Select Medium / माध्यम चुनें:

JAC • Class 6 • Mathematics • Ch 5

Estimated Time: 45 Mins

Study Progress: In Progress

Fractions

In JAC Board Class 6 Mathematics, "Fractions" explores part-whole numerical representation: $\frac{a}{b}$ where $b \ne 0$. Topics include proper, improper, and mixed fractions, representation on the number line, equivalent fractions, simplest (irreducible) form via HCF division, like and unlike fractions, comparing fractions by cross-multiplication/LCM, and addition and subtraction of like and unlike fractions.

View All Chapters JCERT Hindi Textbook

Overview Core Concepts Formulas & Identities Solved Examples Common Traps Summary Self Check Take MCQ Test

🍕 Have You Ever Wondered?

If 3 friends share 2 pizzas equally, how much does each person get, and why is 2/3 identical to 8/12?

Fractions represent fair sharing and division of continuous quantities! Master the art of equivalent fractions and arithmetic operations on rational parts.

Why This Chapter Matters

Before You Begin (Prerequisites)

Division and multiplication
Number line concept

What You Will Learn (Core Objectives)

Represent fractions as parts of a whole or collection.
Classify Proper ($<1$), Improper ($>1$), and Mixed fractions.
Generate Equivalent Fractions and reduce to Simplest Form using HCF.
Compare fractions using LCM of denominators or cross-multiplication.
Add and subtract like and unlike fractions.

Chapter Roadmap & Progression

1 Syllabus and book alignment

2 1. Fraction Types & Number Line

3 2. Equivalent Fractions & Simplest...

4 3. Comparing, Adding & Subtracting...

Complete Concept Guide (100% Curriculum Coverage)

Syllabus and book alignment

JCERT 2026–27: Regular schools (Non-SOE) — Chapter 5 · Fractions. Syllabus pages 93–114. These notes follow this topic. Official syllabus. Official JCERT Hindi textbook. Some source PDFs are damaged. The supplementary reference uses different chapter numbering.

1. Fraction Types & Number Line

A fraction is a number representing part of a whole: $\frac{\text{Numerator}}{\text{Denominator}} = \frac{a}{b}$ ($b \ne 0$).

Proper Fraction: Numerator $<$ Denominator; value is strictly $<1$ (e.g. $\frac{3}{4}, \frac{2}{5}$).
Improper Fraction: Numerator $\ge$ Denominator; value is $\ge 1$ (e.g. $\frac{7}{4}, \frac{5}{2}$).
Mixed Fraction: Combination of a whole number and a proper fraction (e.g. $1\frac{3}{4} = \frac{7}{4}$). Conversion formula:$$\text{Improper} = \frac{(\text{Whole} \times \text{Denominator}) + \text{Numerator}}{\text{Denominator}}$$

2. Equivalent Fractions & Simplest Form

Equivalent Fractions: Fractions representing the same portion of a whole, generated by multiplying or dividing numerator and denominator by the same non-zero number:$$\frac{a}{b} = \frac{a \times k}{b \times k}$$

Simplest Form (Lowest Terms): A fraction $\frac{a}{b}$ is in simplest form when $\text{HCF}(a, b) = 1$. To reduce a fraction, divide both numerator and denominator by their HCF.

3. Comparing, Adding & Subtracting Fractions

Like Fractions: Same denominators (e.g. $\frac{2}{7}, \frac{5}{7}$). Add/subtract numerators directly: $\frac{a}{d} \pm \frac{b}{d} = \frac{a \pm b}{d}$.
Unlike Fractions: Different denominators. Convert to like fractions by finding the LCM of denominators, then add/subtract numerators.
Cross-Multiplication Comparison: For $\frac{a}{b}$ and $\frac{c}{d}$:
If $a \times d > b \times c$, then $\frac{a}{b} > \frac{c}{d}$.

Key Formulas, Identities & Theorems

Mixed to Improper Conversion

$$W\frac{N}{D} = \frac{(W \times D) + N}{D}$$

Conversion formula.

Cross Multiplication Comparison

$$\frac{a}{b} > \frac{c}{d} \iff ad > bc$$

Valid for positive denominators.

Conceptual Solved Examples & Case Studies

Example 1

Simplify: 2/5 + 1/3.

Step-by-Step Solution:

Denominators are 5 and 3. $\text{LCM}(5, 3) = 15$.
Convert to like fractions:
$\frac{2}{5} = \frac{2 \times 3}{15} = \frac{6}{15}$
$\frac{1}{3} = \frac{1 \times 5}{15} = \frac{5}{15}$
Sum $= \frac{6 + 5}{15} = \mathbf{\frac{11}{15}}$.

Example 2

Reduce 36/48 to its simplest form.

Step-by-Step Solution:

Find $\text{HCF}(36, 48) = 12$.
Divide both numerator and denominator by 12:
$$\frac{36 \div 12}{48 \div 12} = \mathbf{\frac{3}{4}}$$.

Common Misconceptions & Examiner Traps

Common Misconception

Adding fractions by adding numerators and adding denominators (e.g. 1/2 + 1/3 = 2/5).

Scientific Reality & Correction

NEVER add denominators! You must find a common denominator (LCM) before adding numerators: $1/2 + 1/3 = 3/6 + 2/6 = 5/6$.

Visual Learning & Conceptual Map

Fraction Classifications

Value Relative to 1

Proper Fraction

Numerator < Denominator
Value < 1 (e.g. 3/4)

Improper Fraction

Numerator > Denominator
Value > 1 (e.g. 7/4)

Mixed Fraction

Whole + Proper
1¾ = 7/4

Chapter Summary & 10 Key Takeaways

Takeaway 1

Fractions represent part of a whole.

Takeaway 2

Types: proper (<1), improper (>=1), mixed (whole + proper).

Takeaway 3

Equivalent fractions share the same value; simplest form has HCF(num, den) = 1.

Takeaway 4

Add/subtract unlike fractions using LCM of denominators.

Check Your Understanding (Diagnostic Practice Questions)

Diagnostic questions testing core conceptual clarity. Answers are hidden initially — solve each problem first, then click to reveal the step-by-step verified solution.

Which fraction is greater: 4/7 or 5/9?

Reveal Answer & Explanation

Answer: Cross-multiply: $4 \times 9 = 36$ and $7 \times 5 = 35$. Since $36 > 35$, $\mathbf{\frac{4}{7} > \frac{5}{9}}$.
Use cross-multiplication.

Chapter practice

CBT tests for this chapter are not published yet. Solve the self-check questions above and compare your answers.

All Class 6 Mathematics Chapters

Ch 1: Knowing Our Numbers Ch 2: Whole Numbers Ch 3: Integers Ch 4: Playing with Numbers Ch 5: Fractions Ch 6: Decimals Ch 7: Ratio and Proportion Ch 8: Algebra Ch 9: Line, Line Segment and Ray Ch 10: Pairs of Lines Ch 11: Angles Ch 12: Polygons Ch 13: Circle Ch 14: Three-Dimensional Shapes Ch 15: Symmetry Ch 16: Practical Geometry Ch 17: Perimeter and Area Ch 18: Data Handling

AI Study Friend

Instant Concept Tutor

Have a doubt in Fractions? Ask our AI study tutor for rapid explanations or customized quizzes.

💬 "Explain core concepts of Fractions" 💬 "What are the common exam traps?" 💬 "How should I prepare for tests?"