Another Peek Beyond the Point – Formula & Equation Sheet
Essential formulas and equations from Ganita Prakash II, tailored for Class 7 in Mathematics.
This one-pager compiles key formulas and equations from the Another Peek Beyond the Point chapter of Ganita Prakash II. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Formulas
Decimal Division Rule: a ÷ 10^n = move decimal point left by n places
Here, 'a' is the number being divided, and 'n' is the number of zeros in the divisor. This rule helps simplify division by powers of ten.
Decimal Multiplication Rule: a × b = (a × b without decimal) / 10^n
This states the product is found by multiplying the numbers as if they were whole, then dividing by 10 raised to the total number of decimal places in the factors (a and b).
Fraction to Decimal: a/b = a ÷ b
Convert a fraction to decimal by performing division. Useful for understanding the relation between fractions and their decimal equivalents.
Area of Rectangle: Area = length × width
Used to calculate the area of a rectangle. Here, the dimensions can be in decimal form, illustrating real-world applications.
Average Speed = Distance / Time
In this formula, distance can be in kilometers and time in hours, giving a practical application for calculating rates.
Cost Calculation: Total Cost = Unit Price × Quantity
Here, you multiply the cost per item by the total number of items. This reflects real-life shopping scenarios.
Decimal expansion: 0.a + 0.b + ... + 0.c = d
Where 'a', 'b', 'c' are the decimal components of a number. Useful for understanding the construction of decimal numbers.
Decimal Quotient Rule: a ÷ b = (a × 10^n) / (b × 10^n) for decimal divisor
If the divisor is decimal, this method converts it into a whole number, allowing for easier division.
Price per kg = Total Price / Weight (in kg)
This calculates the price for 1 kg based on total pricing, a common practical application in shopping.
Total Distance = Speed × Time
This formula allows calculation of distance traveled over time at a constant speed, applicable for travel-related calculations.
Equations
9.5 × 5 = 47.5
To find the total cost when buying pens, multiply the cost of one pen by the number of pens.
12.5 × 7.5 = 93.75
Calculates distance traveled given the fuel consumption rate in km per litre and quantity of litres.
827 ÷ 1000 = 0.827
Converts meters to kilometers, useful for distance conversions.
4.68 ÷ 1.3 = 3.6
Demonstrates division with decimal quotients, useful in many real-world contexts.
1324 ÷ 4 = 331
An example of dividing a whole number evenly among a number of groups.
75.6 ÷ 3.6 = 21
Shows how to simplify division by decimals.
2.46 ÷ 1.5 = 1.64
An example of decimal division, applying to real-life measurements.
0.06 ÷ 5 = 0.012
Demonstrates dividing small decimal numbers, reinforcing decimal division skills.
9.5 ÷ 10 = 0.95
Illustrates how to move the decimal point to divide by ten.
0.827 × 2 = 1.654
Doubling a distance, showing the application of multiplication with decimals.
