Ch 7 of Ganita Prakash introduces fractions — numbers that represent parts of a whole. Fractions are essential in daily life: sharing a pizza equally, measuring ingredients for a recipe, or calculating distances. This chapter covers types of fractions, equivalent fractions, comparing fractions, and basic operations with fractions.
A fraction represents a part of a whole. It is written as a/b, where "a" (numerator) tells how many parts we have and "b" (denominator) tells how many equal parts the whole is divided into. For example, ¾ means 3 parts out of 4 equal parts. Fractions can represent parts of objects, collections, or quantities.
Proper fractions have numerator smaller than denominator (like ¾, ²⁄₅) and represent values less than 1. Improper fractions have numerator equal to or greater than denominator (like ⁷⁄₄, ⁵⁄₃) and represent values equal to or greater than 1. Mixed numbers combine a whole number with a proper fraction (like 1¾).
Equivalent fractions represent the same value. You can create equivalent fractions by multiplying or dividing both the numerator and denominator by the same non-zero number. For example: ½ = 2/4 = 3/6 = 4/8 = 5/10. To check if two fractions are equivalent, cross-multiply: if a/b = c/d, then a × d = b × c.
Like fractions (same denominator) are compared by looking at numerators — the larger numerator is the larger fraction. Unlike fractions need a common denominator (LCM of denominators) before comparing. You can also use cross multiplication: to compare a/b and c/d, compare a×d with b×c.
Like fractions are added/subtracted by keeping the denominator and adding/subtracting numerators: ²⁄₅ + ¹⁄₅ = ³⁄₅. For unlike fractions, first find a common denominator (LCM), convert both fractions, then add/subtract numerators. Always simplify the result to its lowest terms.
Download the official NCERT PDF for Ch 7 "Fractions" from the NCERT website: https://ncert.nic.in/textbook/pdf/fegp107.pdf. You can also download the complete Ganita Prakash textbook: https://ncert.nic.in/textbook/pdf/fegp1ps.zip
In a proper fraction, the numerator is less than the denominator (value < 1). In an improper fraction, the numerator is equal to or greater than the denominator (value ≥ 1). For example, ¾ is proper and ⁷⁄₄ is improper.
Multiply or divide both the numerator and denominator by the same non-zero number. For example, ²⁄₃ × 2/2 = ⁴⁄₆ × 2/2 = ⁸⁄₁₂. All these fractions are equivalent to ²⁄₃.
Fractions can only be added directly when they have the same denominator because the denominator tells us the size of each part. ²⁄₃ means "2 parts of size one-third" and ¹⁄₄ means "1 part of size one-fourth" — these parts are different sizes, so we need to convert them to the same size (common denominator) first.
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