CLASS-7
BASICS DEFINITION OF RATIO

BASICS DEFINITION OF RATIO -

A ratio is a mathematical concept that represents the relationship between two quantities, showing how many times one value contains or is contained within the other. It’s essentially a way to compare two numbers or quantities.

Basic Definition:-

                                          a

A ratio is expressed as "a to b" or ------,

                                          b

Where:-

  • a and b are the two quantities being compared.
  • a is another common way to write a ratio.


Example:-

  1. Simple Ratio:- If there are 2 apples and 3 oranges in a basket, the ratio of apples to oranges is 2:3 or 2/3​.
  2. Scaling Up or Down:- If a recipe requires a ratio of 2 cups of flour to 1 cup of sugar, it means that for every 2 cups of flour, there is 1 cup of sugar. If you wanted to make a larger batch, you could double the ingredients while maintaining the ratio.


Types of Ratios:-

  1. Part-to-Part Ratio:- Compares different parts of a whole. For example, the ratio of red to blue balls in a bag containing both.
  2. Part-to-Whole Ratio:- Compares one part to the entire whole. For example, the ratio of red balls to all balls in the bag.
  3. Equivalent Ratios:- Ratios that express the same relationship between quantities. For example, 1:2 is equivalent to 2:4 or 3:6.


Applications:-

  • Proportions:- If two ratios are equal, they form a proportion, which is useful in solving problems involving scaling.
  • Rates:- Ratios are used in rates to express how one quantity changes relative to another, such as speed (miles per hour) or density (population per square mile).
  • Financial Ratios:- In finance, ratios like the debt-to-equity ratio or profit margin help assess the financial health of a business.

Understanding ratios is fundamental in various fields, including mathematics, science, economics, and everyday problem-solving.