Fractions and Decimals

Overview

Fractions and decimals form the backbone of numerical operations at the primary level and are heavily tested in Bihar TET Paper I Mathematics. This topic bridges whole-number arithmetic with more advanced concepts like ratios, percentages, and measurement—making it essential for both content knowledge and classroom teaching.

For the Bihar TET exam, you must demonstrate two competencies: solving problems involving fraction and decimal operations accurately, and understanding how children develop conceptual understanding of these number forms. Questions typically test conversion between fractions and decimals, ordering, and the four basic operations. Mastery here directly supports topics like percentage, ratio-proportion, and money calculations that appear elsewhere in the syllabus.

Students often struggle with fractions because they require a shift from counting discrete objects to understanding parts of a whole. Your role as a teacher—and as a TET candidate—is to understand both the mathematical procedures and the conceptual hurdles children face.

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 equal parts the whole is divided into; the numerator tells how many parts are taken.

• **Types of fractions**: Proper fractions (numerator < denominator, e.g., 3/5), improper fractions (numerator ≥ denominator, e.g., 7/4), and mixed numbers (whole number + proper fraction, e.g., 1¾).

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

• **Decimal as base-10 fraction**: Decimals extend the place-value system to parts smaller than one. Each place to the right of the decimal point represents division by 10 (tenths, hundredths, thousandths).

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

• **Like and unlike fractions**: Like fractions share the same denominator; unlike fractions have different denominators and require conversion before addition or subtraction.

• **Comparing fractions and decimals**: Convert to common denominators (for fractions) or align decimal places (for decimals) to compare values accurately.

Formulas / Key Facts

| Operation | Rule | |-----------|------| | **Adding like fractions** | a/c + b/c = (a+b)/c | | **Subtracting like fractions** | a/c − b/c = (a−b)/c | | **Adding unlike fractions** | Find LCM of denominators, convert, then add numerators | | **Multiplying fractions** | a/b × c/d = (a×c)/(b×d) | | **Dividing fractions** | a/b ÷ c/d = a/b × d/c (multiply by reciprocal) | | **Decimal to fraction** | Write digits as numerator; denominator = 10, 100, 1000 based on decimal places; simplify | | **Fraction to decimal** | Divide numerator by denominator | | **Adding/subtracting decimals** | Align decimal points, then add/subtract as whole numbers | | **Multiplying decimals** | Multiply as whole numbers; count total decimal places in both factors; place decimal in product | | **Dividing decimals** | Make divisor a whole number by shifting decimal; shift same places in dividend; divide |