnson Z.
Mar 29, 2016

#m=3#

Explanation:

#1#. To solve the equation, you must isolate #m# so that it appears on only one side of the equation. Thus, divide both sides by #2/9#.

#2/3=2/9m#

#2/3-:2/9=2/9m-:2/9#

#2#. Recall that when you divide fractions, you take the reciprocal of the divisor and change the division sign to a multiply sign.

#2/3xx9/2=2/9mxx9/2#

#3#. Simplify the right side of the equation.

#2/3xx9/2=(2xx9)/(9xx2)m#

#2/3xx9/2=m#

#4#. Simplify the left side of the equation. Since #2# appears in the numerator and denominator, they cancel each other out. Similarly, since #9# in the numerator and #3# in the denominator can be divided by a common factor of #3#, their values are reduced as well.

#color(red)cancelcolor(black)2^1/color(teal)cancelcolor(black)3^1xxcolor(teal)cancelcolor(black)9^3/color(red)cancelcolor(black)2^1=m#

#5#. Simplify.

#color(green)(|bar(ul(color(white)(a/a)m=3color(white)(a/a)|)))#

EZ as pi
May 10, 2016

# m = 3#

Explanation:

Equations in this form - one fraction on each side of the equal sign are easy to solve by cross-multiplying.

#3xx2m = 2 xx 9#

#6m = 18 " divide both sides by 3 "#

# m = 3#

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