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

2. Write the additive inverse of each of the following

(i) 2/8
(ii) -5/9
(iii) -6/-5 = 6/5
(iv) 2/-9 = -2/9
(v) 19/-16 = -19/16

3. Verify that: -(-x) = x for.

(i) x = 11/15

(ii) x = -13/17

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Answer 1

Using appropriate properties find.

(i) -2/3 × 3/5 + 5/2 - 3/5 × 1/6

⇒ -2 × 1/5 + 1 - 1/5 × 1/2

⇒ -2/5 + 1 - 1/10

⇒ 1/2

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

⇒ -6/35 - 1/2 × 1/2 + 1/7 × 1/5

⇒ -6/35 - 1/4 + 1/35

⇒ -11/28

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Write the additive inverse of each of the following.

(i) 2/8 ⇒ -2/8

(ii) -5/9 ⇒ 5/9

(iii) -6/-5 ⇒ 6/5

(iv) 2/-9 ⇒-2/9

(v) 19/-16 ⇒ -19/16

_____________________

Verify that: -(-x) = x for.

(i) x = 11/15

RHS: -(-x)

⇒ -(-11/15)

⇒ 11/15

LHS: x

.°. RHS = LHS

(ii) x = -13/17

RHS: -(-x)

⇒ -[-(-13/17)]

⇒ -13/17

LHS: x

.°. RHS = LHS

_____________________

Answer 2

Q) using appropriate property find:

(i) -2/3×3/5+5/2-3/5×1/6

$\huge\underline\mathfrak{solution}$

give:-

= -2/3×3/5-3/5×1/6+5/2

= [-3/5]×[2/3+1/6]+5/2

= (-3/5)×[-4+1/6]+5/2

= [-3/5]×[5/6]+5/2

= -3/5×[5/6]+5/2

= -1/2+5/2

= 4/2

= 2

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

$\huge\underline\mathfrak{solution}$

give:-

= 2/4×[-3/7]+1/14×2/5-1/6×3/2

= [2/5]×[-3/7×1/14]-1/6×3/2

= 2/5×[-6+1/14] -1/6×3/2

= 2/5×[5/14] -1/6×3/2

= -1/7-(-1/4)

= -11/28

Q) Write the additive inverse of each of the following

(i) 2/8

= 2/8= -2/8

(ii) -5/9

= -5/9 = 5/8

(iii) -6/-5

= -6/-5= -6/5

(iv) 2/-9

= 2/-9= 2/9

(v) 19/-16

= 19/-6 = 19/6

Q) Verify that: -(-x) = x for.

(i) x = 11/15

= x = 11/15 = X= 11/15+(-11/+15)= 0

(ii) x = -13/17

= x = -13/17 = X= 13/17+(-13/-17)=0

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