Question

1.
Evaluate the following:​

Answer 1

$\sf \Large Solution!!$

$\sf \to \dfrac{-12}{-5}+\dfrac{7}{-3}+\dfrac{-5}{14}+\dfrac{22}{7}$

Simplifying the fractions.

$\sf \to \dfrac{12}{5}-\dfrac{7}{3}-\dfrac{5}{14}+\dfrac{22}{7}$

Taking the LCM.

$\sf \to \dfrac{504-490-75+660}{210}$

$\sf \to \dfrac{599}{210}$

$\sf \to 2\dfrac{179}{210}$

Answer 2

Question

$\sf \longmapsto \dfrac{ - 12}{ - 5} + \dfrac{7}{ - 3} + \dfrac{ ( - 5)}{14} + \dfrac{22}{7}$

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

$\sf \longmapsto \dfrac{ - 12}{ - 5} + \dfrac{7}{ - 3} + \dfrac{ ( - 5)}{14} + \dfrac{22}{7}$

Concept:

• Plus minus=minus (but sign of bigger value )
• minus minus =plus (but sign of minus)
• Minus minus gets cancelled in multiplication and division.

$\sf \longmapsto \dfrac{12}{5} - \dfrac{7}{3} - \dfrac{5}{14} + \dfrac{22}{7}$

Now, LCM of 5&3 is 15 and LCM of 14 & 7 is 14

$\sf \longmapsto \dfrac{12 \times 3 - 7 \times 5}{15} \dfrac{ - 5 + 22 \times 2}{14}$

$\sf \longmapsto \dfrac{36 - 35}{15} \dfrac{ - 5 + 44}{14}$

$\sf \longmapsto \dfrac{1}{15} + \dfrac{39}{14} \longmapsto \dfrac{14 + 585}{210} \sf \longmapsto\dfrac{599}{210}$

$\sf \longmapsto \dfrac{599}{210} \: or \: 2 \dfrac{179}{210}$