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Multiplying the following fractions:
$\dfrac{5}{6}\times 2\dfrac{3}{7}$

Last updated date: 22nd Jul 2024
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Hint: To multiply the given fraction, first of all we need to change the mixed fraction into improper fraction. Now, we will do the multiplication of fractions in which we will multiply numerator with numerator and denominator with denominator. Since, this is the multiplication with improper fraction; the answer will be improper fraction also. So, we will convert it into a mixed fraction.

Complete step by step answer:
First of all we will check the type of fraction.
So, in the given question $\dfrac{5}{6}\times 2\dfrac{3}{7}$ one fraction is proper fraction and another one is mixed fraction.
Proper fraction$=\dfrac{5}{6}$
Mixed fraction$=2\dfrac{3}{7}$
Now, we will convert the mixed fraction in the improper fraction as:
Improper fraction$=\dfrac{7\times 2+3}{7}=\dfrac{14+3}{7}=\dfrac{17}{7}$
Here, the given question will be:
$\Rightarrow \dfrac{5}{6}\times 2\dfrac{3}{7}=\dfrac{5}{6}\times \dfrac{17}{7}$
Now, we will do multiplication. Numerator will be multiplied with numerator and denominator will be multiplied with denominator as:
$\Rightarrow \dfrac{5\times 17}{6\times 7}$
The product of $5$ and $17$ will be $85$ and the product of $6$ and $7$ will be $42$.
$\Rightarrow \dfrac{85}{42}$
Since, the resultant multiplication is improper fraction. We will convert it into mixed fraction as:
$\Rightarrow 2\dfrac{1}{42}$
Hence, the Multiplying the following fractions $\left( \dfrac{5}{6}\times 2\dfrac{3}{7} \right)$ is $2\dfrac{1}{42}$.

Note: As we know that fraction is a part of the whole number written in the form of \[\dfrac{a}{b}\], where $b\ne 0\text{ and 1}$.
Fraction has three types:
Proper fraction: \[\dfrac{a}{b}\] and $b > a$
Improper fraction: \[\dfrac{a}{b}\] and $b < a$
Mixed fraction: It is written in the form of \[c\dfrac{a}{b}\].
Where, $c$ is a whole number and $b > a$.