Examples of fractions multiplication are presented along with detailed solutions and exercises with answers. A calculator to multiply fractions is included in this website.
How to Multiply Fractions? Rule
To multiply two fractions, we multiply the numerators together and the denominators together. Hence:
\[ \dfrac{a}{b} \times \dfrac{c}{d} = \dfrac{a \times c}{b \times d} \]Multiply Fractions: Examples with Detailed Solutions
Example 1
Multiply and simplify, and express the final answer as a fraction:
\[ \dfrac{2}{3} \times \dfrac{7}{2} \]
Solution
Solution to Example 1
To multiply fractions, you multiply numerators and denominators:
Divide the numerator and the denominator by the common factor \(2\) and simplify:
\[ = \dfrac{7}{3} \]Example 2
Multiply and simplify, and express the final answer as a fraction:
\[ \dfrac{11}{9} \times \dfrac{12}{25} \]
Solution
Solution to Example 2
Multiply numerators and denominators:
12 in the numerator and 9 in the denominator have the greatest common factor equal to 3, hence divide 12 in the numerator and 9 in the denominator by 3:
\[ = \dfrac{11 \times (12 \div 3)}{(9 \div 3) \times 25} \]Simplify:
\[ = \dfrac{11 \times 4}{3 \times 25} = \dfrac{44}{75} \]Example 3 (Multiply a fraction by an integer)
Multiply, simplify, and express the final answer as a fraction:
\[ \dfrac{2}{15} \times 5 \]
Solution
Solution to Example 3
Multiply the numerator of the fraction by 5:
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, simplify, and express the final answer as a fraction:
\[ \dfrac{2}{15} \times 1.5 \]
Solution
Solution to Example 4
Rewrite the decimal number \(1.5\) as a fraction:
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:
\[ = \dfrac{1}{5} \]Exercises with Answers: Multiply Fractions
Multiply, simplify, and express as fractions.
-
\( \dfrac{2}{3} \times \dfrac{7}{6} \)
-
\( \dfrac{23}{30} \times \dfrac{33}{25} \)
-
\( 5 \times \dfrac{2}{25} \)
-
\( 0.14 \times \dfrac{40}{21} \)
Answer
\( \dfrac{7}{9} \)
Answer
\( \dfrac{253}{250} \)
Answer
\( \dfrac{2}{5} \)
Answer
\( \dfrac{4}{15} \)