Working with Fractions – Formula & Equation Sheet
Essential formulas and equations from Ganita Prakash, tailored for Class 7 in Mathematics.
This one-pager compiles key formulas and equations from the Working with Fractions chapter of Ganita Prakash. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Formulas
Distance = Speed × Time
Distance (km) is found by multiplying Speed (km/h) by Time (h). Useful in determining how far an object travels given its speed and time of travel.
Distance covered in t hours = t × (S)
Where S is speed (km/h) and t is time (h). This formula calculates the total distance based on speed and time.
Distance for fractions: Distance = (Fraction of Time) × (Speed)
For calculating distance when time is a fraction, multiply the fraction by speed.
Cost = Rate × Time
Cost (₹) is determined by multiplying Rate (₹/h) by Time (h). Useful for budgeting expenses based on time spent.
Conversion: Mixed Number to Improper Fraction
Convert by multiplying the whole number by the denominator and adding the numerator. Example: 1 1/4 = (1×4 + 1)/4 = 5/4.
Multiplying a Whole Number by a Fraction
When multiplying a whole number by a fraction a/b, use (Whole Number × a)/b to find the product.
a/b × c/d = (a × c) / (b × d)
This formula describes how to multiply two fractions together, where a, b, c, d are integers.
Adding Fractions: a/b + c/d = (ad + bc) / (bd)
To add fractions, find a common denominator and adjust the numerators accordingly.
Subtracting Fractions: a/b - c/d = (ad - bc) / (bd)
Similar to addition, but subtract the numerators after finding a common denominator.
Cost of services: Total Cost = Number of Units × Cost per Unit
This formula helps calculate the total expenditure on services based on the quantity and cost per unit.
Equations
Distance in 5 hours: 5 × 3 = 15 km
If a person walks 3 km in 1 hour, in 5 hours the total distance will be 5 times this value.
Distance in 3 hours for Tortoise: 3 × 1/4 = 3/4 km
Calculates the distance a tortoise can walk if its speed is 1/4 km/h over 3 hours.
Distance in 1/5 hours: 1/5 × 3 = 3/5 km
Shows how to calculate the distance covered when the time is a fraction of an hour.
Total Distance in 2/5 hours: 2/5 × 3 = 6/5 km
Calculates the total distance when walking time is a multiple of a fraction.
Total Land = 5 × 2/3 = 10/3 acres
Calculates the total land distributed to grandchildren if each gets 2/3 acre.
Cost of Internet Time: Cost = 8 × (5/4) = 10 ₹
Determines the cost for 1 1/4 hours of internet given a rate of ₹8 per hour.
Cost = Units × Rate (Rate = 8 ₹)
General formula for calculating costs when the price per unit is known.
a/b × c = (a × c) / b
Describes the multiplication of a fraction by a whole number, adjusting the numerator.
Cost of n hours = n × (Rate)
If Rate is given, this formula allows for quick calculation of total cost for n hours.
Total Distance = Sum of Parts = 3 + 3 + ... (n times)
Utilized for calculating the total distance as a repeated sum of constant speed over time.
