Experts have designed these Class 8 Maths Notes and Part 2 Chapter 1 Fractions in Disguise Class 8 Notes for effective learning.
Class 8 Maths Chapter 1 Fractions in Disguise Notes
Class 8 Fractions in Disguise Notes
In this chapter, we will study how to change fraction into percentage, decimal into percentage, percentage into fraction or decimals and its applications.
Percentage, Profit, Loss and Discount
Percentage
- Percentage means per hundred. It is a way of expressing a number as a fraction out of 100.
- Each part of 100 equal parts is known as the hundredth part.
- Percentage can also be defined as numerators of fractions with denominator 100.
- It is denoted by symbol %, which means per hundred.
To Convert Fraction into Percentage
There are two methods to find percentage of a fraction.
Method I: By converting to equivalent fraction
Convert the fraction to an equivalent form with denominator 100 by multiplying numerator and denominator by the same number.
e.g \(\frac{3}{5}=\frac{3 \times 20}{5 \times 20}=\frac{60}{100}\) = 60%
Method II: We use the idea that a percentage is always taken out of 100.
e.g: \(\frac{3}{5}\)
Let x be the required percentage.
So, \(\frac{1}{2}\) ⇒ 300 = 5x [cross multiplying]
⇒ x = \(\frac{1}{2}\) ⇒ x = 60%
To Convert Decimal into Percentage
To convert decimal into percentage, firstly convert the decimal into fraction and then multiply the fraction by 100.
To Convert Percentage into Fraction:
To convert percentage into fraction, divide it by 100 and remove the percent sign.
To Convert Percentage into Decimal
For converting percentage into decimal, firstly convert the given percentage into fraction and then convert the fraction into decimal form.
To Convert Percentage into Ratio
A percentage can be expressed as a ratio with its second term 100 and first term equal to the given percentage.
To Convert Ratio into Percentage
For converting a ratio into percentage, firstly convert the given ratio into fraction and then multiply the fraction by 100 and put the percent sign.
Bar Models
Bar models are visual diagrams used to represent the data and solve percentage problems.
They show quantities as rectangular bars divided into sections, making it easier to understand relationships between parts and wholes.
Percentages Greater than 100%
A percentage greater than 100% signifies that the current quantity is more than the original or base quantity.
e.g. 120% of a target means the target was achieved completely (100%) plus an additional 20%.
Percentage Increase or Decrease
Percentages are used to describe, how much a value has changed relative to its original amount.
Percentage increase = \(\frac{\text { Amount of increase }}{\text { Original amount }}\) × 100
and percentage decrease = \(\frac{\text { Amount of decrease }}{\text { Original amount }}\) × 100
Profit and Loss
The concepts of profit and loss are used to determine whether a deal was beneficial or not.
Terms related to buying or selling of an item are given below.
- Cost Price (CP) The price at which an article is purchased is called its cost price. In short, it is written as CP.
The overhead expenses like sales tax, labour charges, cartages, etc., are included in the cost price. - Selling Price (SP) The price at which an article is sold is called its selling price. In short, it is written as SP.
- Profit If SP > CP then there is a profit. Profit is always reckoned on CP.
- Profit Percent Profit on ₹ 100 is called profit percent.
- Loss If SP < CP then there is a loss. Loss is always reckoned on CP.
- Loss Percent Loss on ₹ 100 is called loss percent.
- If SP = CP then there is no profit or no loss.
Relevant Formulae Related to Profit and Loss
- Profit = SP- CP
- Loss = CP – SP
- Profit % = \(\frac{\text { Profit }}{\mathrm{CP}}\) × 100
- Loss% = \(\frac{\text { Loss }}{\mathrm{CP}}\) × 100
Discount
- Discount is a reduction given on Marked Price (MP). This is generally given to attract customers to buy goods.
- Marked Price Marked price refers to the original or listed price of a product typically set by the seller. Thus, it is the price that is prominently displayed on the item.
- Sale Price The sale price is the reduced price at which a product is offered for a limited time. The sale price is also known as discounted price.
Discount =Marked Price (MP) -Sale Price (SP)
Rate of discount = Discount% = \(\frac{\text { Discount }}{\mathrm{MP}}\) × 100 - Discount is always calculated on the marked price.
Estimation in Percentages
Sometimes in a shop, while we are getting a particular discount on the bill, we estimate the bill in terms of percentage and pay the amount. If the amount is in decimal, we round off the bill to nearest tens and then estimate the bill.
Taxes
From July 1,2017, Government of India (GOI) introduced GST, which stands for Goods and Services Tax, which is levied on supply of goods or services or both.
India has a dual GST system with three main components.
- CGST (Central Goods and Services Tax) This is collected by the central government and is applied, when the purchase and sales of good take place within the same state (intra-state transactions).
- SGST (State Goods and services Tax) This state tax is applied along with the CGST for intra-state transactions, so that both the central government and the state government get a portion of the tax revenue.
- IGST (Integrated Goods and services Tax) This is levied on inter-state transactions (when the purchase and supply of goods take place between different states).
Note CGST and SGST are usually equal percentages (GST = 18%, so CGST = 9% and SGST = 9%).
Interest Without Compounding or With Compounding
Simple Interest (SI)
When we deposit the money in bank for a fixed period of time then after that time the bank pay us our amount along with some extra amount. This extra amount is called interest.
Terms related to interest are given below.
- Principal The money borrowed (or invested) is called principal.
- Interest The additional money paid by the borrower to the moneylender on the money lent is called interest.
- Amount The total money paid by the borrower to the moneylender is called amount.
Amount = Principal + Interest - Rate It is the interest paid on ₹ 100 for specified period.
- Time It is the time for which money is borrowed (or invested).
In earlier classes, we have learnt to calculate simple interest on a given principal for a given period at fixed rate of interest.
Let the principal be P and the rate of interest per year (in decimal form) be r. Then,
Simple Interest = Prt
Compound Interest (CI):
The interest calculated on the principal and the interest accumulated over the previous period is called compound interest.
If the borrower and the lender agree to fix up a certain interval of time, so that the amount at the end of an interval becomes the principal for the next interval then the total interest over all the intervals calculated in this way is called the compound interest.
Let the principal be P and the rate of interest per year (in decimal form) be r.
After 1 year,
Interest is calaclated on P.
Amount = P (1 + r)
After 2 years,
The amount after 1 year becomes the new principal.
Amount = P (1 + r) (1 + r) = P(1 + r)2
After 3 years,
Interest is again calculated on the increased amount.
Amount = P(1 + r)3
After t years
Amount = P(1 + r)t
Note: In case of simple interest, the principal remains constant for the whole period but in case of compound interest, the principal goes on changing every year.
Applications of Compound Interest Formula
There are some events, where we can use the formula for calculation of amount in compound interest.
Here are a few examples :
- increase (or decrease) in population.
- the growth of a bacteria if the rate of growth is known.
- the value of an item if its price increases or decreases in the intermediate years.
Population Growth and Depreciation Formulae
Let P be the population of a city or a town at the beginning of a certain year. If the constant rate of growth per annum (in decimal form) is r then
Population after t yr = P (1 + r)t
Let P be the population of a city or a town at the beginning of a certain year. If the constant rate of decrease per annum (indecimal form) is R then Population after t yr = P(1 – r)t