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.
(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
- 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.
- 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.
- 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.