Fraction Class 6 ICSE — Maths Chapter 5
Fractions Fraction Class 6 ICSE chapter 5 of the Maths book teaches what a fraction is and how to work with it. You will meet proper, improper and mixed fractions, and learn to compare, add, subtract, multiply and divide them. Each section below follows the book’s own order. Worked examples use fresh numbers so you can practise the method on your own.
Download Fractions Class 6 ICSE Mathematics Chapter 5 PDF
Download the Fractions Class 6 ICSE Mathematics chapter PDF to revise offline or print for practice. It is the full chapter as printed in the book — 15 pages, 13 sections, 38 questions.
What is inside Chapter 5
15 pages · 13 sections · 17 worked examples · 38 exercise questions
| Section | Title |
|---|---|
| 5.1 | BASIC CONCEPT |
| 5.2 | TYPES OF FRACTIONS |
| 5.3 | CONVERTING A MIXED FRACTION INTO AN IMPROPER FRACTION |
| 5.4 | CONVERTING AN IMPROPER FRACTION INTO A MIXED FRACTION |
| 5.5 | CONVERTING UNLIKE FRACTIONS INTO LIKE FRACTIONS |
| 5.6 | REDUCING A FRACTION TO ITS LOWEST TERMS |
| 5.7 | COMPARING FRACTIONS |
| 5.8 | FUNDAMENTAL OPERATIONS ON FRACTIONS |
| 5.9 | ADDITION AND SUBTRACTION |
| 5.10 | MULTIPLICATION AND DIVISION |
| 5.11 | COMBINED OPERATIONS OF MULTIPLICATION AND DIVISION |
| 5.12 | USING 'of' ALONG WITH MULTIPLICATION AND DIVISION |
| 5.14 | PROBLEMS INVOLVING FRACTIONS |
- EXERCISE 5(A): 6 questions
- EXERCISE 5(B): 9 questions
- EXERCISE 5(C): 2 questions
- EXERCISE 5(E): 11 questions
- Revision Exercise (Chapter 5): 10 questions
5.1 BASIC CONCEPT
A fraction expresses a part of a whole. The book opens with rice divided into four equal parts, where each part is one-fourth \frac{1}{4}. An apple split into five equal parts gives each piece as one-fifth \frac{1}{5}. Eat two pieces and three remain, so three-fifths \frac{3}{5} of the apple is left.
Every fraction has two terms. The top number is the numerator, the bottom number is the denominator:
\text{FRACTION} = \frac{\text{NUMERATOR}}{\text{DENOMINATOR}}
So in \frac{7}{11}, the numerator is 7 and the denominator is 11. The mnemonic to remember the order: N for Numerator sits on top, D for Denominator is down below.
Two rules matter from the start. First, every fraction must be in its lowest terms, meaning the terms share no common factor except 1. Second, 5 out of 7 means the whole is cut into 7 equal parts and 5 are taken, written \frac{5}{7}.
Worked pattern: a chocolate bar cut into 6 equal pieces, with 2 eaten, leaves \frac{4}{6} of the bar. Four parts out of six remain.
5.2 TYPES OF FRACTIONS
The book sorts fractions into five groups. Here is the comparison table:
| Type | Rule | Example |
|---|---|---|
| Proper fraction | numerator \lt denominator | \frac{4}{5} |
| Improper fraction | numerator \geq denominator | \frac{7}{5} |
| Mixed fraction | integer + proper fraction | 4\frac{2}{3} |
| Like fractions | same denominator | \frac{3}{5}, \frac{1}{5} |
| Unlike fractions | different denominators | \frac{5}{9}, \frac{7}{8} |
When numerator equals denominator, the value is 1, so \frac{4}{4} = 1. A mixed fraction like 3\frac{2}{5} means 3 + \frac{2}{5}. A negative mixed fraction keeps the sign outside the bracket: -2\frac{1}{8} = -\left(2 + \frac{1}{8}\right).
Equivalent fractions share the same value. Multiplying or dividing both terms by the same non-zero number keeps the value unchanged. So \frac{2}{5} = \frac{8}{20}, because 2 × 4 = 8 and 5 × 4 = 20.
5.3 CONVERTING A MIXED FRACTION INTO AN IMPROPER FRACTION
To turn a mixed fraction into an improper fraction, multiply the integral part by the denominator, add the numerator, and keep the denominator unchanged:
\frac{\text{Integral part} \times \text{Denominator} + \text{Numerator}}{\text{Denominator}}
Worked pattern: convert 4\frac{2}{7}. Multiply 4 × 7 = 28, add 2, giving \frac{30}{7}. The denominator stays 7.
For a negative mixed fraction, keep the minus sign outside the whole expression. So -2\frac{1}{8} becomes -\left(2 + \frac{1}{8}\right) = -\frac{17}{8}.
5.4 CONVERTING AN IMPROPER FRACTION INTO A MIXED FRACTION
Do the reverse conversion by dividing the numerator by the denominator. The quotient is the integral part, and the remainder becomes the new numerator:
\text{Improper fraction} = \text{Quotient}\ \frac{\text{Remainder}}{\text{Denominator}}
Worked pattern: convert \frac{29}{6}. Divide 29 by 6: quotient 4, remainder 5. The mixed fraction is 4\frac{5}{6}.
