7.1 Recalling Ratios and Percentages | Class 8 Mathematics Notes

7.1 Recalling Ratios and Percentages

This section revisits the fundamental concepts of ratios and percentages, which are essential mathematical tools used to compare quantities and express proportions. A ratio is a way to compare two or more quantities of the same kind by division, showing how many times one quantity is contained in another. For example, if there are 3 apples and 4 oranges, the ratio of apples to oranges is 3:4. Ratios can be expressed in three forms: a to b, a:b, or as a fraction a/b. Ratios are dimensionless and must compare quantities of the same unit.

Percentages are a special type of ratio where the comparison is made with respect to 100. The word 'percent' means 'per hundred.' For example, 45% means 45 out of 100. Percentages are widely used in daily life to express discounts, marks obtained in exams, interest rates, and more.

To convert a ratio to a percentage, first convert the ratio to a fraction and then multiply by 100. Conversely, to convert a percentage to a ratio, express the percentage as a fraction over 100 and simplify.

Understanding ratios and percentages allows us to solve problems involving comparisons, proportions, and conversions in various real-life contexts such as finance, statistics, and measurement. This section also recalls how to express quantities in fractional and decimal forms and how to interpret them in terms of ratios and percentages.

The section emphasizes the importance of simplifying ratios to their lowest terms for easier interpretation and calculation. It also revisits the concept that percentages can be converted to decimals by dividing by 100, which is useful for calculations involving percentages.

Overall, this section lays the groundwork for more advanced topics in the chapter by reinforcing the understanding of ratios and percentages, their interrelation, and their practical applications.

📊 Diagram: The section includes diagrams illustrating the concept of ratio using objects such as apples and oranges arranged in groups to show the ratio 3:4. Another diagram shows a pie chart representing percentages, for example, a circle divided into 100 equal parts with a shaded portion representing a certain percentage.

🧪 Activity: An activity involves students counting objects like pencils and erasers in the classroom, writing their ratio, converting it to a fraction, and then expressing it as a percentage to understand the practical use of ratios and percentages.

🔗 Connection: This section provides the foundational understanding of ratios and percentages, which is essential for the next sections that deal with comparing quantities, converting between fractions, decimals, and percentages, and solving problems involving these concepts.