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Working with Fractions - Multiplication of Fractions

Grade 7CBSE

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

🔑Concepts

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To multiply a fraction by a whole number, multiply the numerator of the fraction by the whole number and keep the denominator the same: n×ab=n×abn \times \frac{a}{b} = \frac{n \times a}{b}.

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The operator 'of' in mathematics represents multiplication. For example, 12\frac{1}{2} of 2424 means 12×24\frac{1}{2} \times 24.

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To multiply two fractions, multiply the numerators together to get the product's numerator and multiply the denominators together to get the product's denominator: Product=Product of NumeratorsProduct of Denominators\text{Product} = \frac{\text{Product of Numerators}}{\text{Product of Denominators}}.

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When multiplying mixed fractions, always convert them into improper fractions first before applying the multiplication rule.

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The product of two proper fractions is always less than each of the two fractions. For example, 23×45=815\frac{2}{3} \times \frac{4}{5} = \frac{8}{15}, where 815<23\frac{8}{15} < \frac{2}{3} and 815<45\frac{8}{15} < \frac{4}{5}.

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The product of two improper fractions is always greater than each of the two fractions.

📐Formulae

ab×cd=a×cb×d\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}

a×bc=a×bca \times \frac{b}{c} = \frac{a \times b}{c}

Value of ’of’⇒ab of C=ab×C\text{Value of 'of'} \Rightarrow \frac{a}{b} \text{ of } C = \frac{a}{b} \times C

💡Examples

Problem 1:

Find the product of 59\frac{5}{9} and 1212.

Solution:

59×12=5×129=609=203=623\frac{5}{9} \times 12 = \frac{5 \times 12}{9} = \frac{60}{9} = \frac{20}{3} = 6\frac{2}{3}.

Explanation:

Multiply the numerator 55 by the whole number 1212 and divide by the denominator 99. Simplify the resulting fraction.

Problem 2:

Calculate 37\frac{3}{7} of 1415\frac{14}{15}.

Solution:

37×1415=3×147×15=42105\frac{3}{7} \times \frac{14}{15} = \frac{3 \times 14}{7 \times 15} = \frac{42}{105}. Simplifying by dividing both by 2121, we get 25\frac{2}{5}.

Explanation:

The word 'of' is replaced by the multiplication sign. We then multiply the numerators and denominators separately and simplify.

Problem 3:

Multiply 2132\frac{1}{3} by 3253\frac{2}{5}.

Solution:

First, convert to improper fractions: 213=732\frac{1}{3} = \frac{7}{3} and 325=1753\frac{2}{5} = \frac{17}{5}. 73×175=7×173×5=11915\frac{7}{3} \times \frac{17}{5} = \frac{7 \times 17}{3 \times 5} = \frac{119}{15} Converting back to a mixed fraction: 119÷15=7119 \div 15 = 7 with a remainder of 1414, so 714157\frac{14}{15}.

Explanation:

Mixed fractions must be converted to improper fractions before multiplication.

Problem 4:

Perform the multiplication 45×2345 \times 23 to find the product of numerators for a larger fraction problem.

Solution:

45×231359001035\begin{array}{r} 45 \\ \times 23 \\ \hline 135 \\ 900 \\ \hline 1035 \end{array}

Explanation:

Vertical multiplication is used to find the product of larger numerators or denominators in fraction problems.