NCERT Solution Class 8th Maths Chapter – 1 Rational Numbers All Examples

Example 1: Find 3/7 + (-6/11) + (-8/21) + (5/22)

Solution:

3/7 + (-6/11) + (-8/21) + (5/22)
= 198/462 + (-252/462) + (-176/462) + (105/462) (Note that 462 is the LCM of
7, 11, 21 and 22)
= 198 – 252 – 176 + 105/462 = -125/462

We can also solve it as.
3/7 + (-6/11) + (-8/21) + (5/22)
= [3/7 + (-8/21)] + [-6/11 + 5/22] (by using commutativity and associativity)
= [9 + (-8)/21] + [-12 + 5/22] (LCM of 7 and 21 is 21; LCM of 11 and 22 is 22)
= 1/21 + (-7/22) = 22-147/462 -125/462

Do you think the properties of commutativity and associativity made the calculations easier?

Example 2: Find -4/5 x 3/7 x 15/16 x (-14/9)

Solution:

We have
-4/5 x 3/7 x 15/16 x (-14/9)
= (-4×3/5×7) x (15x(-14)/16×9)
= -12/35 x (-35/24) = -12 x (-35)/35×24 = 1/2

We can also do it as.
-4/5 x 3/7 x 15/16 x (-14/9)
= (-4/5 x 15/16) x [3/7 x (-14/9)] (Using commutativity and associativity)
= -3/4 x (-2/3) = 1/2

Example 3: Find 2/3 x -3/7 – 1/14 – 3/7 x 3/5

Solution:

2/5 x -3/7 – 1/14 – 3/7 x 3/5
= 2/5 x -3/7 – 3/7 x 3/5 – 1/14 (by commutativity)
= 2/5 x -3/7 + (-3/7) x 3/5 – 1/14
= -3/7 (2/5 + 3/5) – 1/14 (by distributivity)
= -3/7 x 1- 1/14 = -6-1/14 = -1/2