Question

What number should be added \[\dfrac{7}{6}\] to get \[\dfrac{2}{9}\]?

Answer 1

Hint: Assume that the number that should be added is x. Now take the sum of a given rational number with x and equate it with \[\dfrac{2}{9}\]to form a linear equation with x. solve this equation for the value of x to get the answer.

Complete step-by-step solution:
Here, we have been asked to find the number that must be added to given rational number\[\dfrac{7}{6}\]
As the resultant fraction we get:
Now, by considering that the number that should be added is x. The number should be added as x.
So, we need to add \[\dfrac{7}{6}\]with x to get \[\dfrac{2}{9}\]therefore, the expression will be given as:
\[x+\left( \dfrac{7}{6} \right)=\dfrac{2}{9}\]
Clearly this is a linear equation in x so we need to solve for the value of x. Leaving x in the LHS and taking all other terms to the R.H.S we get:
\[x=\dfrac{2}{9}-\dfrac{7}{6}\]
After simplifying further we get:
Taking the LCM of 9 and 6 which is 54 we get:
\[x=\dfrac{\left( 2\times 6 \right)-\left( 7\times 9 \right)}{54}\]
By simplifying further we get:
\[x=\dfrac{12-63}{54}\]
By further solving on above equation we get:
\[x=\dfrac{-51}{54}\]
By reducing the fraction we get:
\[x=\dfrac{-17}{18}\]
Hence, the required number that must be added is \[\dfrac{-17}{18}\]

Note: You'll need to recall how to multiply and divide two rational numbers. It's worth noting that we use the LCM of the denominators, not the numerators, to add fractions. To solve a linear equation using x, we must leave x in the LHS and transfer all other terms to the RHS, then simplify to obtain the value of x.