Fractions form one of the most essential building blocks in primary mathematics and appear consistently in the WB TET Paper I Mathematics section. A fraction represents a part of a whole or a ratio between two quantities. Mastery of fractions is critical because nearly every subsequent arithmetic topic—percentages, ratios, decimals, and basic algebra—depends on a solid understanding of how fractions work.
For the WB TET, you must be comfortable identifying fraction types, converting between them, performing basic operations, and understanding their decimal equivalents. Questions often test conceptual understanding alongside computation, so knowing *why* fraction rules work is just as important as memorising procedures. Teachers must also be able to explain fractions using visual models (like area models or number lines) to young learners.
Key Concepts
**Fraction as part-whole**: A fraction a/b means 'a' equal parts out of 'b' total equal parts. The whole must be divided into equal parts for the fraction to be meaningful.
**Numerator and Denominator**: The top number (numerator) tells how many parts we have; the bottom number (denominator) tells how many equal parts make the whole.
**Proper Fraction**: Numerator is less than denominator (e.g., 3/5). Value is always less than 1.
**Improper Fraction**: Numerator is greater than or equal to denominator (e.g., 7/4). Value is 1 or greater.
**Mixed Fraction**: A whole number combined with a proper fraction (e.g., 2¾). It represents a quantity greater than 1.
**Equivalent Fractions**: Different fractions that represent the same value (e.g., 1/2 = 2/4 = 3/6). Multiply or divide both numerator and denominator by the same non-zero number.
**Decimal Fraction**: A fraction whose denominator is a power of 10 (10, 100, 1000, etc.). These convert directly to decimal notation (e.g., 7/10 = 0.7).
**Like and Unlike Fractions**: Like fractions have the same denominator; unlike fractions have different denominators. Converting to like fractions is essential for addition and subtraction.
Formulas / Key Facts
**Conversion: Improper to Mixed** Divide numerator by denominator. Quotient = whole number part; Remainder = new numerator; Denominator stays same. Example: 17/5 = 3 whole and 2/5 = 3²/₅
**Conversion: Mixed to Improper** (Whole number × Denominator) + Numerator = New numerator; Denominator stays same. Example: 4³/₇ = (4×7 + 3)/7 = 31/7
**Equivalent Fractions** a/b = (a×k)/(b×k) for any non-zero k. Example: 2/3 = 4/6 = 6/9
**Simplest Form (Lowest Terms)** Divide numerator and denominator by their HCF. Example: 12/18 → HCF is 6 → 2/3
**Addition/Subtraction of Like Fractions** a/c + b/c = (a+b)/c a/c − b/c = (a−b)/c
**Addition/Subtraction of Unlike Fractions** Find LCM of denominators, convert to like 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 the reciprocal.
**Fraction to Decimal** Divide numerator by denominator. For denominator as power of 10, shift decimal point. Example: 3/4 = 0.75; 23/100 = 0.23
**Decimal to Fraction** Write decimal as fraction over appropriate power of 10, then simplify. Example: 0.125 = 125/1000 = 1/8
Worked Examples
**Example 1: Convert 23/6 to a mixed fraction.**
Step 1: Divide 23 by 6. 23 ÷ 6 = 3 remainder 5
Step 2: Write as mixed fraction. Whole part = 3, Fraction part = 5/6
Answer: 3⁵/₆
---
**Example 2: Add 2/5 and 3/4.**
Step 1: Find LCM of denominators 5 and 4. LCM(5, 4) = 20
Step 2: Convert to like fractions. 2/5 = (2×4)/(5×4) = 8/20 3/4 = (3×5)/(4×5) = 15/20
Step 3: Add numerators. 8/20 + 15/20 = 23/20
Step 4: Convert to mixed fraction if needed. 23/20 = 1³/₂₀
Answer: 23/20 or 1³/₂₀
---
**Example 3: Convert 0.375 to a fraction in lowest terms.**
Step 1: Write as fraction over power of 10. 0.375 = 375/1000
**Adding/subtracting numerators and denominators separately**: Students write 2/3 + 1/4 = 3/7. *Correct approach*: Find common denominator first, then add only numerators.
**Forgetting to simplify**: Leaving answers like 6/8 when 3/4 is expected. *Always check* if the fraction can be reduced to lowest terms.
**Confusing improper and mixed conversion direction**: Multiplying instead of dividing when going improper → mixed. *Remember*: Improper to mixed uses division; mixed to improper uses multiplication then addition.
**Ignoring the whole number in mixed fraction operations**: When adding 2¹/₃ + 1²/₃, students sometimes add only the fraction parts. *Correct approach*: Add whole numbers separately, add fractions, then combine (and carry over if fraction sum exceeds 1).
**Decimal point errors**: Writing 7/100 as 0.7 instead of 0.07. *Rule*: The number of zeros in the denominator equals the number of decimal places.
**Reciprocal confusion in division**: Flipping the wrong fraction. *Remember*: Keep the first fraction, flip only the second (the divisor), then multiply.
Quick Reference
Proper fraction: numerator < denominator; value < 1.
Improper fraction: numerator ≥ denominator; value ≥ 1.
Mixed to improper: (whole × denominator) + numerator over same denominator.
Unlike fractions: convert to LCM-based common denominator before adding/subtracting.
Division by a fraction: multiply by its reciprocal.
Decimal fraction 0.ab = ab/100; always simplify by HCF.
You read the notes — now try one
A teacher asks students to convert the mixed fraction 3 2/5 into an improper fraction. What is the correct answer?
Tap an option to check your answer.
👥 Study this together
Invite your prep group — read the same notes, then discuss doubts in this topic's shared room.
A teacher asks students to convert the mixed fraction 3 2/5 into an improper fraction. What is the correct answer?
Q2 · Fractions · MEDIUM
Ravi spent 3/8 of his pocket money on books and 1/4 of it on snacks. What fraction of his pocket money did he spend in total?
Q3 · Fractions · MEDIUM
A student needs to arrange the following decimal fractions in ascending order: 0.45, 0.405, 0.5, 0.054. Which option shows the correct arrangement?
Q4 · Fractions · HARD
A rectangular field is 5 3/4 metres long and 3 1/2 metres wide. What is the area of the field in square metres? (Express your answer as a mixed fraction)