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Question
For each set of rational number, given below, verify the associative property of addition of rational number:
(iv) `-1, 5/6 and (-2)/3`
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Solution
Show that :
This verifies associative property of the addition of rational numbers.
`(-1)/1+(5/6+(-2)/3)=((-1)/1+5/6)+(-2)/3`
∴`(-1)/1+(5/6+(-2)/3)`
| 2 | 6, 3 |
| 3 | 3, 3 |
| 1, 1 |
∴ LCM of 6 and 3 = 6
=`(-1)/1+((5xx1)/(6xx1)+(-2xx2)/(3xx2))` (∴LCM of 6 and 3 = 6)
=`(-1)/1+((5-4)/6)`
=`(-1)/1+1/6`
=`(-1xx6)/(1xx6)+(1xx1)/(6xx1)` (∴ LCM of 1 and 6 = 1)
=`(-6+1)/6=(-5)/6`
And, `((-1)/1+5/6)+(-2)/3`
=`((-1xx6)/(1xx6)+(5xx1)/(6xx1))+(-2)/3` (∴LCM of 1 and 6 =6)
=`((-6+5)/6)+(-2)/3`
=`(-1)/6+(-2)/3` (∴ LCM of 1 and 6 = 6)
=`(-1xx1)/(6xx1)+(-2xx2)/(3xx2)`
=`(-1-4)/6=(-5)/6` (∴LCM of 6 and 3 = 6)
∴`(-1)/1+(5/6+(-2)/3)=((-1)/1+5/6)+(-2)/3`
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