Clear 3/2 = ((1/2) = (5/2)) * ((3/2) = (1/2)) = (5/2) What is the conclusion of the above statement?
a. Division is not associative for rational numbers.
b. Multiplicative identity of rational numbers
c. Subtraction is associative for rational numbers
d. Commutativity property of rational numbers under the operation of addition
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Answer:
(i) -2/3 * 3/5 + 5/2 – 3/5 * 1/6
= -2/3 * 3/5 – 3/5 * 1/6 + 5/2 [Using associative property]
= 3/5 * (-2/3 – 1/6) + 5/2 [Using distributive property]
= 3/5 * {(-4 - 1)/6} + 5/2 [LCM (3, 2) = 6]
= 3/5 * (-5/6) + 5/2
= -3/6 + 5/2
= -1/2 + 5/2
= (-1 + 5)/2
= 4/2
= 2
(ii) 2/5 * (3/-7) – 1/6 * 3/2 + 1/14 * 2/5
= 2/5 * (-3/7) + 1/14 * 2/5 – 1/6 * 3/2 [Using associative property]
= 2/5 * (-3/7 + 1/14) – 1/2 * 1/2 [Using distributive property]
= 2/5 * {(-6 + 1)/14} – 1/4 [LCM (7, 14) = 14]
= 2/5 * (-5/14) – 1/4
= -1/7 – 1/4
= (-4 -7)/28 [LCM (7, 4) = 28]
= -11/28
Step-by-step explanation:
We know that additive inverse of a rational number a/b is (-a/b) such that a/b + (-a/b) = 0
(i) Additive inverse of 2/8 = -2/8
(ii) Additive inverse of -5/9 = 5/9
(iii) -6/-5 = 6/5
Additive inverse of 6/5 = -6/5
(iv) 2/-9 = -2/9
Additive inverse of -2/9 = 2/9
(v) 19/-6 = -19/6
Additive inverse of -19/6 = 19/6
(i) Putting x = 11/15 in -(-x) = x, we get
=> -(-11/15) = 11/15
=> 11/15 = 11/15
=> LHS = RHS
Hence, verified.
(i) Putting x = -13/17 in -(-x) = x, we get
=> -{-(-13/17)} = -13/17
=> -(13/17) = -13/17
=> -13/17 = -13/17
=> LHS = RHS
Hence, verified.
We know that multiplicative inverse of a rational number a is 1/a such that a * 1/a = 1
(i) Multiplicative inverse of -13 = -1/13
(ii) Multiplicative inverse of -13/19 = -19/13
(iii) Multiplicative inverse of 1/5 = 5
(iv) (-5/8)*(-3/7) = (5 * 3)/(8 * 7) = 15/56
Multiplicative inverse of 15/56 = 56/15
(v) -1 * (-2/5) = 2/5
Multiplicative inverse of 2/5 = 5/2
(vi) Multiplicative inverse of -1 = 1/-1 = -1