Question

Identify the laws in the following statements : 1) -3+ 5 = 5 +(-3) ii) [(-5) * 2)] × 3 = (-5) * ((2 * 3)] v) -5x 6 = -30 ii) -2 x 1 = 1 × (-2) = -2 iv) 18 x [7 +(-3)] = [18 x 7] + [18 (-3)] vi) -3 + 0 = 0 +(-3) = -3​

Answer 1

Explanation:

Identify the laws in the following statements : 1) -3+ 5 = 5 +(-3) ii) [(-5) * 2)] × 3 = (-5) * ((2 * 3)] v) -5x 6 = -30 ii) -2 x 1 = 1 × (-2) = -2 iv) 18 x [7 +(-3)] = [18 x 7] + [18 (-3)] vi) -3 + 0 = 0 +(-3) = -3

Answer 2

Concept:

Commutative property

The commutative property states that expressions can be added or multiplied in any order.

x + y = y + x

xy = yx

For example, 23 + 7 = 7 + 23 and 5 × 8 = 8 × 5.

Associative property

The associative property states that when three or more expressions are added or multiplied, they may be grouped without affecting the answer. The commutative property applies within the associative property.

(x + y) + z = x + (y + z)

(xy)z = x(yz)

Distributive property

The distributive property states that multiplying an expression times the sum of expressions is the same as multiplying the expression times each item in the sum.

x(y + z) = xy + xz

Given:

1) -3+ 5 = 5 +(-3)

ii) [(-5) * 2)] × 3 = (-5) * ((2 * 3)]

iii) -2 x 1 = 1 × (-2) = -2

iv) 18 x [7 +(-3)] = [18 x 7] + [18 (-3)]

v) -3 + 0 = 0 +(-3) = -3​

Find:

Identify the laws in the following statements

Solution:

1) -3+ 5 = 5 +(-3)

Commutative property

ii) [(-5) * 2)] × 3 = (-5) * ((2 * 3)]

Associate property

iii) -2 x 1 = 1 × (-2) = -2

Commutative property

iv) 18 x [7 +(-3)] = [18 x 7] + [18 (-3)]

Distributive property

v) -3 + 0 = 0 +(-3) = -3​

Commutative property

Therefore, 1,3,5 is Commutative property  and 2 is associate property and 4 is distributive property

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