Fraction Calculation Formulas

Mathematics & Education
$$\frac{a}{b} \pm \frac{c}{d} = \frac{ad \pm bc}{bd}, \quad \frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}, \quad \frac{a}{b} \div \frac{c}{d} = \frac{ad}{bc}$$

Fraction arithmetic rules govern addition, subtraction, multiplication, and division of rational numbers by finding common denominators or multiplying numerators and denominators directly.

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GPA Formula (Grade Point Average)

Mathematics & Education
$$\text{GPA} = \frac{\sum (\text{Grade Points}_i \times \text{Credit Hours}_i)}{\sum \text{Credit Hours}_i}$$

Grade Point Average (GPA) is a weighted average calculation that measures academic performance by multiplying each course grade point value by its credit weight, summing the total quality points, and dividing by total credit hours attempted.

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Gratuity Formula

Finance
$$Gratuity = \frac{15 \times Last\ Drawn\ Salary \times Service\ Years}{26}$$

Gratuity is a lump-sum payment made by an employer to an employee as a token of appreciation for services rendered, typically after completing 5 or more years of continuous employment.

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GST Formula

Tax
$$\begin{aligned} \text{GST Amount} &= \text{Original Cost} \times \frac{\text{GST\%}}{100} \\ \text{Total Price} &= \text{Original Cost} + \text{GST Amount} \end{aligned}$$

Goods and Services Tax (GST) is a comprehensive indirect tax levied on the supply of goods and services. When computing transactions, you either add GST to find the final customer price, or subtract (remove) GST from the final retail price to find the pre-tax base cost.

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Home Loan Eligibility Formula

Real Estate
$$\begin{aligned} \text{Max EMI} &= (\text{Monthly Salary} \times \text{FOIR}) - \text{Existing EMI} \\ \text{Eligible Loan} &= \text{Max EMI} \times \frac{(1+r)^n - 1}{r(1+r)^n} \end{aligned}$$

Banks use the Fixed Obligation to Income Ratio (FOIR) method to decide how much of your monthly income can go toward loan repayments. The FOIR percentage itself rises with income (40% for lower incomes up to 55% for higher earners), reflecting that higher earners can comfortably commit more of their salary. Once the maximum affordable EMI is known, the eligible loan amount is reverse-calculated using the standard loan annuity formula.

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HRA Exemption Formula

Tax
$$HRA\ Exempt = \min\left( \text{Actual HRA}, \text{Rent Paid} - 10\%\ \text{Basic}, 50\%\ \text{Basic\ (Metro)}\ \text{or}\ 40\%\ \text{Basic\ (Non-Metro)} \right)$$

House Rent Allowance (HRA) exemption is calculated under Section 10(13A) of the Income Tax Act. It determines the tax-exempt portion of the HRA received by salaried individuals living in rented accommodations.

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Ideal Body Weight Formula

Health
$$\begin{aligned} \text{Devine (1974):} \quad &\text{Men} = 50 + 2.3 \times (h_{in} - 60) \text{ kg} \\ &\text{Women} = 45.5 + 2.3 \times (h_{in} - 60) \text{ kg} \\[1ex] \text{Robinson (1983):} \quad &\text{Men} = 52 + 1.9 \times (h_{in} - 60) \text{ kg} \\ &\text{Women} = 49 + 1.7 \times (h_{in} - 60) \text{ kg} \\[1ex] \text{Miller (1983):} \quad &\text{Men} = 56.2 + 1.41 \times (h_{in} - 60) \text{ kg} \\ &\text{Women} = 53.1 + 1.36 \times (h_{in} - 60) \text{ kg} \\[1ex] \text{Hamwi (1964):} \quad &\text{Men} = 48 + 2.7 \times (h_{in} - 60) \text{ kg} \\ &\text{Women} = 45.5 + 2.2 \times (h_{in} - 60) \text{ kg} \end{aligned}$$

There is no single, universally agreed-upon Ideal Body Weight (IBW) formula. Devine (1974), Robinson (1983), Miller (1983), and Hamwi (1964) are four separate, independently published clinical equations, each developed by different researchers using different population data, and each still in use today for different purposes (Devine, for example, is widely used in medical drug-dosage calculations). All four share the same basic structure — a base weight at 5 feet tall, plus a fixed amount added per inch of height above that — but use different constants, so they produce different results for the same person. Comparing all four together, rather than presenting one as definitive, gives a more complete and honest picture of what "ideal weight" estimates actually represent: a range, not a single number.

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In-Hand Take-Home Salary Formula

Finance
$$\text{In-Hand Salary} = \text{Gross Monthly Pay} - (\text{EPF} + \text{Professional Tax} + \text{ESI} + \text{Monthly TDS})$$

In-hand salary (take-home pay) is the net amount deposited into an employee bank account after statutory payroll deductions and monthly tax withholding under New or Old Tax Regimes.

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Inches to Centimeters Formula

Unit Converters
$$\text{Centimeters} = \text{Inches} \times 2.54$$

To convert inches to centimeters, multiply the inch value by 2.54.

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Income Tax Formula

Tax
$$\begin{aligned} \text{Net Taxable Income} &= \text{Gross Income} - \text{Deductions} \\ \text{Total Tax} &= \text{Slab Tax} - \text{Rebate} + \text{Cess (4\%)} \end{aligned}$$

Income tax is computed progressively based on income tax slabs. Taxpayers can choose between the Old Regime (which allows major deductions but has higher tax rates) and the New Regime (which has lower rates but restricts most deductions).

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