A common mistake is swapping the quotient and remainder. The quotient is the whole-number part; the remainder is only the numerator of the fractional part. The denominator never changes.
5.5 CONVERTING UNLIKE FRACTIONS INTO LIKE FRACTIONS
This section uses a two-step method. First, find the LCM of all denominators. Second, multiply each fraction’s numerator and denominator by the number that brings its denominator to that LCM.
Worked pattern: convert \frac{2}{3}, \frac{1}{4} and \frac{5}{6} into like fractions. The LCM of 3, 4 and 6 is 12. Multiply each fraction: \frac{8}{12}, \frac{3}{12} and \frac{10}{12}.
This skill matters twice in this ICSE chapter. It sits behind comparing fractions in section 5.7 and behind addition and subtraction in section 5.9. You already met the LCM in Chapter 4, Factors and Multiples.
5.6 REDUCING A FRACTION TO ITS LOWEST TERMS
A fraction is in its lowest terms when its numerator and denominator are co-prime, meaning they share no common factor other than 1. The book gives two methods to reduce.
HCF method: find the HCF of both terms and divide each by it. Prime factorisation method: write each term as a product of primes and cancel the common factors.
Worked pattern: reduce \frac{36}{84}. The HCF of 36 and 84 is 12, so \frac{36 \div 12}{84 \div 12} = \frac{3}{7}. The prime path gives the same result: \frac{2 \times 2 \times 3 \times 3}{2 \times 2 \times 3 \times 7} = \frac{3}{7}.
Dividing or multiplying both terms by the same number never changes the value of the fraction.
5.7 COMPARING FRACTIONS
Comparing fractions means finding which value is greater or smaller. The book offers two methods. Comparing fractions is a core skill in the Class 6 ICSE syllabus.
Method 1 — equalise denominators: convert to like fractions; the larger numerator is the larger fraction. Method 2 — equalise numerators: the fraction with the smaller denominator is larger.
Worked pattern: compare \frac{5}{6} and \frac{7}{9}. LCM of 6 and 9 is 18, so \frac{15}{18} and \frac{14}{18}. Since 15 \gt 14, \frac{5}{6} is greater. By the numerator method, LCM of 5 and 7 is 35, giving \frac{35}{42} and \frac{35}{45}; the smaller denominator, 42, belongs to the larger fraction.
Ordering four fractions: \frac{2}{3}, \frac{5}{8}, \frac{7}{12}, \frac{1}{2}. LCM of denominators is 24, giving \frac{16}{24}, \frac{15}{24}, \frac{14}{24}, \frac{12}{24}. Descending order: \frac{2}{3} \gt \frac{5}{8} \gt \frac{7}{12} \gt \frac{1}{2}.
5.8 FUNDAMENTAL OPERATIONS ON FRACTIONS
The four fundamental operations on fractions are addition, subtraction, multiplication and division. The rest of the chapter performs these operations step by step. Section 5.9 covers addition and subtraction, section 5.10 covers multiplication and division, and sections 5.11 and 5.12 combine them.
5.9 ADDITION AND SUBTRACTION
The book gives four steps for adding and subtracting fractions. First, convert any mixed fraction to an improper fraction. Second, convert to equivalent fractions with a common denominator. Third, combine the numerators over that denominator. Fourth, reduce to lowest terms and convert back to a mixed fraction if needed.
Worked pattern (addition): \frac{2}{3} + \frac{3}{4}. LCM of 3 and 4 is 12, so \frac{8}{12} + \frac{9}{12} = \frac{17}{12} = 1\frac{5}{12}.
Worked pattern (subtraction): 1\frac{1}{6} - \frac{3}{8}. Convert to \frac{7}{6} - \frac{3}{8}. LCM of 6 and 8 is 24, giving \frac{28}{24} - \frac{9}{24} = \frac{19}{24}.
Common mistakes and corrections:
- Adding denominators directly — convert to like fractions first, then add only the numerators.
- Keeping a mixed fraction unchanged — always convert it to an improper fraction before adding or subtracting.
- Not reducing the final answer — always reduce to lowest terms, then to a mixed fraction if the numerator is larger.
5.10 MULTIPLICATION AND DIVISION
For multiplication, make sure no fraction is in mixed form. Then multiply the numerators together and the denominators together, and reduce the result if needed.
For division, multiply the dividend by the reciprocal of the divisor. A whole number is written as itself over 1 before taking its reciprocal, so the reciprocal of 5 is \frac{1}{5}.
Worked pattern (multiplication): \frac{3}{5} \times \frac{10}{9} = \frac{30}{45} = \frac{2}{3}.
Worked pattern (division): \frac{4}{7} \div \frac{8}{21} = \frac{4}{7} \times \frac{21}{8} = \frac{84}{56} = \frac{3}{2} = 1\frac{1}{2}.
The most common mistake in division is forgetting to flip the divisor. You multiply by the reciprocal of the second fraction, never divide straight across.
