Fractions and Decimals

Overview

Fractions and decimals form the backbone of numerical reasoning in the AP TET Mathematics section. This topic tests your ability to perform basic operations, convert between forms, and apply these concepts to word problems—skills essential for teaching primary and upper primary students.

Expect questions on simplifying fractions, comparing unlike fractions, performing operations on mixed numbers, and converting recurring decimals to fractions. These concepts also underpin later topics like percentage, ratio-proportion, and mensuration. A strong grip here saves time across multiple question types.

Mastery requires both procedural fluency (can you compute quickly and accurately?) and conceptual clarity (can you explain *why* 0.25 equals 1/4 to a student?). Both dimensions appear in AP TET questions.

Key Concepts

• **Fraction** = Part of a whole, written as numerator/denominator (e.g., 3/5 means 3 parts out of 5 equal parts).

• **Types of fractions**: Proper (numerator < denominator), Improper (numerator ≥ denominator), Mixed (whole number + proper fraction).

• **Equivalent fractions**: Different fractions representing the same value (2/4 = 3/6 = 1/2). Multiply or divide both numerator and denominator by the same non-zero number.

• **Decimal**: A way of writing fractions using place value (tenths, hundredths, thousandths). Example: 0.75 = 75/100.

• **Terminating decimals**: Decimals that end (e.g., 0.25, 0.125). Occur when denominator has only 2 and/or 5 as prime factors.

• **Non-terminating recurring decimals**: Decimals that repeat infinitely (e.g., 1/3 = 0.333...). Indicated by a bar over repeating digits.

• **Like fractions** share the same denominator; **unlike fractions** have different denominators. Convert to like fractions before adding/subtracting.

• **LCM of denominators** is used to find the common denominator for unlike fractions.

Formulas / Key Facts

| Operation | Rule | |-----------|------| | Addition/Subtraction of like fractions | a/c ± b/c = (a ± b)/c | | Addition/Subtraction of unlike fractions | Find LCM, convert to equivalent 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) — multiply by reciprocal | | Fraction to decimal | Divide numerator by denominator | | Decimal to fraction | Write decimal as fraction over power of 10, then simplify | | Recurring decimal to fraction | Let x = decimal, multiply to shift repeating part, subtract, solve |