Multiply Fractions

Examples of fractions multiplication are presented along with detailed solutions and exercises with answers on are presented. 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 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
\( = \dfrac{1}{5} \)



Exercises with Answers: Multiply Fractions

Multiply, simplify and express as fractions.

1.     \( \dfrac{2}{3} \times \dfrac{7}{6} \)

2.     \( \dfrac{23}{30} \times \dfrac{33}{25} \)

3.     \( 5 \times \dfrac{2}{25} \)

4.     \( 0.14 \times \dfrac{40}{21} \)

Answers to Above Exercises:.

1.     \( \dfrac{7}{9} \)

2.     \( \dfrac{253}{250} \)

3.     \( \dfrac{2}{5} \)

4.     \( \dfrac{4}{15} \)



More References and Links

Fractions
Adding Fractions
Fraction Division
Fraction calculator
Fractions
Fractions calculators.