How to Solve Proportions
In this page we are going to discuss about solving proportion .The How to Solve Proportions is the way of
expressing the ratio between the part and the whole. A proportion is an equation in which two ratios are set
equal to each other. In this concept, cross product can be used to find the unknown number. Here we use
letter x in place of unknown number. The condition for proportion is, if four quantities, a, b, c, d, are said to be
in proportion if [a/b] = [c/d] . Now let us going to see some of the example problems for solving proportion in
this article.
Proportion is also defined as equivalent of two fractions. When we are going to write equivalent fractions, we
need to create a proportion
For example:
[2/6] = [4/12]
This is called as proportion
2 x 12 = 24
6 x 4 = 24
So The two cross products are equal.
If any one of the four number is unknown, cross product can be used to find the unknown number. This
process is known as Here we use letter X in place of unknown number.
Let us learn about how to solve proportions.
How to solve a proportion
Proportion can be expressed in three forms,
[a/b] [c/d] (or) a:b = c:d (or) a:b :: c:d
Important property:
Product of extremes = Product of means
Not
e: (i) The first and fourth terms are called extremes and
(ii) The second and third terms are called middle terms or means.
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Example : Verify 3 : 4 = 9 : 12 is a proportion or not.

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Solution: Product of extremes = 3 * 12 = 36
Product of means = 4 *9 = 36
36 = 36
These two products are equal.
Therefore 3 : 4 = 9: 12 is a proportion.
Steps for solving simple proportion
To solve the proportion, we have three steps.
Step 1: Applying cross multiplication
Step 2: Make an equation
Step 3: Solve for x variable
Solved Examples
Example 1:
[11/13] = [55/x] Solve this How to Solve Proportions
Solution:
The given proportion:
= [11/13] = [55/x]
Step 1: Applying Cross multiply.
11 * X = 13 * 55
Step 2: Make an equation.
11X = 715
Step 3: Solving for X variable.
Divide by 11 each side.
= [(11X)/(11)] = [715/11]
Simplify it,
X = 65.
Example 2:
If 2 : 3 = 14 : x is a solve for x.
Solution:
Productof extremes = 2 x x
Produc of means = 3 x 14
Since it a proportion, 2 x x = 42
2x = 42


Divide 2 on both sides,
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= [(2x)/2] = [42/2]
x = 21

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