Fractions and Decimals

Overview

Fractions and decimals form the backbone of primary mathematics and appear consistently in OTET Paper I. This topic tests your conceptual understanding of part-whole relationships and your ability to perform arithmetic operations accurately. Questions typically involve addition, subtraction, multiplication, and division of fractions and decimals, along with conversion between the two forms.

For aspiring primary teachers, mastery of this topic is essential not just for clearing the exam but for effective classroom teaching. Students often struggle with fractions and decimals because these concepts require a shift from whole-number thinking. Understanding common misconceptions helps you both answer pedagogy-linked questions and teach more effectively.

Expect 3-5 direct questions from this topic, often combined with word problems involving money, measurement, or ratio-proportion contexts.

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). Example: 3/4 is proper, 7/4 is improper, 1¾ is mixed.

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

• **Like and unlike fractions**: Like fractions have the same denominator; unlike fractions have different denominators. Converting to like fractions is essential before adding or subtracting.

• **Decimal as fraction with denominator 10, 100, 1000...**: 0.7 = 7/10, 0.35 = 35/100. Place value determines the denominator.

• **Place value in decimals**: Tenths (first place after decimal), hundredths (second place), thousandths (third place). Example: In 3.257, the 2 is in tenths place, 5 in hundredths, 7 in thousandths.

• **Relationship between fractions and decimals**: Every fraction can be converted to a decimal by dividing numerator by denominator. Terminating decimals have denominators with only 2 and 5 as prime factors.

Formulas / Key Facts

**Fraction Operations:**

• Addition/Subtraction (like fractions): a/c ± b/c = (a ± b)/c
• Addition/Subtraction (unlike fractions): Find LCM of denominators, convert to equivalent fractions, then add/subtract