Question

How do you multiply $\dfrac{5}{9}\times \dfrac{42}{6}\times \dfrac{12}{15}$ ?

Answer 1

Hint: To solve these types of questions which involve the multiplication of fractions, just cancel out any like terms from the denominator and numerator and then simply multiply all the values in the numerator and the denominator to get the final answer.

Complete step by step answer:
A fraction can be defined as a representation of a part of a whole. A general fraction includes a numerator and a denominator which is non-zero. The numerator and denominator are separated by a slash or a line. Apart from general or common fractions, there are many other types of fractions as well, which include compound fractions, complex fractions, and mixed fractions. A simple fraction is also called a vulgar fraction.
Given:
$\dfrac{5}{9}\times \dfrac{42}{6}\times \dfrac{12}{15}$
In the above expression, we can see that each term present in the numerator or denominator is a multiple of another value in present in the fractions. $15\;$ Is a multiple of$5$, $12\;$ and $9$ are multiples of $3$and $42\;$ is a multiple of$6$. Hence, these terms can be easily cancelled out and reduced to simpler values.
Therefore,
$\Rightarrow \dfrac{5}{9}\times \dfrac{42}{6}\times \dfrac{12}{15}$
Can be written in factors form as,
$\Rightarrow \dfrac{5}{3\times 3}\times \dfrac{6\times 7}{6}\times \dfrac{12}{3\times 5}$
Now cancel the common terms from both the numerator and the denominator.
$\Rightarrow \dfrac{1}{3}\times \dfrac{7}{1}\times \dfrac{4}{3}$
Now, just simplify the above expression by multiplying together the values in the numerator and denominator to get a final answer:
$\Rightarrow \dfrac{1}{3}\times \dfrac{7}{1}\times \dfrac{4}{3}=\dfrac{28}{9}$
Since the obtained fraction can no longer be simplified, hence the final answer after multiplying the expression $\dfrac{5}{9}\times \dfrac{42}{6}\times \dfrac{12}{15}$ is $\dfrac{28}{9}$

Note: To multiply any two fractions, just multiply all the values of numerators and the denominators and then proceed to further simplify the fraction if needed. Sometimes only a single whole number is given in place of a fraction for multiplication, in such a case treating the whole number as a fraction itself by taking the denominator as $1$ .