CBSE Class 7 Maths — Fractions and Decimals

Chapter Overview & Weightage

Fractions and Decimals is Chapter 2 in CBSE Class 7 Maths (NCERT). This chapter extends your understanding from Class 6 fractions — now you multiply and divide fractions, and perform all four operations on decimals.

This chapter typically carries 8–10 marks in Class 7 annual exams. Operations on fractions (especially division) and decimal multiplication/division are the most frequently tested topics. Questions appear as both direct computation and word problems.

What this chapter covers:

Multiplication of fractions (proper, improper, mixed)
Division of fractions
Multiplication of decimals (by 10, 100, 1000, and by other decimals)
Division of decimals
Word problems combining both

Key Concepts You Must Know

Fractions — Quick Review

A fraction $\frac{p}{q}$ where $p$ is the numerator and $q$ is the denominator.

Proper fraction: $p < q$ (e.g., $\frac{3}{5}$ )
Improper fraction: $p > q$ (e.g., $\frac{7}{3}$ )
Mixed number: Integer + proper fraction (e.g., $2\frac{1}{3}$ )

Always convert mixed numbers to improper fractions before multiplying or dividing: $2\frac{1}{3} = \frac{7}{3}$

Multiplying Fractions

\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}

Always simplify before multiplying (cancel common factors) — it reduces computational errors.

Example: $\frac{3}{8} \times \frac{4}{9} = \frac{3 \times 4}{8 \times 9}$ . Cancel: $\frac{\cancel{3} \times \cancel{4}}{\cancel{8} \times \cancel{9}} = \frac{1}{6}$ . Much easier than $\frac{12}{72} = \frac{1}{6}$ .

”Of” Means Multiply

” $\frac{1}{2}$ of 60” = $\frac{1}{2} \times 60 = 30$ .

This comes up constantly in word problems: “He spent $\frac{3}{4}$ of his pocket money” → multiply.

Dividing Fractions — Reciprocal Rule

To divide by a fraction, multiply by its reciprocal (flip the divisor):

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

The reciprocal of $\frac{c}{d}$ is $\frac{d}{c}$ . The reciprocal of a whole number $n$ is $\frac{1}{n}$ .

Decimals — Multiplication

Multiply normally, ignoring decimal point
Count total decimal places in both numbers
Place decimal in product from the right

Multiply by powers of 10: Move decimal right (×10: 1 place, ×100: 2 places, ×1000: 3 places)

Example: $0.35 \times 10 = 3.5$ | $0.35 \times 100 = 35$ | $0.35 \times 1000 = 350$

Decimals — Division

Divide by whole number: divide normally, place decimal directly above
Divide by decimal: convert divisor to whole number by multiplying both by appropriate power of 10

Example: $4.2 \div 0.7 = 42 \div 7 = 6$ (multiplied both by 10)

Important Formulas

Multiplication: $\dfrac{a}{b} \times \dfrac{c}{d} = \dfrac{ac}{bd}$

Division: $\dfrac{a}{b} \div \dfrac{c}{d} = \dfrac{a}{b} \times \dfrac{d}{c} = \dfrac{ad}{bc}$

Mixed to Improper: $a\dfrac{b}{c} = \dfrac{ac + b}{c}$

$n \times 0.1 = n \div 10$

$n \times 0.01 = n \div 100$

$n \div 0.1 = n \times 10$

$n \div 0.01 = n \times 100$

Solved Previous Year Questions

PYQ 1 — Multiplication of Mixed Numbers

Q: Find $3\frac{1}{4} \times 1\frac{3}{5}$ . (CBSE Class 7 Sample Paper)

Solution: Convert to improper fractions:

3\frac{1}{4} = \frac{13}{4}, \quad 1\frac{3}{5} = \frac{8}{5}

\frac{13}{4} \times \frac{8}{5} = \frac{13 \times 8}{4 \times 5} = \frac{13 \times \cancel{8}}{\cancel{4} \times 5} = \frac{13 \times 2}{5} = \frac{26}{5} = 5\frac{1}{5}

PYQ 2 — Division of Decimals Word Problem

Q: A wire of length 12.5 m is cut into pieces of 0.25 m each. How many pieces are obtained? (CBSE Class 7 Annual Exam pattern)

Solution: Number of pieces = $12.5 \div 0.25$

Convert: $12.5 \div 0.25 = 1250 \div 25 = 50$

50 pieces are obtained.

PYQ 3 — Combined Operations

Q: Shyam spent $\frac{1}{4}$ of his salary on rent, $\frac{1}{3}$ on food, and saved the rest. If his salary is Rs 12,000, find his savings.

Solution: Fraction spent = $\frac{1}{4} + \frac{1}{3} = \frac{3}{12} + \frac{4}{12} = \frac{7}{12}$

Fraction saved = $1 - \frac{7}{12} = \frac{5}{12}$

Savings = $\frac{5}{12} \times 12000 = 5000$

Savings = Rs 5,000

Difficulty Distribution

Difficulty	Question Types	Marks
Easy (40%)	Direct multiplication/division of fractions; decimal ×10, ×100	1–2 marks
Medium (40%)	Mixed number operations; decimal word problems; simplify fractions	2–3 marks
Hard (20%)	Multi-step word problems; combined fraction and decimal operations	4–5 marks

Expert Strategy

The biggest time-saver in this chapter: cancel before you multiply. Students who don’t cancel first get stuck with large numbers like $\frac{36}{144}$ when they could have simplified to $\frac{1}{4}$ immediately by cancelling 4 and 9 before multiplying.

For word problems involving fractions: always identify whether the operation is “of” (multiply) or “into” (divide). “What fraction of 80 is 20?” → Divide: $20 \div 80 = \frac{1}{4}$ . “Find $\frac{1}{4}$ of 80” → Multiply: $\frac{1}{4} \times 80 = 20$ .

Topper strategy for decimal division: Never divide by a decimal directly. Always convert to whole number divisor first: $\frac{3.6}{0.04} = \frac{360}{4} = 90$ . Much cleaner.

For time checks: after getting your answer, quickly estimate — is it roughly the right size? $3.25 \times 4 \approx 3 \times 4 = 12$ . If your answer is 0.12 or 1200, something’s wrong with the decimal placement.

Common Traps

Trap 1 — Adding fractions during multiplication: Students confuse fraction multiplication with addition. $\frac{2}{3} \times \frac{4}{5} \neq \frac{2+4}{3+5} = \frac{6}{8}$ . For multiplication, multiply numerators together and denominators together: $\frac{2 \times 4}{3 \times 5} = \frac{8}{15}$ .

Trap 2 — Forgetting to flip when dividing: $\frac{3}{4} \div \frac{2}{5} \neq \frac{3 \times 2}{4 \times 5}$ . Division means multiply by the reciprocal: $\frac{3}{4} \times \frac{5}{2} = \frac{15}{8}$ .

Trap 3 — Decimal point placement error: $0.3 \times 0.3 = 0.09$ (NOT 0.9). Count decimal places: 1 + 1 = 2. So answer has 2 decimal places. Many students write 0.9, losing a mark.

Trap 4 — Not converting mixed numbers first: Directly multiplying $2\frac{1}{3} \times 3\frac{1}{4}$ by “multiplying the integer parts” — i.e., writing $6\frac{1}{12}$ . WRONG. Convert both to improper fractions first.