Question

| verify the associative property for addition and multiplication rational number -10/11,2/3,6/5​

Answer 1

Answer:For each set of rational numbers given below verify the associative property of addition of rational numbers:

(i) 1/2, 2/3 and -1/6

(ii) -2/5, 4/15 and -7/10

(iii) -7/9, 2/ -3 and -5/18

(iv) -1, 5/6 and -2/3

rational numbers

 

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answered Apr 24, 2019 by priya12 (-12,635 points)

(i) 1/2, 2/3 and -1/6

Show that:

1/2 + (2/3 + (-1/6) = (1/2 + 2/3) + (-1/6)

∵ 1/2 + (2/3 + (-1/6)

∴ LCM of 3 and 6 = 6

= 1/2 + (2 × 2/3 × 2) + (-1 × 1/6 ×1)

= 1/2 + (4/6 – 1/6)

= 1/2 + [(4-1)/6]

=1/2 + (3/6)

= (1 × 3/2 × 3) + (3 × 1/6 × 1)  (∵ LCM of 2 and 6 = 3)

= (3 + 3)/6 = 6/6 = 1

And, (1/2 + 2/3) + (-1/6)

∴ LCM of 2 and 3 = 6

= (1 × 3/2 × 3) + (2 × 2/3 × 2) + (-1/6)

= (3 + 4)/6 + -1/6

= (7 – 1)/6 = 6/6 = 1

∴ 1/2 + (2/3 + (-1/6) = (1/2 + 2/3) + (-1/6)

This verifies associative property of the addition of rational numbers.

(ii) -2/5, 4/15 and -7/10

Show that:

-2/5 + (4/15 + (-7/10) = (-2/5 + 4/15) + (-7/10)

∵ -2/5 + (4/15 + (-7/10)

∴ LCM of 15, 10 = 2 × 3 × 5 = 30

= -2/5 + (4 × 2/15 × 2) + (-7 × 3/10 × 3)

(∵ LCM of 15 and 10 = 30)

= -2/5 + [(8 – 21)/30]

= -2/5 – 13/30 = (-2 × 6/5 × 6) – (13 × 1/30 × 1)

= (-12 -13)/30 = -25/30 = -5/6

And, (-2/5 + 4/15) + -7/10

∴ LCM of 5 and 15 = 3 × 5 = 15

= (-2 × 3/5 × 3) + (4 × 1/15 ×1) + -7/10

∴ LCM of 5 and 15 = 15

= (-6 + 4)/15 + (-7/10)

= -2/15 + (-7/10)

= (-2 × 2/15 × 2) – (7 × 3/10 × 3)

= -4/30 – 21/30 = -25/30 = -5/6

∴ -2/5 + (4/15 + (-7/10) = (-2 /5 + 4/15) + (-7/10)

This verifies associative property of the addition of rational numbers.

(iii) -7/9, 2/ -3 and -5/18

Show that:

-7/9 + (2/-3 + (-5/18) = (-7/9 + 2/3) + (-5/18)

∵ -7/9 + (2/-3 + (-5/18)

∴ LCM of 3 and 18 = 2 × 3 × 3 = 18

= -7/9 + (-2 × 6/3 × 6) + (-5 ×1/18 ×1)

(∵ LCM of 3 and 18 = 18)

= -7/9 + [(-12 -5)/18]

= -7/9 + -17/18

= (-7 × 2/9 ×2) – (17 ×1/18 × 1)

(∵ LCM of 9 and 18 = 18)

= (-14 -17)/18 = -31/18

And, (-7/9 + 2/-3) + (-5/18)

∴ LCM of 3 and 9 = 3

= (-7 × 1/9 × 1) + (-2 × 3/3 × 3) + (-5/18)

(∵ LCM of 9 and 3= 9)

= (-7 -6)/9 + (-5/18)

= -13/9 + (-5/18)

= (-13 × 2/9 × 2) + (-5 × 1/18 × 1) =

Step-by-step explanation: