In some instances, comparing two amounts using the division method is very useful. A ratio is a contrast or condensed type of two quantities of the exact nature. This relationship tells us how many times one amount equals another. Simply put, a ratio is a number used to express one quantity as a percentage of another.

When the two numbers in a ratio have the same unit, they may be compared. Ratios are used to equate different items. A ratio is denoted by the symbol ‘:’.

Important points to keep in mind:

• Both quantities of the same form, only then there will be a ratio.
• When contrasting two items, the units must be comparable.
• There should be a logical order to the words.
• If the ratios are equal, such as fractions, the two ratios can be compared.

Proportion is a mathematical expression that states that two ratios are equal. In other terms, the proportion declares that the two percentages or ratios are identical. In proportion, two sets of defined numbers are directly proportional to each other, whether they increase or decrease in the same ratio.

• A fraction is an amount that represents a portion of a whole or a community. The denominator is the cumulative number of equivalent parts separated into the whole.
• A ratio is a pair of numbers compared.

For example, in five students with four boys and one woman, the female fraction is one-fifth of the class. Four-fifths of the people in the group are male. Since the whole group comprises five students, the denominator would still be five.

In the case above, the girls-to-boys ratio is one-fourth, and the boys-to-girls ratio is four over one. The girl-to-student ratio is one-fifth, while the boy-to-student ratio is four-fifths.

• Ratios are determined by the numbers compared.
• A fraction is sufficient when representing a portion of a whole.
• When matching two figures, you can use a ratio.

The unitary approach entails first determining the value of a single unit and determining the value of a specified number of units.

Assume you head to the store to buy six apples. The shopkeeper informs you that ten apples are available for Rs 100. The apples are the units in this situation, and the expense of the apples is the amount. It’s essential to understand the units and values while using the unitary approach to solve an issue.

The value of a unit quantity is measured first in the unitary system before the other units’ value is calculated. There are two kinds of variations.

1. Direct Variation
   A decrease or increase in a quantity produces decreases or increases in another amount. A rise in the number of products, for example, would result in a higher price.Furthermore, one man’s sum of work would be smaller than that done by several men. As a result, as the number of workers increases, so does the amount of jobs.
2. Inverse Variation
   Direct variance is the opposite of this. When one quantity increases, the value of another quantity decreases. If we raise our pace, for example, we will cover the distance in less time. As a result, as speed increases, travel time decreases.

Find the ratio of girls and boys out of the total number of students in a class, if the number of boys is six and the number of girls is two.

Answer: The ratio is written as 6:2. (Boys:Girls). The ratio can also be expressed as a factor, such as 6/2.

In this chapter, we learn about the basics of ratio and proportions, proportion as equality of two ratios, and variation and types.

1. With an example, explain what a ratio is.
   A ratio is a mathematical equation written as a:b, where a and b are any two integers. It is used to express a fraction. E.g., 2:3 equals 2/3.
2. With an example, explain what a proportion is.
   A proportion is a statement that compares two or more ratios. E.g., 2/3 = 4/6 = 6/9.
3. What are the fundamental ratios?
   A ratio is a way of matching two numbers or integers, such as a:b, a to b, or a/b, where b isn’t equal to zero.
4. What is the meaning of the term “ratio”?The ratio definition allows one to equate two proportions, while the proportion concept is an equation that demonstrates that two ratios are equal.
5. What is the aim of ratio analysis?
   Ratio analysis compares line-item details from financial statements to uncover information about a company’s performance, liquidity, operating quality, and solvency.