Fractions and Decimals

Overview

Fractions and decimals form the backbone of numerical reasoning in TN TET Mathematics. This topic tests your ability to perform arithmetic operations, convert between representations, and solve word problems—skills essential for teaching Classes 1–8. Questions typically appear as direct calculations or embedded in mensuration, ratio, and percentage problems.

Mastery here requires fluency in three areas: operations on fractions (addition, subtraction, multiplication, division), operations on decimals, and seamless conversion between fractions, decimals, and percentages. The pedagogy section also expects you to explain these concepts to young learners using visual models like number lines and area diagrams.

Expect 3–5 questions directly on this topic in Paper I and Paper II Mathematics sections. Speed and accuracy matter—most are calculation-based with close answer options designed to trap careless errors.

Key Concepts

• **Fraction** = Part/Whole. Numerator (top) counts parts taken; denominator (bottom) counts equal parts in the whole.

• **Types of fractions**: Proper (numerator < denominator), Improper (numerator ≥ denominator), Mixed (whole number + proper fraction).

• **Equivalent fractions**: Multiply or divide both numerator and denominator by the same non-zero number. Example: 2/3 = 4/6 = 6/9.

• **Like fractions** share the same denominator; **unlike fractions** have different denominators and must be converted before adding/subtracting.

• **Decimal place values**: Tenths (1/10), hundredths (1/100), thousandths (1/1000). Moving decimal right multiplies by 10; moving left divides by 10.

• **Terminating decimals** end after finite digits (1/4 = 0.25). **Non-terminating repeating decimals** have a recurring pattern (1/3 = 0.333...).

• **Conversion rule**: Fraction to decimal—divide numerator by denominator. Decimal to fraction—write decimal over appropriate power of 10 and simplify.

Formulas / Key Facts

| Operation | Rule | |-----------|------| | Adding/Subtracting fractions | Make denominators same (LCM), then add/subtract numerators. | | Multiplying fractions | (a/b) × (c/d) = ac / bd | | Dividing fractions | (a/b) ÷ (c/d) = (a/b) × (d/c) — multiply by reciprocal | | Mixed to improper | Whole × Denominator + Numerator, keep same denominator | | Decimal × 10ⁿ | Shift decimal point n places right | | Decimal ÷ 10ⁿ | Shift decimal point n places left | | Fraction to percentage | Multiply by 100% | | Decimal to percentage | Multiply by 100 |

**Key conversions to memorise:**