Can someone please help me with these?
Simplify each of the following using appropriate property. Also name the property.
(a) 2 upon 5 × 1 upon 14 - 1 upon 4 + 2 upon 5 × −3 upon 7
(b) 2 upon 7 × -3 upon 5 - 1 upon 10 - 3 upon 5 × 3 upon 7
(c) -3 upon 11 × 4 upon 7 + 7 upon 5 × 5 upon 11 - 4 upon 7 × 1 upon 8
(a) Simplify :
−13 upon 24 × −12 upon 5 × 35 upon 36 × −6
-(-5 upon 8) = 5 upon 8 [true or false?]
Simplify each of the following using appropriate property. Also name the property.
(a) 2 upon 5 × 1 upon 14 - 1 upon 4 + 2 upon 5 × −3 upon 7
(b) 2 upon 7 × -3 upon 5 - 1 upon 10 - 3 upon 5 × 3 upon 7
(c) -3 upon 11 × 4 upon 7 + 7 upon 5 × 5 upon 11 - 4 upon 7 × 1 upon 8
(a) Simplify :
−13 upon 24 × −12 upon 5 × 35 upon 36 × −6
-(-5 upon 8) = 5 upon 8 [true or false?]
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Answer:
(a) [(½) × (¼)] + [(½) × 6]
Solution:-
The given set of rational numbers is according to the rule of distributive law over addition.
The distributive property states, if a, b and c are three rational numbers, then;
a x (b+c) = (a x b) + (a x c)
Let us take ½ as common.
So
= 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 given set of rational numbers is according to the rule of distributive law over subtraction.
The distributive property states, if a, b and c are three rational numbers, then;
a x (b+c) = (a x b) + (a x c)
Let us take 1/5 as common.
So
= 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 given set of rational numbers is according to the rule of distributive law over addition.
The distributive property states, if a, b and c are three rational numbers, then;
a x (b+c) = (a x b) + (a x c)
= (-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