Question

What should be subtracted from \[ - \dfrac{4}{9}\] to get \[\dfrac{5}{{12}}\]?

Answer 1

Hint: Here we have to find difference or sum of the given data. Here the data is in the form of fraction. Since in the given data are in fraction the value of denominator is different so we find the LCM for the both the denominators and then we add the numbers. hence, we obtain the required solution for the given question.

Complete step-by-step solution:
We apply the arithmetic operations on the fractions. Here in this question, we add and subtract the two fractions. the LCM is a least common multiple. The LCM will be common for both the numbers.
Now consider the given question, here the minuend value will be \[ - \dfrac{4}{9}\] and the subtrahend is unknown and we have to determine this and the value of difference is \[\dfrac{5}{{12}}\].
So therefore, the given data is written as
\[ - \dfrac{4}{9} - x = \dfrac{5}{{12}}\]
The subtrahend is unknown so we take it as x, now take \[ - \dfrac{4}{9}\] to RHS and the above equation is written as
\[ \Rightarrow - x = \dfrac{5}{{12}} + \dfrac{4}{9}\]
The denominators are different so we have to take LCM for the numbers 12 and 9. The LCM for the numbers 12 and 9 is 36
Therefore the above inequality is written as
\[ \Rightarrow - x = \dfrac{{\dfrac{5}{{12}} \times 36 + \dfrac{4}{9} \times 36}}{{36}}\]
On simplifying we have
\[ \Rightarrow - x = \dfrac{{5 \times 3 + 4 \times 4}}{{36}}\]
On further simplifying we have
\[ \Rightarrow - x = \dfrac{{15 + 16}}{{36}}\]
On adding the 15 and 16 we get
\[ \Rightarrow - x = \dfrac{{31}}{{36}}\]
Take minus sign to RHS and it is written as
\[ \Rightarrow x = - \dfrac{{31}}{{36}}\]

Therefore \[ - \dfrac{{31}}{{36}}\] should be subtracted from \[ - \dfrac{4}{9}\] to get \[\dfrac{5}{{12}}\].

Note: While adding the two fractions we need to check the values of the denominator, if both denominators are having the same value then we can add the numerators. Suppose if the fractions have different denominators, we have to take LCM for the denominators and we simplify for further.