Question

Subtract the sum of -5/7 and 5/14 from the sum of 3/14 and -2/7

Answer 1

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

The answer is $\sf{\dfrac{2}{7}}$

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

Given :

The values -

• $\sf{\dfrac{ - 5}{7}}$

• $\sf{\dfrac{5}{14}}$

• $\sf{\dfrac{3}{14}}$

• $\sf{\dfrac{ -2}{7}}$

To Find :

The difference between the sum of $\sf{\dfrac{ - 5}{7}}$ and $\sf{\dfrac{5}{14}}$ and the sum of $\sf{\dfrac{3}{14}}$ and $\sf{\dfrac{ -2}{7}}$

Solution :

★ $\textbf{Case I}$

• Add $\sf{\dfrac{ - 5}{7}}$ and $\sf{\dfrac{5}{14}}$

$\implies\sf{\dfrac{ - 5}{7}} + {\dfrac{5}{14}}$

$\textsf{LCM of 7 and 14 = 14}$

$\sf{\implies} \: \dfrac{ - 5 \times 2}{7 \times 2} + \dfrac{5}{14}$

$\sf{\implies} \: \dfrac{ - 10 + 5}{14}$

$\bf{\implies} \: \dfrac{ - 5}{14}$

$\rule{300}{1.5}$

★ $\textbf{Case II}$

• Add $\sf{\dfrac{3}{14}}$ and $\sf{\dfrac{ -2}{7}}$

$\sf{\implies} \:{\dfrac{3}{14}} + {\dfrac{ -2}{7}}$

$\textsf{LCM of 7 and 14 = 14}$

$\sf{\implies} \: \dfrac{3}{14} + \dfrac{ - 2 \times 2}{7 \times 2}$

$\sf{\implies} \: \dfrac{3 - 4}{14}$

$\bf{\implies} \: \dfrac{ - 1}{14}$

$\rule{300}{1.5}$

★ Subtract $\sf{\dfrac{ - 5}{14}}$ from $\sf{\dfrac{ - 1}{14}}$

$\sf{\implies \: {\dfrac{ - 1}{14} - {\dfrac{ - 5}{14}}}}$

$\sf{\implies \: {\dfrac{ - 1 - ( - 5)}{14}}}$

$\sf{\implies \: {\dfrac{ - 1 + 5}{14}}}$

$\sf{\implies \: {\dfrac{4}{14}}}$

$\textsf{Reduce the Fraction}$

$\sf{\implies} \: \dfrac{4 \div 2}{14 \div 2}$

$\bf{\implies} \: \dfrac{2}{7}$

$\therefore$ The answer is $\sf{\dfrac{2}{7}}$

Answer 2

Answer:

- 2/7

Step-by-step explanation:

Given;

★-5/7

★5/14

★3/14

★-2/7

Now,

To find the difference between the sum of first two rational number and last two rational number :-

☆{( -5/7) +(5/14)}-{(3/14)+(-2/7)}

So, let us find

__________________________

Case 1:-

{(-5/7) + (5/14)}

= -5/7 + 5/14

= (-10 + 5)/14

= -5/14

Case 2:-

{(3/14)+(-2/7)}

= (3-4)/14

= -1/14

Now subtract -5/14 from -1/14

{(-1/14) -(-5/14)}

-1/14 + 5/14

(-1+5)/4

4/14

2/7