Ratio:
A ratio is a comparison of two or more quantities. It shows how much one quantity is in relation to another. Ratios can be expressed in different ways, such as using numbers, fractions, or in the form of a proportion.

Proportion:
A proportion is a statement that two ratios are equal. It states that two ratios are equivalent and can be solved using cross-multiplication. In a proportion, the product of the means is equal to the product of the extremes.

Example:
Let's solve the given proportion: 27 : x :: 63 : 84

To find the value of 'x', we can set up the proportion as follows:
27/x = 63/84

Cross Multiplication:
To solve the proportion, we can use cross multiplication. This involves multiplying the numerator of one ratio with the denominator of the other ratio.

27 * 84 = 63 * x

Solve for x:
Now, we can solve for 'x' by dividing both sides of the equation by 63.

(27 * 84) / 63 = x

3584 / 63 = x

x = 56.79 (approx)

Therefore, the value of 'x' in the given proportion is approximately 56.79.

Conclusion:
In this example, we used the concept of ratios and proportions to find the value of 'x' in a given proportion. Ratios and proportions are important mathematical tools that help us compare quantities and solve problems involving unknown values. It is essential to understand the relationship between ratios and proportions to solve such problems effectively. Practicing more examples and understanding the underlying concepts will further strengthen your skills in this area.