Students can go through AP 8th Class Maths Notes Chapter 8 Comparing Quantities to understand and remember the concepts easily.
Class 8 Maths Chapter 8 Notes Comparing Quantities
→ Discount is a reduction given on marked price.
Discount = Marked Price – Sale Price.
→ Discount can be calculated when discount percentage is given.
Discount = Discount % of Marked Price
→ Additional expenses made after buying an article are included in the cost price and are known as overhead expenses.
CP = Buying price + Overhead expenses
→ Sales tax is changed on the sale of an item.by the government and is added to the Bill Amount. Sales tax = Tax% of Bill Amount
→ GST stands for Goods and Services Tax and is levied on supply of goods or services or both.
→ Compound interest is the interest calculated on the previous year’s amount (A = P + I)
→ (i) Amount when interest is compounded annually
= P(1 + \(\frac{\mathrm{R}}{100}\))n ; P is principal, R is rate of interest, n is time period
(ii) Amount when interest is compounded half yearly
P(1 + \(\frac{\mathrm{R}}{200}\))2n{ \(\frac{R}{2}\) is half yearly rate and 2n = number of ‘half-years’
→ We use different methods to compare quantities.
→ Ratio and percentage are two such methods used to compare things / quantities.
→ In a ratio we can compare any number of quantities in their order (having same units)
For example : In a cricket team
3 all rounders, 2 bowlers, 4 and the 5 are batsman and 1 wicket keepr are there then ratio of bowlers, all rounders, batsman and wicket keepers
= 2 : 3 : 5 : 1
→ In a school bag 5 textbooks, 4 notes, 3 workbooks are kept.
then ratio of workbooks, school notes, and textbooks are 3 : 4 : 5
→ In a class of 36 students 20 are boys then ratio of Girls and boys are …………….
ratio of girls and boys =16 : 20
If the ratio has only two things, then we can write it in fraction from = \(\frac{16}{20}\) = \(\frac{4}{5}\) (by simplication)
Thus a: b can be written as (\(\frac{\mathrm{a}}{\mathrm{~b}}\)) also.
→ We can express this ratio form in percentage form also.
→ Percentage means, considering it to the quantity out of ‘100’.
→ For example : A student scored 16 out of 20 then the same can be calculated for out of 100 (using unitary method)
Here Out of 20 score is 16
then out of 100 (= 20 × 5)
score will be 16 × 5 = 80
So it means he iscores 80 out of 100 which can be expressed as 16 : 20 (or) \(\frac{16}{20}\) (or) 80%
→ Expressing in percentages is a good habbit for comparison.
→ To convert a fraction into percentage we have to multiply that fraction with 100.
Example : 1) \(\frac{4}{5}\) then \(\frac{4}{5}\) × 100 = 80%
So \(\frac{4}{5}\) means 80%
2) \(\frac{1}{4}\) then \(\frac{1}{4}\) × 100 = 25%
So 1 : 4 or \(\frac{1}{4}\) or 25%
→ To convert given percentage into fraction we divide it with 100 and simplify it.
Example : 40% = \(\frac{40}{100}\) = \(\frac{2}{5}\) So 40% = \(\frac{2}{5}\).
Convert 35% into fraction.
35% = \(\frac{35}{100}\) = \(\frac{7}{20}\) ; So 35% = \(\frac{7}{20}\).
Now checking \(\frac{7}{20}\) into percentage to convert the fraction into percentage, we have to mulitply it with 100.
So \(\frac{7}{20}\) × 100 = 7 × 5 = 30% hence verified.