RBSE Class 7 Maths Notes Chapter 8 Comparing Quantities

These comprehensive RBSE Class 7 Maths Notes Chapter 8 Comparing Quantities will give a brief overview of all the concepts.

RBSE Class 7 Maths Chapter 8 Notes Comparing Quantities

→ We are often required to compare two quantities in our daily life. They may be heights, weights, salaries, marks etc.

→ While comparing two quantities we can write in the form of ratio.

→ Ratio is a relation between two quantities having same unit and saying how many times or what part one quantity is of the other.

→ Two ratios can be compared by converting them to like fractions. If the two fractions are equal, we say the two given ratios are equivalent.

→ If two ratios are equivalent then the four quantities are said to be in proportion. For example, the ratio 8 : 2 and 16 : 4 are equivalent, therefore 8, 2,16 and 4 are in proportion.

→ A way of comparing quantities is percentage.

→ Percentages are numerators of fractions with denominator 100. Percent means per hundred. For example, \(\frac{25}{100}\) = 25%.

→ Percentage is represented by the symbol %.

→ Fractions can be converted to percentages and vice-versa. For example,
\(\frac{1}{4}=\frac{1}{4}\) × 100% = 25%, whereas 75% = \(\frac{75}{100}=\frac{3}{4}\)

→ Decimals too can be converted to percentages and vice-versa. For example,
0.25 = 0.25 × 100% = 25% and 25% = \(\frac{25}{100}\) = 0.25.

→ Percentages are widely used in our daily life.
(a) We have learnt to find exact number when a certain percent of the total quantity is given.
(b) When parts of quantity are given to us as ratios, we have seen how to convert them to percentages.
(c) The increase or decrease in a certain quantity can also be expressed as percentage.
(d) The profit or loss incurred in a certain transaction can be expressed in terms of percentages.
(e) While computing interest on an amount borrowed, the rate of interest is given in terms of percents.

→ Percent profit = \(\frac{\text { Profit }}{\text { Cost price }}\) × 100 

→ Percent loss = \(\frac{\text { Loss }}{\text { Cost price }}\) × 100

→ Simple Interest = \(\frac{\text { Principal } \times \text { Time } \times \text { Rate }}{100}\)

→ Amount = Principal + Interest