Question

What number should be added to 8/14 to get -2/7 ???​

Answer 1

Let us consider the number to be added as x .

So according to the question :

$\longrightarrow{\tt{ \dfrac{8}{14} + x = \dfrac{(-2)}{7}}}$

Now , to find the value of x ; we need to transpose the terms to the same side of the equal to sign.

Note that ; when a digit is transposed to another side of the equation ; the sign changes.

$\longrightarrow{\tt{x = \dfrac{(-2)}{7} - \dfrac{8}{14}}}$

For the subtraction of the fractions ; we need to take their LCM .

$\begin{array}{c | c} 7 &7 , 14 \\\cline{1-2} 2 & 1 , 2 \\\cline{1-2} & 1,1 \end{array}$

So the LCM is 14.

As we have changed the denominators the numerators will also change :

$\longrightarrow{\tt{\dfrac{(-2) \times 2}{7 \times 2} = \dfrac{-4}{14}}}$

$\longrightarrow{\tt{\dfrac{8 \times 1}{14 \times 1} = \dfrac{8}{14}}}$

Now we can continue the process :

$\longrightarrow{\tt{x = \dfrac{(-4) - 8}{14}}}$

$\longrightarrow{\tt{x = \dfrac{(-12)}{14}}}$

$\longrightarrow{\tt{x = \cancel{\dfrac{(-12)}{14}}}}$

$\large{\boxed{\implies{\tt{ x = \dfrac{(-6)}{7}}}}}$

Verification :

$\longrightarrow{\tt{\dfrac{(-6)}{7} + \dfrac{8}{14} = \dfrac{(-2)}{7}}}$

$\longrightarrow{\tt{\dfrac{(-12) + 8}{14} = \dfrac{(-2)}{7}}}$

$\longrightarrow{\tt{\dfrac{(-4)}{14} = \dfrac{(-2)}{7}}}$

$\longrightarrow{\tt{\cancel{\dfrac{(-4)}{14}} = \dfrac{(-2)}{7}}}$

$\longrightarrow{\tt{\dfrac{(-2)}{7} = \dfrac{(-2)}{7}}}$

LHS = RHS

Answer 2

Answer:

6 + 8 = 14. ... When we become students of physics and approach the task of adding vector quantities, we soon become aware of the ... Thus, vectors with magnitudes of 6 + 8 will not necessarily sum to 14.