Fractions in Disguise – Formula & Equation Sheet
Essential formulas and equations from Ganita Prakash Part II, tailored for Class 8 in Mathematics.
This one-pager compiles key formulas and equations from the Fractions in Disguise chapter of Ganita Prakash Part II. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Formulas
Percentage Formula: P = (A / T) × 100
P represents the percentage, A is the part (or actual value), and T is the total. This formula calculates the percentage based on part-to-whole relationships, useful in various real-world scenarios including finance and academic scoring.
Fraction to Percentage: f = (n / d) × 100
f is the percentage, n is the numerator, and d is the denominator. This converts any fraction into a percentage, simplifying comparisons between different quantities.
Finding a Percentage of a Quantity: s = (p / 100) × q
s is the resultant value, p is the percentage, and q is the total quantity. Useful for calculating discounts and interest.
Convert Percentage to Fraction: z% = z / 100
z represents the percentage. This formula provides the fraction equivalent of a percentage, facilitating easier comparisons in mathematical problems.
To express (a/b) as a percentage: p% = (a/b) × 100
p is the percentage, a is the part, and b is the whole. This shows how to convert any rational number into a percentage, applicable in statistics.
Equivalent Fractions: a/b = m/n
a and b are one fraction, while m and n are another. This shows that fractions can be equivalent; useful for comparing sizes without calculating.
Percentage Increase: New Value = Old Value × (1 + p/100)
This formula calculates the new value after a percentage increase, where p is the increase percentage. It is often used in economics.
Percentage Decrease: New Value = Old Value × (1 - p/100)
Calculates the new value after a percentage decrease, where p is the decrease percentage. Vital for understanding pricing strategies.
Percent of a Total: Part = (Total × Percent) / 100
Calculates the part of a whole when given a percentage. Practical in budgeting and resource allocation.
Percentage Difference: PD = |A - B| / Average of A and B × 100
PD calculates the percentage difference between two values A and B, useful for comparing performance metrics.
Equations
Example of Fraction to Percentage: 3/4 = x/100
This equation helps to find x using cross multiplication, allowing fractions to be expressed as percentages.
Finding Percentage: 2/5 = x/100
To find x, we can rearrange to x = (2/5) × 100, resulting in 40%, illustrating how fractions convert to percentages.
Finding Equivalent Fractions: 24% = 24/100 = 12/50
Shows how to find equivalent fractions for a percentage, useful in simplifying ratios.
Percentage of Group: 15/80 = x/100
This equation helps calculate the percentage of students walking to school, derived from a known fraction.
Percentage Change Formula: PC = [(New Value - Old Value) / Old Value] × 100
This calculates how much a value has changed in percentage terms, crucial for economic evaluations.
Determining Proportion: 30 out of 50 = x%
Sets up the proportion to find x, demonstrating how to translate raw counts into percentages.
Simple Percentage Calculation: 75 out of 100 = x%
This equation establishes a direct relationship, emphasizing basic percentage calculations.
Relative Value Comparison: 9/34 = 26.47%
Demonstrates the conversion of a fraction to its percentage form, facilitating easier comprehension in comparisons.
Simple Calculation of Percent Contribution: A = 20% of B
Illustrates how to find A given a percentage of B, often employed in financial reports.
Percentile Value Representation: P = Number of Students Below/Total Students × 100
Defines how to calculate percentiles in a dataset, very important in academic performance evaluation.
