\[ \dfrac{a}{b} \times \dfrac{c}{d} = \dfrac{a \times c}{b \times d}\]
\( \) \( \)\( \)\( \)
Example 1
Multiply and simplfy, and express the final answer as a fraction.
\[ \dfrac{2}{3} \times \dfrac{7}{2} \]
Solution to Example 1
To multiply fractions you multiply numerators and denominators
\( \dfrac{2}{3} \times \dfrac{7}{2} = \dfrac{2 \times 7}{3 \times 2} \)
Divide the numerator and the denominator by the common factor 2 and simplify
\( \dfrac{ \cancel{2} \times 7}{3 \times \cancel{2}} = \dfrac{7}{3} \)
Example 2
Multiply and simplfy, and express the final answer as a fraction.
\[ \dfrac{11}{9} \times \dfrac{12}{25} \]
Solution to Example 2
Multiply numerators and denominators
\( \dfrac{11}{9} \times \dfrac{12}{25} = \dfrac{11 \times 12}{9 \times 25} \)
12 in the numeartor and 9 in the denominator have the greatest common factor equal to 3, hence divide 12 in numerator and 9 denominator by 3.
\( = \dfrac{11 \times (12\div 3)}{(9\div 3) \times 25} \)
and simplify
\( \dfrac{11 \times 4}{3 \times 25} = \dfrac{44}{75} \)
Example 3 (Multiply a fraction by an integer)
Multiply, simplfy and express the final answer as a fraction.
\[ \dfrac{2}{15} \times 5 \]
Solution to Example 3
Multiply numerator of first fraction by 5
\( \dfrac{2}{15} \times 5 = \dfrac{2 \times 5}{15} \)
5 in the numerator and 15 in the denominator have the greatest common factor equal to 5, hence divide 5 in the numerator and 15 in the denominator by \( 5 \) to simplify
\( \dfrac{2 \times (5 \div 5)}{15 \div 5} = \dfrac{2}{3} \)
Example 4 (Multiply a fraction by a decimal number)
Multiply, simplfy and express the final answer as a fraction.
\[ \dfrac{2}{15} \times 1.5 \]
Solution to Example 4
Rewrite the decimal number \(1.5\) as a fraction
\( 1.5 = \dfrac{1.5}{1} = \dfrac{1.5 \times 10}{1 \times 10} = \dfrac{15}{10} \)
Rewrite the given expression using fractions
\( \dfrac{2}{15} \times 1.5 = \dfrac{2}{15} \times \dfrac{15}{10} \)
Multiply numerators and denominators
\( = \dfrac{2 \times 15}{15 \times 10} \)
Divide numerator and denominator by \( 15 \) and simplify
\( = \dfrac{2}{10} \)
Divide numerator and denominator by \( 2 \) and simplify
\( = \dfrac{1}{5} \)
Answers to Above Exercises:.
1. \( \dfrac{7}{9} \)
2. \( \dfrac{253}{250} \)
3. \( \dfrac{2}{5} \)
4. \( \dfrac{4}{15} \)