Question

Solve $\dfrac{2}{7} - \left( { - \dfrac{5}{6}} \right)$.

Answer 1

Hint: Here, first we will take the least common factors for denominator terms and then use the cross multiplication method. Also, we know one fact that $ - 1 \times - 1$ is $1$.

Complete step by step solution
Given:

The given expression is $\dfrac{2}{7} - \left( { - \dfrac{5}{6}} \right)$.

Since, we know the fact that $ - 1 \times - 1 = 1$.

Now, let us take the least common factor for denominators. The least common factor can be found by the taking multiple of 6 and 7, that is,
$6 = 2 \times 3$ and $7 = 7 \times 1$

The least common factor is $2 \times 3 \times 7$ which is equal to $42$.

Now take the first term that is $\dfrac{2}{7}$ and multiply and divide the numerator and denominator by $6$we get,
 $\dfrac{2}{7} \times \dfrac{6}{6} = \dfrac{{12}}{{42}}$

Now, we will take the second term that is $\dfrac{5}{6}$and multiply and divide the numerator and denominator by $7$we get,
 $\dfrac{5}{6} \times \dfrac{7}{7} = \dfrac{{35}}{{42}}$

On adding the two numbers $\dfrac{{12}}{{42}}$ and $\dfrac{{35}}{{42}}$ we get,
$\dfrac{{12}}{{42}} + \dfrac{{35}}{{42}}$

Since, the denominator is the same, we can add the numerators.
$\dfrac{{12 + 35}}{{42}} = \dfrac{{47}}{{42}}$

Hence the value for the $\dfrac{2}{7} - \left( { - \dfrac{5}{6}} \right)$ is $\dfrac{{47}}{{42}}$.

Note: This can be calculated in direct method that is first, find the greatest common factor for the denominator terms if greatest common factor is then multiply the denominators terms and in the numerator term multiply the first numerator term with the second denominator and multiply the second numerator term with the first denominator.