Question

How do you solve \[\dfrac{9}{6}=\dfrac{x}{10}\]?

Answer 1

Hint: To solve \[\dfrac{9}{6}=\dfrac{x}{10}\], we need to first consider the left-hand side of the equation. Since 3 are common in both the numerator and denominator of the fraction, we can cancel 3 from the fraction. Then substitute the simplified LHS in the given equation. And multiply the obtained equation with 10 so that the denominator of the right-hand side of the equation gets cancelled. Then make necessary calculations to bring all the ‘x’ terms to the left hand side of the equation. Then, simplify the equation to find the value of x which is the required answer.

Complete step by step answer:
According to the question, we are asked to solve \[\dfrac{9}{6}=\dfrac{x}{10}\].
We have been given the equation is \[\dfrac{9}{6}=\dfrac{x}{10}\]. --------(1)
First, we have to consider the left-hand side of the equation (1).
That is \[\dfrac{9}{6}\].
We know that \[9=3\times 3\] and \[6=3\times 2\].
Substituting this in the fraction to simplify, we get
\[\dfrac{9}{6}=\dfrac{3\times 3}{3\times 2}\]
Here, 3 are common in both the numerator and denominator.
Let us cancel 3 from the numerator and denominator.
\[\Rightarrow \dfrac{9}{6}=\dfrac{3}{2}\]
Now substitute the simplified LHS in the equation (1).
Therefore, we get
\[\Rightarrow \dfrac{3}{2}=\dfrac{x}{10}\]
Let us now exchange the LHS and RHS. We get
\[\dfrac{x}{10}=\dfrac{3}{2}\] -----------(2)
Now multiply the whole equation by 10. This step is to cancel the denominator of the LHS.
\[\Rightarrow \dfrac{x}{10}\times 10=\dfrac{3}{2}\times 10\]
We find that 10 are common in both the numerator and denominator of LHS.
Cancelling out the numerator and denominator from the LHS, we get
\[x=\dfrac{3}{2}\times 10\]
We know that \[10=5\times 2\].
Therefore, we get
\[x=\dfrac{3}{2}\times 5\times 2\]
Here, we find that 2 are common in the numerator and denominator of RHS.
Let us cancel 2 from the RHS, we get
\[x=3\times 5\]
\[\Rightarrow x=15\]

Therefore, the value of x in \[\dfrac{9}{6}=\dfrac{x}{10}\] is 15.

Note: We can also solve this question by cross multiplying the given equation.
Therefore, we get
\[9\times 10=x\times 6\]
\[\Rightarrow 6x=90\]
Then, make a necessary calculation that is by dividing the whole equation by 6, we can find the value of x.
Using this method, we can reduce the number of steps.