Fractions and Decimals

Overview

Fractions and decimals form the backbone of numerical reasoning at the primary level and appear consistently in TS TET Mathematics. This topic tests both your computational fluency and your ability to explain these concepts to young learners. Questions typically involve operations (addition, subtraction, multiplication, division), conversions between fractions and decimals, and word problems requiring application of these skills.

Mastery here is essential because fractions and decimals connect directly to percentages, ratios, and measurement—topics that build upon this foundation. As a prospective teacher, you must understand not just *how* to solve problems but *why* the procedures work, since pedagogy questions often ask about common student misconceptions and effective teaching strategies.

Expect 3–5 questions on this topic, ranging from straightforward computation to conceptual questions about equivalent forms and ordering.

Key Concepts

• **Fraction as part of a whole**: A fraction a/b represents 'a' equal parts out of 'b' total parts. The numerator tells how many parts we have; the denominator tells how many equal parts make the whole.

• **Types of fractions**: Proper fractions (numerator < denominator), improper fractions (numerator ≥ denominator), and mixed numbers (whole number + proper fraction) are interchangeable forms of the same value.

• **Equivalent fractions**: Multiplying or dividing both numerator and denominator by the same non-zero number gives an equivalent fraction. Example: 2/3 = 4/6 = 6/9.

• **Decimal place value**: Each place to the right of the decimal point represents a power of ten—tenths (1/10), hundredths (1/100), thousandths (1/1000), and so on.

• **Terminating vs repeating decimals**: Fractions with denominators whose only prime factors are 2 and 5 give terminating decimals. Others produce repeating (recurring) decimals.

• **Like and unlike fractions**: Like fractions share the same denominator; unlike fractions have different denominators and require a common denominator for addition/subtraction.

• **Reciprocal**: The reciprocal of a/b is b/a. Division by a fraction equals multiplication by its reciprocal.

Formulas / Key Facts

| Operation | Rule | |-----------|------| | Addition/Subtraction of fractions | Find LCM of denominators, convert to like fractions, then add/subtract numerators | | Multiplication of fractions | (a/b) × (c/d) = (a×c)/(b×d) | | Division of fractions | (a/b) ÷ (c/d) = (a/b) × (d/c) | | Fraction to decimal | Divide numerator by denominator | | Decimal to fraction | Write decimal as fraction over power of 10, then simplify | | Mixed to improper | (whole × denominator + numerator)/denominator | | Improper to mixed | Divide numerator by denominator; quotient = whole part, remainder = new numerator |