Example 1: Fraction

Solve for n.

=   n:

Proportions are usually solved using cross multiplication. For this problem, there are two possible ways of solving for n. An alternate solution is also shown below.

First, to make the problem easier to solve, replace the original fraction with a simplified fraction.

Since = , the problem becomes =

Solution: Cross Multiplication
When we cross multiply (as shown above), it results in 2 × 18 = 3 × n

Now solve for n.

2 × 18	=	3 × n
(2 × 18) ÷ 3	=	(3 × n) ÷ 3
12	=	n

Alternate Solution: Common Denominator

=       Rewrite the equation so that n is on the left side = =   Solve by finding the common denominator

So n = 12.

The answer is n:

Example 2: Ratio

Solve for n.
95 : 85 = n : 34
n:

First, rewrite the ratios as fractions.

95 : 85 = n : 34   becomes =

Then, to make the problem easier to solve, replace the original fraction with a simplified fraction.

Since = , the problem becomes =

Solution: Cross Multiplication
When we cross multiply (as shown above), it results in 19 × 34 = 17 × n

Now solve for n.

19 × 34	=	17 × n
(19 × 34) ÷ 17	=	(17 × n) ÷ 17
38	=	n

The answer is n: