Question

For the pair of rational numbers, verify the commutative property of the addition of rational numbers:

`(-4)/5  "and"  (-13)/(-15)`

Answer 1

`(-4)/5  "and"  (-13)/(-15)`

To verify commutative property, the addition of rational numbers is shown.

`(-4)/5 + ((-13)/(-15)) = ((-13)/(-15)) + ((-4)/5)`

5	5, 15
3	1, 3
	1, 1

5 × 3 = 15

LCM of 5 & 15 = 15

`4/5 xx 15 = 12`

LHS = `(-4)/5 + ((-13)/(-15)) = (-4)/5 + 13/15 = (-12 + 13)/15 = 1/15`

RHS = `((-13)/(-15)) + ((-4)/5) = 13/15 + ((-4)/5) = (13 - 12)/15 = 1/15`

Since LHS = RHS, this verifies the commutative property for the addition of rational numbers.