5.11 COMBINED OPERATIONS OF MULTIPLICATION AND DIVISION
When an expression mixes division and multiplication, complete the division first, then do the multiplication. You can flip all the divisions at once and multiply the chain directly.
Worked pattern: \frac{5}{6} \div \frac{3}{4} \times \frac{2}{5}. Rewrite as \frac{5}{6} \times \frac{4}{3} \times \frac{2}{5}. Multiply across: \frac{5 \times 4 \times 2}{6 \times 3 \times 5} = \frac{40}{90} = \frac{4}{9}.
The direct form is faster: flip each divisor to its reciprocal and multiply the whole chain in one line.
5.12 USING ‘of’ ALONG WITH MULTIPLICATION AND DIVISION
The word ‘of’ between two fractions works like multiplication, but it is done before division and multiplication. The full order is fixed by BODMAS: Brackets, Of, Division, Multiplication, Addition, Subtraction. Fractions inside brackets are combined first. BODMAS appears often in Class 6 ICSE fraction problems.
Worked pattern (‘of’ first): \frac{1}{2} of \frac{4}{5} \div \frac{2}{3}. Operate ‘of’ first: \frac{2}{5} \div \frac{2}{3} = \frac{2}{5} \times \frac{3}{2} = \frac{3}{5}.
Worked pattern (bracket first): \frac{1}{4} + \left(\frac{3}{8} \times \frac{2}{3}\right) \div \frac{1}{2}. Solve the bracket: \frac{6}{24} = \frac{1}{4}. Then \frac{1}{4} + \frac{1}{4} \div \frac{1}{2} = \frac{1}{4} + \frac{1}{2} = \frac{3}{4}.
Remember the order with the mnemonic: Brackets First, Of Second, Division Third, Multiplication Fourth, Addition Fifth, Subtraction Last.
5.14 PROBLEMS INVOLVING FRACTIONS
Word problems in this ICSE chapter rest on one central rule: the whole quantity is taken as 1. If a fraction of the whole is used, the remaining part is 1 - \text{fraction used}.
Worked pattern (finding the whole): a student spends \frac{3}{5} of pocket money and is left with ₹40. Money left is 1 - \frac{3}{5} = \frac{2}{5}. Since \frac{2}{5} of the original = ₹40, the original amount = ₹40 × \frac{5}{2} = ₹100.
Worked pattern (two parts): out of 200 books, \frac{1}{4} are damaged and \frac{1}{5} are borrowed. Damaged = 50, borrowed = 40, so books left = 200 − 50 − 40 = 110.
The same approach handles journey problems, money problems and quantity problems. Take the whole as 1, subtract the used fraction, then multiply by the reciprocal to recover the whole. You will use this skill again in Chapter 6, Decimal Fractions.
What to practise from Fractions Class 6 ICSE
The book groups its practice into five blocks. Each exercise targets the skill taught in specific sections of this ICSE chapter:
- EXERCISE 5(A) — 6 questions, covering sections 5.1 to 5.5 (basic concept, types, conversions).
- EXERCISE 5(B) — 9 questions, covering sections 5.6 and 5.7 (lowest terms and comparison).
- EXERCISE 5(C) — 2 questions, covering section 5.9 (addition and subtraction).
- EXERCISE 5(E) — 11 questions, covering section 5.14 (word problems).
- Revision Exercise (Chapter 5) — 10 questions, spanning the whole chapter.
Note that the book has no EXERCISE 5(D) in this chapter, and the section numbering jumps from 5.12 to 5.14. Work through the blocks in order, and revisit the section that teaches each skill before attempting its exercise. You can browse all of Class 6 Maths chapters for more context.
Fractions Class 6 ICSE frequently asked questions
What is a fraction in Class 6 ICSE?
A fraction is a quantity that expresses a part of a whole. It is written as \frac{\text{Numerator}}{\text{Denominator}}, where the numerator is the top term and the denominator is the bottom term.
How do I convert a mixed fraction to an improper fraction?
Multiply the integral part by the denominator, add the numerator, and keep the denominator unchanged. For example, 4\frac{2}{7} = \frac{4 \times 7 + 2}{7} = \frac{30}{7}.
What is the difference between like and unlike fractions?
Like fractions share the same denominator but have different numerators, such as \frac{3}{5} and \frac{1}{5}. Unlike fractions have different denominators, such as \frac{5}{9} and \frac{7}{8}.
How do I compare two fractions that have different denominators?
Convert them to like fractions using the LCM of the denominators, then compare the numerators. The fraction with the larger numerator is larger. Alternatively, make the numerators equal; then the smaller denominator belongs to the larger fraction.
When do I use BODMAS in fraction problems?
Use BODMAS whenever an expression involves three or more operations. The order is Brackets, Of, Division, Multiplication, Addition, Subtraction. Operate the bracket first, then ‘of’, then division and multiplication before addition and subtraction.
The syllabus this chapter follows is set by the CISCE board.
Reference: ICSE Class 6 Mathematics textbook material, chapter 5: Fractions — CISCE-aligned.