Fractions and Decimals

Overview

Fractions and decimals form the backbone of numerical reasoning in HP TET Mathematics. This topic tests your ability to perform arithmetic operations—addition, subtraction, multiplication, and division—on both fractions and decimals, and to convert between the two forms. Questions frequently appear in both the content section and pedagogical contexts, where you may need to identify common student errors.

Mastery here directly supports success in related topics like percentage, ratio-proportion, and mensuration calculations. Expect 3–5 direct questions on this topic, often embedded in word problems involving money, measurement, or data interpretation. The key is speed and accuracy—build fluency through practice rather than memorising procedures mechanically.

Key Concepts

• **Fraction as part of a whole**: A fraction a/b represents 'a' equal parts out of 'b' total parts. The numerator (top) counts parts taken; the denominator (bottom) shows total equal parts.

• **Types of fractions**: Proper fractions have numerator < denominator (3/7). Improper fractions have numerator ≥ denominator (9/4). Mixed fractions combine a whole number with a proper fraction (2¼).

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

• **Decimal place value**: Each digit after the decimal point represents tenths, hundredths, thousandths, etc. In 3.456, the 4 is in tenths place, 5 in hundredths, 6 in thousandths.

• **Terminating vs recurring decimals**: Fractions with denominators having only 2 and 5 as prime factors give terminating decimals (1/4 = 0.25). Others give recurring decimals (1/3 = 0.333...).

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

• **Lowest terms (simplest form)**: A fraction is in lowest terms when HCF of numerator and denominator is 1.

Formulas / Key Facts

**Conversion formulas**:

• Fraction to decimal: Divide numerator by denominator (3/4 = 3 ÷ 4 = 0.75)
• Decimal to fraction: Write decimal over appropriate power of 10, then simplify (0.125 = 125/1000 = 1/8)
• Mixed to improper: (whole × denominator + numerator)/denominator → 2¾ = (2×4+3)/4 = 11/4
• Improper to mixed: Divide numerator by denominator → quotient is whole part, remainder is new numerator

**Operations on fractions**: