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Working with Fractions - Division of Fractions

Grade 7CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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The Reciprocal (Multiplicative Inverse): Two non-zero numbers are reciprocals of each other if their product is 11. The reciprocal of a fraction ab\frac{a}{b} is ba\frac{b}{a}. Note that 00 has no reciprocal.

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Division of Whole Number by a Fraction: To divide a whole number by a fraction, multiply the whole number by the reciprocal of the fraction. Example: 3÷12=3×23 \div \frac{1}{2} = 3 \times 2.

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Division of a Fraction by a Whole Number: To divide a fraction by a whole number, multiply the fraction by the reciprocal of the whole number. For a whole number nn, the reciprocal is 1n\frac{1}{n}.

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Division of a Fraction by another Fraction: To divide one fraction (dividend) by another fraction (divisor), multiply the dividend by the reciprocal of the divisor.

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Mixed Fractions: When dealing with mixed fractions, always convert them into improper fractions first before performing the division.

📐Formulae

Reciprocal of ab=ba\text{Reciprocal of } \frac{a}{b} = \frac{b}{a}

ab÷cd=ab×dc=a×db×c\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{a \times d}{b \times c}

a÷bc=a×cba \div \frac{b}{c} = a \times \frac{c}{b}

ab÷c=ab×1c\frac{a}{b} \div c = \frac{a}{b} \times \frac{1}{c}

💡Examples

Problem 1:

Find the value of 49÷23\frac{4}{9} \div \frac{2}{3}.

Solution:

49÷23=49×32\frac{4}{9} \div \frac{2}{3} = \frac{4}{9} \times \frac{3}{2} Result=4×39×2=1218\text{Result} = \frac{4 \times 3}{9 \times 2} = \frac{12}{18} Simplified Result=23\text{Simplified Result} = \frac{2}{3}

Explanation:

To divide 49\frac{4}{9} by 23\frac{2}{3}, we multiply 49\frac{4}{9} by the reciprocal of 23\frac{2}{3}, which is 32\frac{3}{2}. We then simplify the resulting fraction.

Problem 2:

Divide 5135\frac{1}{3} by 44.

Solution:

513=(5×3)+13=1635\frac{1}{3} = \frac{(5 \times 3) + 1}{3} = \frac{16}{3} 163÷4=163×14\frac{16}{3} \div 4 = \frac{16}{3} \times \frac{1}{4} Result=16×13×4=1612\text{Result} = \frac{16 \times 1}{3 \times 4} = \frac{16}{12} Simplified Result=43=113\text{Simplified Result} = \frac{4}{3} = 1\frac{1}{3}

Explanation:

First, convert the mixed fraction 5135\frac{1}{3} into the improper fraction 163\frac{16}{3}. Then, multiply by the reciprocal of 44, which is 14\frac{1}{4}.

Problem 3:

A wire of length 121212\frac{1}{2} m is cut into 1010 pieces of equal length. Find the length of each piece.

Solution:

Total length=1212=252 m\text{Total length} = 12\frac{1}{2} = \frac{25}{2} \text{ m} Number of pieces=10\text{Number of pieces} = 10 Length of each piece=252÷10\text{Length of each piece} = \frac{25}{2} \div 10 Length=252×110=2520\text{Length} = \frac{25}{2} \times \frac{1}{10} = \frac{25}{20} Simplified Length=54=114 m\text{Simplified Length} = \frac{5}{4} = 1\frac{1}{4} \text{ m}

Explanation:

We divide the total length of the wire by the number of pieces. Convert the mixed fraction to an improper fraction first, then multiply by the reciprocal of 1010.