a)use the distributivity of multlplication of rational numbers over addition to simplify the given expressions i)3/5 (35/24+10/1). ii) -5/4 (8/5+16/15)
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Answer:
Ans: (i) (3/5) × [(35/24) + (10/1)]
According to the distributivity property of multiplication of rational numbers over addition, a × (b + c) = a × b + a × c
Here the values of a, b and c are:, a =3/5, b =35/24, c = 10/1
Then, (3/5) × [(35/24) + (10/1)] = ((3/5) × (35/24)) + ((3/5) × (10/1))
= ((1/1) × (7/8)) + ((3/1) × (2/1))
= (7/8) + (6/1)
= (7 + 48)/8
= 55/8
Ans: (ii) (-5/4) × [(8/5) + (16/15)]
According to the distributivity property of multiplication of rational numbers over addition, a × (b + c) = a × b + a × c
Here the values of a, b and c are:, a =-5/4, b =8/5, c = 16/15
Then, (-5/4) × [(8/5) + (16/15)] = ((-5/4) × (8/5)) + ((-5/4) × (16/15))
= ((-1/1) × (2/1)) + ((-1/1) × (4/3))
= (-2/1) + (-4/3)
= (-6 – 4)/3
= -10/3
NOTE: YOU CAN FURTHER CHANGE THE IMPROPER FRACTION TO MIXED FRACTION.