Fractions and Decimals

Overview

Fractions and decimals form the backbone of numerical operations at the primary level and are heavily tested in JTET Paper I Mathematics. This topic bridges whole number arithmetic with more advanced concepts like percentages, ratio-proportion, and measurement—all of which appear frequently in the exam.

For JTET, you must master not just mechanical calculations but also conceptual understanding and common student misconceptions. Questions typically test conversion between fractions and decimals, ordering, and word problems involving all four operations. The pedagogy section often asks how to teach these concepts using concrete materials like fraction strips or decimal squares.

A strong grasp here directly supports your performance in Percentage, Profit-Loss, and Mensuration topics. Expect 3–5 direct questions plus indirect applications across the mathematics section.

Key Concepts

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

• **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—multiply or divide both numerator and denominator by the same non-zero number (2/3 = 4/6 = 6/9).

• **Decimal as extension of place value**: Decimals use places to the right of the decimal point—tenths (1/10), hundredths (1/100), thousandths (1/1000).

• **Fraction-decimal relationship**: Every fraction can be written as a decimal by dividing numerator by denominator. Terminating decimals have denominators with only 2 and 5 as prime factors.

• **Like and unlike fractions**: Like fractions share the same denominator; unlike fractions require finding LCD (Least Common Denominator) before addition or subtraction.

• **Comparison rule**: For like fractions, compare numerators. For unlike fractions, convert to like fractions first or use cross-multiplication.

Formulas / Key Facts

| Operation | Fractions | Decimals | |-----------|-----------|----------| | **Addition/Subtraction** | Convert to like fractions, 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 | | **Division** | (a/b) ÷ (c/d) = (a/b) × (d/c) | Make divisor a whole number by shifting decimal in both numbers equally |