Question

Fill in the missing fraction: - $\dfrac{7}{10}-?=\dfrac{3}{10}$?

Answer 1

Hint: Assume that the number or fraction that should be filled is x. Now, multiply both the sides with 10 to simplify the fractions on both the sides. Form a linear equation in x and solve for the value of x to get the answer. Make the coefficient of x equal to 1 and accordingly change the R.H.S to get the answer.

Complete step by step answer:
Here we have been provided with the equality $\dfrac{7}{10}-?=\dfrac{3}{10}$ and we are asked to find the missing fraction.
Now, let us assume that the number or fraction that should be filled is x, so we get,
$\Rightarrow \dfrac{7}{10}-x=\dfrac{3}{10}$
Multiplying both the sides with 10 to make the terms on both the sides free from the fractional part we get,
$\begin{align}
  & \Rightarrow 10\left( \dfrac{7}{10}-x \right)=10\times \dfrac{3}{10} \\
 & \Rightarrow 7-10x=3 \\
\end{align}$
Now, let us solve the above linear equation for the value of x, so leaving the term containing the variable x in the L.H.S and taking all the constant terms to the R.H.S we get,
$\begin{align}
  & \Rightarrow -10x=3-7 \\
 & \Rightarrow -10x=-4 \\
\end{align}$
Multiplying both the sides with -1 and using the property $\left( -1 \right)\times \left( -1 \right)=1$ we get,
$\Rightarrow 10x=4$
Dividing both the sides with 10 and cancelling the common factors to simplify the fraction we get,
$\begin{align}
  & \Rightarrow x=\dfrac{4}{10} \\
 & \therefore x=\dfrac{4}{10} \\
\end{align}$

Hence, the missing fraction is $\dfrac{4}{10}$

Note: Note that it is not necessary to multiply both the sides with 10 to simplify. If you know the process of addition and subtraction of two rational numbers or fractions by taking the L.C.M of the denominator then you can directly subtract $\dfrac{3}{10}$ from $\dfrac{7}{10}$ to get the answer. We know that the L.C.M of the denominators will be 10 and therefore we just need to take the difference of the numerators directly.