Question

1. Which of the following pairs is equivalent? (i) -20/12,5/3 (ii) 16/-30,-8/15 (iii) -18/36,-20/44 (iv) 7/-5,-5/7 2. 3/4÷ (5/8+1/2)= (i) 13/10 (ii) 2/3 (iii) 3/2 (iv) 5/8 3. 1/2- (3/4 -5/6) ≠ (1/2-3/4) - 5/6 illustrates that subtraction does not satisfy the__________property for rational numbers. (i)Commutative (ii) closure (iii) distributive (iv) associative 4. (1-1/2) x (1/2-1/4)÷(3/4-1/2) = (i) 1/2 (ii) 3/4 (iii) 1/4 (iv) -1/2

Answer 1

solutions :(1)

$\frac{ - 20}{12} = \frac{5}{3} \:$

$- 20 \times 3 = 5 \times 12$

$- 60 = 60$

not rational number equilevant.

solutions:(2).

$\frac{16}{ - 30} = \frac{ - 8}{15}$

$16 \times 15 = ( - 8) \times (- 30)$

$240 = 240$

it is rational number equilevant. solutions:(3).

$\frac{ - 18}{36} = \frac{ - 20}{44}$

$- 18 \times 44 = - 20 \times 36$

$- 792 = - 720$

it is not rational number equilevant

Answer 2

1) (ii) 16/-30 , -8/15 is an equivalent fraction

16/-30 = 16 ÷ (-2)/ - 30 ÷ (-2) = -8/15

2) (ii) 2/3

3/4 ÷ (5/8 + 1/2) = 3/4 ÷ (5+4/8)

= 3/4 ÷ 9/8 = 3/4 × 8/9 = 2/3

3) (iv) Associative property

4) (i) 1/2

(1-1/2)× (1/2 - 1/4) ÷ (3/4-1/2)

(2-1/2)×(2-1/4) ÷ (3-2/4)

= 1/2 × 1/4 ÷1/4

=1/2 × 1/4 × 4 = 1/2

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