Question

Q-3 Solve the following
1) Verify the following:
12 x [ 4 + (-3) ] = [ 12 x 4 ]+[ 12 (-3) ]
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Answer 1

Answer ⤵️

Question 1:

Using appropriate properties, find:

(i) -2/3 * 3/5 + 5/2 – 3/5 * 1/6 (ii) 2/5 * (3/-7) – 1/6 * 3/2 + 1/14 * 2/5

Answer:

(i) -2/3 * 3/5 + 5/2 – 3/5 * 1/6

= -2/3 * 3/5 – 3/5 * 1/6 + 5/2 [Using associative property]

= 3/5 * (-2/3 – 1/6) + 5/2 [Using distributive property]

= 3/5 * {(-4 - 1)/6} + 5/2 [LCM (3, 2) = 6]

= 3/5 * (-5/6) + 5/2

= -3/6 + 5/2

= -1/2 + 5/2

= (-1 + 5)/2

= 4/2

= 2

(ii) 2/5 * (3/-7) – 1/6 * 3/2 + 1/14 * 2/5

= 2/5 * (-3/7) + 1/14 * 2/5 – 1/6 * 3/2 [Using associative property]

= 2/5 * (-3/7 + 1/14) – 1/2 * 1/2 [Using distributive property]

= 2/5 * {(-6 + 1)/14} – 1/4 [LCM (7, 14) = 14]

= 2/5 * (-5/14) – 1/4

= -1/7 – 1/4

= (-4 -7)/28 [LCM (7, 4) = 28]

= -11/28

Question 2:

Write the additive inverse of each of the following:

(i) 2/8 (ii) -5/9 (iii) -6/-5 (iv) 2/-9 (v) 19/-6

Answer:

We know that additive inverse of a rational number a/b is (-a/b) such that a/b + (-a/b) = 0

(i) Additive inverse of 2/8 = -2/8

(ii) Additive inverse of -5/9 = 5/9

(iii) -6/-5 = 6/5

Additive inverse of 6/5 = -6/5

(iv) 2/-9 = -2/9

Additive inverse of -2/9 = 2/9

(v) 19/-6 = -19/6

Additive inverse of -19/6 = 19/6

Question 3:

Verify that -(-x) = x for:

(i) x = 11/15 (ii) x = -13/17

Answer:

(i) Putting x = 11/15 in -(-x) = x, we get

=> -(-11/15) = 11/15

=> 11/15 = 11/15

=> LHS = RHS

Hence, verified.

(i) Putting x = -13/17 in -(-x) = x, we get

=> -{-(-13/17)} = -13/17

=> -(13/17) = -13/17

=> -13/17 = -13/17

=> LHS = RHS

Hence, verified.