Question

What number should be subtract from the product of $\dfrac{2}{7}$ and $\dfrac{3}{8}$ to get $\dfrac{-3}{7}$?

Answer 1

Hint: For this question , at first we should multiply the given numbers with the help of fraction multiplication rule , then apply fraction subtraction rule to get the answer.

Complete step by step solution:
The given fractions are $\dfrac{2}{7}$ and $\dfrac{3}{8}$
First we have to multiply them and we know that in fraction or rational number top number or numerator multiply to numerator and denominator multiply to denominator
$\dfrac{2}{7}\times \dfrac{3}{8}$ = $\dfrac{3}{28}$
According to the question, suppose that x should be subtracted from the product of given numbers i.e. $\dfrac{3}{28}$ to get $\dfrac{-3}{7}$.
$\dfrac{3}{28}-x=\dfrac{-3}{7}$
On transferring numbers one side, we get
$\begin{align}
& x=\dfrac{3}{28}+\dfrac{3}{7} \\
& \\
\end{align}$ ……………………….(i)
Now to add the above term, first we have to take the LCM.

Therefore LCM of 28, 28 and 7 will be 28.
Then convert each fraction into a common denominator, as we observed that one fraction has already $28$ as a denominator. So that , we have to change only one of the denominators.
Then, $\dfrac{3\times 4}{7\times 4}=\dfrac{12}{28}$
Now , on putting the above value in equation (i) we get
$x=\dfrac{3}{28}+\dfrac{12}{28}$
$\begin{align}
& x=\dfrac{3+12}{28} \\
& \\
\end{align}$
After adding the numerators , we get
$\begin{align}
& x=\dfrac{15}{28} \\
& \\
\end{align}$

Hence we get $\dfrac{15}{28}$ after the subtraction.

Additional information: LCM- In maths the least common factor of any two integers, usually denoted by LCM, is the smallest positive integer that is divisible by the both integers.

Note: We can add the above fraction with the help of this formula,
Addition of two fraction = $\dfrac{first\,fraction\times LCM+\,fraction\times LCM}{LCM\,of\,denominator}$
It is also applicable for the subtraction, that all we have to do to change the sign with subtraction.
Sometimes students make mistakes on subtraction.