Question

Complete the following table by finding the sums:

+	`-1/9`	`4/11`	`(-5)/6`
`2/3`
`-5/4`		`(-39)/44`
`-1/3`

Answer 1

Let

+	`-1/9`	`4/11`	`(-5)/6`
`2/3`	a	b	c
`-5/4`	d	`(-39)/44`	e
`-1/3`	f	g	h

Here, a = `2/3 + (-1/9)`

= `2/3 - 1/9`

= `(2 xx 3)/(3 xx 3) - (1 xx 1)/(9 xx 1)`  ......[∵ LCM of 3 and 9 = 9]

= `6/9 - 1/9`

= `(6 - 1)/9`

= `5/9`

b = `2/3 + 4/11`

= `(2 xx 11)/(3 xx 11) + (4 xx 3)/(11 xx 3)`  ......[∵ LCM of 3 and 11 = 33]

= `22/33 + 12/33`

= `(22 + 12)/33`

= `34/33`

c = `2/3 + (-5/6)`

= `2/3 - 5/6 = (2 xx 2)/(3 xx 2) - (5 xx 1)/(6 xx 1)`  ......[∵ LCM of 3 and 6 = 6]

= `4/6 - 5/6`

= `(4 - 5)/6`

= `-1/6`

and d = `-5/4 + (-1/9) = (-5)/4 - 1/9`

= `(-5 xx 9)/(4 xx 9) - (1 xx 4)/(9 xx 4)`  ......[∵ LCM of 4 and 9 = 36]

= `(-45)/36 - 4/36`

= `(-45 - 4)/36`

= `(-49)/36`

e = `-5/4 + (-5/6) = - 5/4 - 5/6`

= `(-5 xx 3)/(4 xx 3) - (5 xx 2)/(6 xx 2)` ......[∵ LCM of 4 and 6 = 12]

= `(-15)/12 - 10/12`

= `(-15 -10)/12`

= `-25/12`

and f = `-1/3 + (-1/9) = - 1/3 - 1/9`

= `(-1 xx 3)/(3 xx 3) - (1 xx 1)/(9 xx 1)` ......[∵ LCM of 3 and 9 = 3]

= `(-3)/9 - 1/9`

= `(-3 - 1)/9`

= `(-4)/9`

g = `-1/3 + 4/11`

= `(-1 xx 11)/(3 xx 11) + (4 xx 3)/(11 xx 3)`   ......[∵ LCM of 3 and 11 = 33]

= `(-11)/33 + 12/33`

= `(-11 + 12)/33`

= `1/33`

h = `-1/3 + ((-5)/6) = - 1/3 - 5/6`

= `(-1 xx 2)/(3 xx 2) - (5 xx 1)/(6 xx 1)` ......[∵ LCM of 3 and 6 = 6]

= `(-2)/6 - 5/6`

= `(-2 - 5)/6`

= `(-7)/6`

Hence, the complete table is

+	`-1/9`	`4/11`	`(-5)/6`
`2/3`	`bb(5/9)`	`bb(34/33)`	`bb((-1)/6)`
`-5/4`	`bb((-49)/36)`	`(-39)/44`	`bb((-25)/12)`
`-1/3`	`bb((-4)/9)`	`bb(1/33)`	`bb((-7)/6)`