Class 8 Exam > Class 8 Notes > Mathematics (Maths) Class 8 > Important Formulae: Comparing Quantities
Important Formulae: Comparing Quantities | Mathematics (Maths) Class 8 PDF Download
Terms
1. Unitary Method
Unitary method is on the most useful method to solve ratio, proportion and percentage problems. In this we first find value of one unit and then find the value of required number of units.
So in Short Unitary method comprises two following steps:
- Step 1: Find the value of one unit.
- Step 2: Then find the value of required number of units.
2. Percentages
- Percentages are ways to compare quantities. They are numerators of fractions with denominator 100 or it basically means per 100 value
- Percent is derived from Latin word ‘per centum’ meaning ‘per hundred’
It is denoted by % symbol
1% means 1/100= .01 - We can use either unitary method or we need to convert the fraction to an equivalent fraction with denominator 100
3. Discounts
- Discount is a reduction given on the Marked Price (MP) of the article.
- This is generally given to attract customers to buy goods or to promote sales of the goods.
- You can find the discount by subtracting its sale price from its marked price.
So, Discount = Marked price – Sale price
Question for Important Formulae: Comparing QuantitiesTry yourself: What is the unitary method used for?View Solution
4. Interest: Interest is the extra money paid by institutions like banks or post offices on money deposited (kept) with them. Interest is also paid by people when they borrow money.
5. Simple Interest
- Principal (P): The original sum of money loaned/deposited. Also known as capital.
- Time (T): The duration for which the money is borrowed/deposited.
- Rate of Interest (R): The percent of interest that you pay for money borrowed, or earn for money deposited.
- Simple interest is calculated as
- Total amount at the end of time period
A= P + SI
6. Compound interest
- Principal (P): The original sum of money loaned/deposited.
- Time (n): The duration for which the money is borrowed/deposited.
- Rate of Interest (R): The percent of interest that you pay for money borrowed, or earn for money deposited
- Compound interest is the interest calculated on the previous year’s amount (A = P + I).
The document Important Formulae: Comparing Quantities | Mathematics (Maths) Class 8 is a part of the Class 8 Course Mathematics (Maths) Class 8.
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FAQs on Important Formulae: Comparing Quantities - Mathematics (Maths) Class 8
| 1. What is the formula for calculating the percentage increase or decrease in quantities? |  |
Ans. The formula for calculating the percentage increase is:
\[
\text{Percentage Increase} = \left( \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \right) \times 100
\]
For percentage decrease, the formula is:
\[
\text{Percentage Decrease} = \left( \frac{\text{Old Value} - \text{New Value}}{\text{Old Value}} \right) \times 100
\]
| 2. How can I compare two quantities using the ratio method? | |
Ans. To compare two quantities using the ratio method, you divide one quantity by the other. The formula is:
\[
\text{Ratio} = \frac{\text{Quantity A}}{\text{Quantity B}}
\]
This gives you a fraction that can be simplified to show how many times one quantity is greater or lesser than the other.
| 3. What is the difference between simple interest and compound interest in the context of comparing quantities? | |
Ans. Simple interest is calculated on the principal amount throughout the entire duration, using the formula:
\[
\text{Simple Interest} = \text{Principal} \times \text{Rate} \times \text{Time}
\]
Compound interest, however, is calculated on the principal and also on the accumulated interest of previous periods, using the formula:
\[
\text{Compound Interest} = \text{Principal} \times \left(1 + \frac{\text{Rate}}{n}\right)^{n \times t} - \text{Principal}
\]
Comparing these two helps in understanding how much more can be earned with compound interest over time.
| 4. How do I convert fractions to percentages when comparing quantities? | |
Ans. To convert a fraction to a percentage, divide the numerator by the denominator and then multiply by 100. The formula is:
\[
\text{Percentage} = \left( \frac{\text{Numerator}}{\text{Denominator}} \right) \times 100
\]
For example, to convert \(\frac{3}{4}\) to a percentage:
\[
\text{Percentage} = \left( \frac{3}{4} \right) \times 100 = 75\%
\]
| 5. What are the applications of comparing quantities in real-life scenarios? | |
Ans. Comparing quantities is essential in various real-life scenarios such as budgeting, calculating discounts during sales, assessing performance metrics, and making investment decisions. By understanding how to compare quantities, one can make informed choices regarding finance, purchasing, and resource allocation.
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