Chapter 2 covers Fractions (भिन्न) and Decimals (दशमलव), focusing on their multiplication and division as per the rationalized syllabus.

These exercises deal with finding products of fractions, including mixed fractions.

Q. No.	Type	Example (Step-by-Step Solution)	Key Concept
1	Fraction $\times$ Whole	Find: $\frac{3}{5}$ of 15 Solution: $\frac{3}{5} \times 15$ $= \frac{3 \times 15}{5} = \frac{45}{5} = \mathbf{9}$	Multiplying a fraction by a whole number.
2	Fraction $\times$ Fraction	Find the product: $\frac{2}{3} \times \frac{4}{5}$ Solution: $\frac{2 \times 4}{3 \times 5} = \frac{8}{15}$	Product of numerators divided by product of denominators.
3	Mixed Fraction $\times$ Fraction	Multiply: $3 \frac{1}{2} \times \frac{5}{7}$ Convert to improper fraction: $\frac{7}{2} \times \frac{5}{7}$ Cancel the 7s: $\frac{1}{2} \times \frac{5}{1} = \frac{5}{2} = \mathbf{2 \frac{1}{2}}$	Convert mixed fraction to improper fraction before multiplying.
4	Word Problem	A car runs 16 km using 1 litre of petrol. How much distance will it cover using $2 \frac{3}{4}$ litres? Distance $= 16 \times 2 \frac{3}{4} = 16 \times \frac{11}{4}$ $= 4 \times 11 = \mathbf{44 \text{ km}}$	Application of fraction multiplication.

This section covers the multiplication of decimal numbers.

Q. No.	Type	Example (Step-by-Step Solution)	Key Concept
1	Decimal $\times$ Whole	Find: $2.5 \times 6$ Solution: $25 \times 6 = 150$. Since there is one decimal place in 2.5, the result is $\mathbf{15.0}$ or 15.	Count the total decimal places in the factors.
2	Decimal $\times$ Decimal	Find the product: $0.2 \times 3.17$ Multiply integers: $2 \times 317 = 634$. Total decimal places = $1 + 2 = 3$. Result: $\mathbf{0.634}$	The decimal point is placed to give the total number of decimal places in the factors.
3	Decimal $\times$ Powers of 10	Find: $1.5 \times 1000$ Solution: Move the decimal point 3 places to the right. Result: $\mathbf{1500}$	Multiplying by $10^n$ moves the decimal $n$ places to the right.

This exercise introduces the reciprocal and applies it to the division of fractions.

Q. No.	Type	Example (Step-by-Step Solution)	Key Concept
1	Reciprocal	Find the reciprocal of $\frac{3}{5}$ Solution: $\mathbf{\frac{5}{3}}$	Reciprocal: The inverse fraction (numerator and denominator swapped).
2	Fraction $\div$ Whole	Find: $7 \div \frac{2}{5}$ Solution: $7 \times (\text{Reciprocal of } \frac{2}{5})$ $= 7 \times \frac{5}{2} = \frac{35}{2} = \mathbf{17 \frac{1}{2}}$	Division is multiplication by the reciprocal of the divisor.
3	Fraction $\div$ Fraction	Find: $\frac{3}{4} \div \frac{9}{8}$ Solution: $\frac{3}{4} \times \frac{8}{9}$ $= \frac{24}{36}$. Simplify by dividing by 12: $\mathbf{\frac{2}{3}}$	$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$

This covers the division of decimal numbers by whole numbers and other decimals.

Q. No.	Type	Example (Step-by-Step Solution)	Key Concept
1	Decimal $\div$ Whole	Find: $6.4 \div 2$ Solution: $64 \div 2 = 32$. Place decimal point: $\mathbf{3.2}$	Perform division as with whole numbers, then place the decimal.
2	Decimal $\div$ Powers of 10	Find: $4.8 \div 100$ Solution: Move the decimal point 2 places to the left. Result: $\mathbf{0.048}$	Dividing by $10^n$ moves the decimal $n$ places to the left.
3	Decimal $\div$ Decimal	Find: $7.75 \div 0.25$ Convert divisor to whole number by multiplying both by 100: $775 \div 25 = \mathbf{31}$	Multiply the dividend and divisor by a power of 10 until the divisor is a whole number.

RBSE Class 7 Maths Chapter 2 – Fractions and Decimals Solutions

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