About Lesson
Comparing Quantities Class 7 Notes: Chapter 8
Prices related to an item
- Prices related to an item are: (i) Selling price
(ii) Cost price - Selling price (SP) is the price at which a product is sold out.
- Cost price (CP) is the buying price of an item.
- Profit = Selling price – Cost price
- Loss = Cost price – Selling price
- If SP > CP , then it is profit.
- If SP = CP , then it is neither profit nor loss.
- If CP > SP , then it is loss.
Finding the profit or loss percentage
Comparing Quantities : Introduction
- To compare two quantities, the units must be the same.
- Examples:
(i) Joe’s height is 150 cm and Tom’s is 100 cm.
Ratio of Joe’s height to Tom’s height would be Joe’s height : Tom’s height.
= 150 : 100 = 3: 2
(ii) Ratio of 3 km to 30 m is 3 km : 30 m.
= 3000 m : 30 m
= 300 : 1
Ratios
- Ratio is a relation between two quantities showing the number of times one value contains or is contained within the other.
- Example: If there are four girls and seven boys in a class, then the ratio of number of girls to number of boys is 4:7.
Equivalent Ratios
- By multiplying numerator and denominator of a rational number by a non zero integer, we obtain another rational number equivalent to the given rational number. These are called equivalent fractions.
- Example:1/3=1/3×2/2=2/6 and 1/3 are equivalent fractions.
Proportions
- If two ratios are equal, then they are said to be in proportion.
- Symbol “::” or “=” is used to equate the two ratios.
- Example: (i) Ratios 2:3 and 6:9 are equal. They can be represented as 2:3 :: 6:9 or 2:3 = 6:9.
(ii) Ratios 1:2 and x:4 are in proportion.
⇒12=x4
⇒1×4=x×2
⇒2x=4
⇒x=2
