Fractions and Decimals

Overview

Fractions and decimals form the backbone of numerical reasoning in primary mathematics and appear consistently in GTET Paper-I and Paper-II. This topic tests your ability to perform arithmetic operations, convert between representations, and apply these concepts to word problems involving money, measurement, and daily-life situations.

For GTET, expect questions that combine multiple operations (e.g., adding fractions then converting to decimals), comparison problems, and application-based questions. Mastery here also supports topics like percentage, ratio-proportion, and mensuration. Focus on speed and accuracy—most errors come from careless mistakes in finding common denominators or misplacing decimal points.

Key Concepts

• **Fraction fundamentals**: A fraction a/b represents 'a' parts out of 'b' equal parts. The numerator (top) counts parts; the denominator (bottom) names the size of each part.

• **Types of fractions**: Proper fractions (numerator < denominator, e.g., 3/5), improper fractions (numerator ≥ denominator, e.g., 7/4), and mixed numbers (whole + fraction, e.g., 1¾).

• **Equivalent fractions**: Fractions that represent the same value (e.g., 2/4 = 1/2 = 3/6). Multiply or divide both numerator and denominator by the same non-zero number.

• **Lowest terms**: A fraction is in lowest terms when HCF of numerator and denominator is 1. Always simplify final answers.