Answer
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Hint: Here, we are asked to find the value of $ - \dfrac{4}{7} - \dfrac{2}{{ - 3}}$ .
Firstly, simplify the given question by removing the negative sign of the denominator.
Then, take the LCM of the two denominators.
Thus, find the value of the required answer.
Complete step-by-step answer:
Here, we are asked to find the value of $ - \dfrac{4}{7} - \dfrac{2}{{ - 3}}$ .
We will firstly simplify the given question as
$
- \dfrac{4}{7} - \dfrac{2}{{ - 3}} \times \dfrac{{ - 1}}{{ - 1}} \\
= - \dfrac{4}{7} - \left( { - \dfrac{2}{3}} \right) \\
= - \dfrac{4}{7} + \dfrac{2}{3} \\
= \dfrac{2}{3} - \dfrac{4}{7} \\
$
Now, we will solve the value of $\dfrac{2}{3} - \dfrac{4}{7}$ .
To do so, we need to find the LCM of 7 and 3.
The numbers 7 and 3 will give the LCM as $7 \times 3 = 21$ .
$\therefore \dfrac{2}{3} - \dfrac{4}{7} = \left( {\dfrac{2}{3} \times \dfrac{7}{7}} \right) - \left( {\dfrac{4}{7} \times \dfrac{3}{3}} \right)$
$
= \dfrac{{14}}{{21}} - \dfrac{{12}}{{21}} \\
= \dfrac{{14 - 12}}{{21}} \\
= \dfrac{2}{{21}} \\
$
Thus, we get the value of $ - \dfrac{4}{7} - \dfrac{2}{{ - 3}}$ as $\dfrac{2}{{21}}$ .
Note: LCM of numbers:
Least Common Multiple (LCM) of any two numbers, say x and y, is the smallest positive integer that is divisible by both x and y. It is usually denoted by \[LCM\left( {x,y} \right)\] .
For example, the given two numbers are 3 and 5. So, the LCM of the numbers 3 and 5 will be $3 \times 5 = 15$. Thus, LCM of the numbers 3 and 5 is 15, which is divisible by both 3 and 5.
Firstly, simplify the given question by removing the negative sign of the denominator.
Then, take the LCM of the two denominators.
Thus, find the value of the required answer.
Complete step-by-step answer:
Here, we are asked to find the value of $ - \dfrac{4}{7} - \dfrac{2}{{ - 3}}$ .
We will firstly simplify the given question as
$
- \dfrac{4}{7} - \dfrac{2}{{ - 3}} \times \dfrac{{ - 1}}{{ - 1}} \\
= - \dfrac{4}{7} - \left( { - \dfrac{2}{3}} \right) \\
= - \dfrac{4}{7} + \dfrac{2}{3} \\
= \dfrac{2}{3} - \dfrac{4}{7} \\
$
Now, we will solve the value of $\dfrac{2}{3} - \dfrac{4}{7}$ .
To do so, we need to find the LCM of 7 and 3.
The numbers 7 and 3 will give the LCM as $7 \times 3 = 21$ .
$\therefore \dfrac{2}{3} - \dfrac{4}{7} = \left( {\dfrac{2}{3} \times \dfrac{7}{7}} \right) - \left( {\dfrac{4}{7} \times \dfrac{3}{3}} \right)$
$
= \dfrac{{14}}{{21}} - \dfrac{{12}}{{21}} \\
= \dfrac{{14 - 12}}{{21}} \\
= \dfrac{2}{{21}} \\
$
Thus, we get the value of $ - \dfrac{4}{7} - \dfrac{2}{{ - 3}}$ as $\dfrac{2}{{21}}$ .
Note: LCM of numbers:
Least Common Multiple (LCM) of any two numbers, say x and y, is the smallest positive integer that is divisible by both x and y. It is usually denoted by \[LCM\left( {x,y} \right)\] .
For example, the given two numbers are 3 and 5. So, the LCM of the numbers 3 and 5 will be $3 \times 5 = 15$. Thus, LCM of the numbers 3 and 5 is 15, which is divisible by both 3 and 5.
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