Fractions

Overview

Fractions form one of the most essential building blocks in primary mathematics and appear consistently in the WB TET Paper I Mathematics section. A fraction represents a part of a whole or a ratio between two quantities. Mastery of fractions is critical because nearly every subsequent arithmetic topic—percentages, ratios, decimals, and basic algebra—depends on a solid understanding of how fractions work.

For the WB TET, you must be comfortable identifying fraction types, converting between them, performing basic operations, and understanding their decimal equivalents. Questions often test conceptual understanding alongside computation, so knowing *why* fraction rules work is just as important as memorising procedures. Teachers must also be able to explain fractions using visual models (like area models or number lines) to young learners.

Key Concepts

• **Fraction as part-whole**: A fraction a/b means 'a' equal parts out of 'b' total equal parts. The whole must be divided into equal parts for the fraction to be meaningful.

• **Numerator and Denominator**: The top number (numerator) tells how many parts we have; the bottom number (denominator) tells how many equal parts make the whole.

• **Proper Fraction**: Numerator is less than denominator (e.g., 3/5). Value is always less than 1.

• **Improper Fraction**: Numerator is greater than or equal to denominator (e.g., 7/4). Value is 1 or greater.

• **Mixed Fraction**: A whole number combined with a proper fraction (e.g., 2¾). It represents a quantity greater than 1.

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

• **Decimal Fraction**: A fraction whose denominator is a power of 10 (10, 100, 1000, etc.). These convert directly to decimal notation (e.g., 7/10 = 0.7).

• **Like and Unlike Fractions**: Like fractions have the same denominator; unlike fractions have different denominators. Converting to like fractions is essential for addition and subtraction.

Formulas / Key Facts

**Conversion: Improper to Mixed** Divide numerator by denominator. Quotient = whole number part; Remainder = new numerator; Denominator stays same. Example: 17/5 = 3 whole and 2/5 = 3²/₅

**Conversion: Mixed to Improper** (Whole number × Denominator) + Numerator = New numerator; Denominator stays same. Example: 4³/₇ = (4×7 + 3)/7 = 31/7

**Equivalent Fractions** a/b = (a×k)/(b×k) for any non-zero k. Example: 2/3 = 4/6 = 6/9