Question

what should be added to twice the rational number
$\frac{ - 7}{3} to \: get \: \frac{3}{7}$
????​

Answer 1

Answer:

Twice the number is

$\frac{-7}{3} \times 2 = \frac{-14}{3}$

so,

let the number to be added be x

$\frac{-14}{3} + x = \frac{3}{7} \\ \\ x = \frac{3}{7} - \frac{-14}{3} \\ \\ x = \frac{3 \times 3}{7 \times 3} + \frac{14 \times 7}{3 \times 7 } = \frac{9 + 98}{21} = \frac{ 107}{21}$

Answer 2

Let the rational number be a/b

Now, an equation can be formed.

Solve and find the value of a/b

2(-7/3) +a/b = 3/7

-14/3 + a/b = 3/7

- 14/3 + a/b = 3/7

a/b = 3/7 + 14/3

a/b = 107/21

∴ The required rational number is 107/21