Fractions and Decimals

Overview

Fractions and decimals form the backbone of arithmetic reasoning at the primary level and appear consistently in JKTET Paper I Mathematics. This topic tests your ability to perform operations (addition, subtraction, multiplication, division) on both fractions and decimals, convert between the two forms, and apply these skills to word problems.

For the TET exam, you must demonstrate not only computational accuracy but also conceptual clarity—understanding *why* procedures work, since pedagogy questions often probe whether you can explain these concepts to young learners. Expect 3–5 direct questions on this topic, often mixed with word problems involving money, measurement, or ratio contexts relevant to daily life in J&K.

Mastery here builds the foundation for percentage, ratio-proportion, and profit-loss topics that follow in the syllabus. A student confident with fractions and decimals will find the rest of commercial mathematics straightforward.

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 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 + proper 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.

• **Decimal place value**: In 45.378, the digits after the decimal point represent tenths (3), hundredths (7), and thousandths (8). Each place is 1/10 of the previous.

• **Fraction-decimal relationship**: Every fraction can be written as a decimal (divide numerator by denominator). Terminating decimals occur when the denominator has only 2 and 5 as prime factors.

• **Like and unlike fractions**: Like fractions share the same denominator; unlike fractions require a common denominator before adding or subtracting.

• **Reciprocal**: The reciprocal of a/b is b/a. Used in division of fractions ("invert and multiply").

Formulas / Key Facts

| Operation | Fractions | Decimals | |-----------|-----------|----------| | Addition/Subtraction | Convert to like fractions (same denominator), then add/subtract numerators | Align decimal points, then add/subtract as whole numbers | | Multiplication | (a/b) × (c/d) = ac/bd | Multiply as whole numbers; count total decimal places in both factors and place decimal in product | | Division | (a/b) ÷ (c/d) = (a/b) × (d/c) | Move decimal in divisor to make it whole; move decimal in dividend equally; then divide |