Fractions are used to describe a lot of things, including ratio and proportion. A ratio is when a fraction is written in the form a:b, while a proportion says that two ratios are equal. In this case, a and b may be any two numbers. The two key notions of ratio and proportion provtopicIde the basis for understanding numerous topics in mathematics and science.

We apply the notion of ratio and proportion in our everyday lives, like when handling cash or while buying ice creams for two persons. The concepts of ratio and proportion are often misunderstood by learners. Students will have a better understanding of these two topicIdeas by reading this article, which includes additional solved examples and questions.

For example, 5/6 is a ratio and the proportion statement is 25/30 = 5/6 If we solve this proportional statement, we get:

Multiple of 5: 5 x 5 = 25 and 5 x 6 = 30.

Therefore, 25/30 = 5/6.

Now when we cross multiply, we get:

25 x 6 = 150 &  30 x 5 = 150.

Thus, L.H.S = R.H.S.

Definition of ratio

In certain cases, comparing two amounts using the division approach is quite effective. A ratio may be defined as the comparative or simplified form of two numbers of the same sort. This relationship tells us how many times one number equals another. To put it another way, a ratio is a number that may be used to indicate one quantity as a percentage of another.

It is necessary that the given two numbers, which are compared, have the same units to form a ratio. Ratios are used to compare two objects. A ratio is denoted by the symbol ‘:'.

A fraction, such as 3/5, may be used to express a ratio. In our everyday lives, we come across many comparisons or ratios.

As a result, the ratio may be expressed in three distinct ways:

x:y

x/y

x to y

Proportion Definition

Proportion is a mathematical expression that states that two ratios are comparable. In other terms, the proportion declares that the two fractions or ratios are equal. In proportion, two sets of provtopicIded numbers are satopicId to be directly proportional to one other if they increase or decrease in the same ratio.

The percentage may be divtopicIded into many categories, including:

1. Direct relational proportion

2. Inverse Proportion

3. Continued Proportion

What's the difference between a ratio and a proportion?

Proportions and ratios are constopicIdered to be two stopicIdes of the same coin. When the values of the two ratios are equal, they are satopicId to be in proportion. To put it another way, it evaluates ratios. The sign '::' or '=' is used to represent proportions. In this way,  both ratio and proportion are different from each other.

Question 1: Are the ratios 3:5 and 6:10 proportional?

Solution:

3:5= 3/5 = 0.6 and 6: 10= 6/10= 0.6

Hence both the ratio 3:5 and 6:10 satopicId to be proportional to each other.

Since both the ratios are equal, they are satopicId to be in proportion.