Question

10. Subtract the sum of-6/7 and
-4/14 from the sum of 1/2 and -2/7​

Answer 1

Given:

Four numbers -

$\bf \bullet \: 1st \: no. : \dfrac{-6}{7} \\ \\ \bf \bullet \: 2nd \: no. : \dfrac{-4}{14} \\ \\ \bf \bullet \: 3rd \: no. : \dfrac{1}{2} \\ \\ \bf \bullet \: 4th \: no. : \dfrac{-2}{7}$

What To Find:

We have to,

• Find the sum of the 1st and 2nd numbers.
• Find the sum of the 3rd and 4th numbers.
• Find the difference between these sums.

Solution:

• Finding the sum of the 1st and 2nd numbers.

$\sf \dfrac{-6}{7} + \dfrac{-4}{14}$

Take the LCM of 7 and 14 ie 14,

$\sf \implies \dfrac{-6 \times 2}{7 \times 2} + \dfrac{-4 \times 1}{14 \times 1}$

Multiply them,

$\sf \implies \dfrac{-12}{14} + \dfrac{-4}{14}$

Add them,

$\sf \implies \dfrac{-16}{14}$

• Finding the sum of the 3rd and 4th numbers.

$\sf \dfrac{1}{2} + \dfrac{-2}{7}$

Take the LCM of 2 and 7 ie 14,

$\sf \implies \dfrac{1 \times 7}{2 \times 7} + \dfrac{-2 \times 2}{7 \times 2}$

Multiply them,

$\sf \implies \dfrac{7}{14} + \dfrac{-4}{14}$

Add them,

$\sf \implies \dfrac{3}{14}$

• Finding the difference between them.

$\sf \dfrac{3}{14} - \dfrac{-16}{14}$

Subtract them,

$\sf \implies \dfrac{19}{14}$

Final Answer:

$\underline{\boxed{ \bf Thus, the \: difference \: is \: \dfrac{19}{14}.}}$