Simplify each of the following by using suitable property.

(a) [(½) × (¼)] + [(½) × 6]

The arrangement of the given rational number is as per the rule of distributive law over addition.

Now take out ½ as common.

Then,

= ½ [¼ + 6]

= ½ [(1 + 24)/4]

= ½ [25/24]

= ½ × (25/24)

= 25/8

(b) [(1/5) × (2/15)] – [(1/5) × (2/5)]

Solution:-

The arrangement of the given rational number is as per the rule of distributive law over subtraction.

Now take out 1/5 as common.

Then,

= 1/5 [(2/15) – (2/5)]

The LCM of the denominators 15 and 5 is 15

(2/15) = [(2×1)/ (15×1)] = (2/15)

and (2/5) = [(2×3)/ (5×3)] = (6/15)

= 1/5 [(2 – 6)/15]

= 1/5 [-4/15]

= (1/5) × (-4/15)

= -4/75

(c) (-3/5) × {(3/7) + (-5/6)}

Solution:-

The arrangement of the given rational number is as per the rule of distributive law over addition.

= (-3/5) × {(3/7) + (-5/6)}

The LCM of the denominators 7 and 6 is 42

(3/7) = [(3×6)/ (7×6)] = (18/42)

and (-5/6) = [(-5×7)/ (6×7)] = (-35/42)

= -3/5 [(18 – 35)/42]

= -3/5 [-17/42]

= (-3/5) × (-17/42)

= 51/210 … [divide both denominator and numerator by 3]

= 17/30