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How do you simplify $\dfrac{5}{6} + \dfrac{2}{3} - \dfrac{4}{9}$?

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Last updated date: 20th Jun 2024
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Answer
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Hint: We are given an expression of rational fractions having operations of addition and subtraction expressions. We will follow the rule of BODMAS.
Here B= bracket; O= of; D= division; M= multiplication; A= addition; S= subtraction.
By following this rule we will solve the expression. By following the sequence of operations given in the rule. But in the given expression we are given there are only two operations i.e. addition and subtraction. So first we will perform the addition and then subtraction according to the rule. As the expression has fractions then we will first find the L.C.M of the denominator then we will perform addition and subtraction.

Complete step-by-step answer:
We are given an expression i.e. $\dfrac{5}{6} + \dfrac{2}{3} - \dfrac{4}{9}$
In this we will follow the rule of BODMAS. According to this rule first we will find out the L.C.M of the denominator i.e. of $6,3$. For L.C.M we will do factor of both the numbers then find the common factors and the rest numbers.
$ \Rightarrow 6 = 2 \times 3$
$ \Rightarrow 3 = 3 \times 1$
L.C.M$ = 3 \times 2 \times 1$
L.C.M$ = 6$
Taking$6$as L.C.M on solving
$ \Rightarrow \dfrac{{5 + 4}}{6} - \dfrac{4}{9}$
$ \Rightarrow \dfrac{9}{6} - \dfrac{4}{9}$
Step2: Now we will do the subtraction firstly by finding the L.C.M of the denominator $6,9$
$ \Rightarrow 6 = 2 \times 3$
$ \Rightarrow 9 = 3 \times 3$
L.C.M=$3 \times 3 \times 2$
L.C.M=$18$
By taking $18$ as L.C.M we will get:
$ \Rightarrow \dfrac{9}{6} - \dfrac{4}{9}$
$ \Rightarrow \dfrac{{\left( {18 \div 6 \times 9} \right) - \left( {18 \div 9 \times 4} \right)}}{{18}}$
On solving the expression we will get:
$ \Rightarrow \dfrac{{\left( {3 \times 9} \right) - \left( {2 \times 4} \right)}}{{18}}$
On multiplying the terms we will get:
$ \Rightarrow \dfrac{{27 - 8}}{{18}}$
On subtracting we will get:
$ \Rightarrow \dfrac{{19}}{{18}}$
Step3: As it is a improper fraction we will convert it into mixed fraction form by dividing $19$ by $18$
$ = 1\dfrac{1}{{18}}$

Hence, answer is $1\dfrac{1}{{18}}$

Note:
In such types of questions just follow the rule of BODMAS whether the small expression or lengthy one. If we strictly follow these rules then the chance of getting questions solved wrong is very low but this type of questions are very lengthy so be careful while doing the Calculation and while solving the expressions. Be cautious for the signs of digits students make mistakes in this and if you feel that there are a lot of signs so we can separate the terms by using the bracket by doing this students did not get confused with the signs and make the question easy to solve.