pls do it with a clear explanation or a pic
Answers
Answer:
3/9×(-1/2+-5/8)=3/9×-1/2+3/9×-5/8
Step-by-step explanation:
5/2 – 3/5 * 1/6 (ii) 2/5 * (3/-7) – 1/6 * 3/2 + 1/14 * 2/5
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
Question 2:
Write the additive inverse of each of the following:
(i) 2/8 (ii) -5/9 (iii) -6/-5 (iv) 2/-9 (v) 19/-6
Answer:
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
Question 3:
Verify that -(-x) = x for:
(i) x = 11/15 (ii) x = -13/17
Answer:
(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.
Question 4:
Find the multiplicative inverse of the following:
(i) -13 (ii) -13/19 (iii) 1/5 (iv) (-5/8)*(-3/7) (v) -1 * (-2/5) (vi) -1
Answer:
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
Question 5:
Name the property under multiplication used in each of the following:
(i) -4/5 * 1 = 1 * -4/5
(ii) -13/17 * -2/7 = -2/7 * -13/17
(iii) -19/29 * 29/-19 = 1
Answer:
(i) 1 is the multiplicative identity.
(ii) Commutative property.
(iii) Multiplicative Inverse property.
Question 6:
Multiply 6/13 by the
Step-by-step explanation:
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