For each of the following verify the closure property and commutative property of multiplication. (a) 2/5,3/7 (b) 3/8,-2/9 (c) -4/11,22/13 (d) -5/8 , 4/-3
Answers
The closure property and commutative property of multiplication hold for all the given pairs of fractions.
Given:
(a) 2/5, 3/7 (b) 3/8, -2/9 (c) -4/11, 22/13 (d) -5/8, 4/-3
To find:
For each of the following verify the closure property and commutative property of multiplication.
Solution:
To verify the closure property of multiplication, check if the product of any two given fractions is also a fraction.
To verify the commutative property of multiplication, check if swapping the order of the fractions in the multiplication operation gives the same result.
Let's go through each case:
(a) 2/5, 3/7:
The product of 2/5 and 3/7 is (2/5) × (3/7) = 6/35, which is a fraction.
Swapping the order, (3/7) × (2/5) = 6/35, which is the same result.
Hence, The closure property and commutative property of multiplication hold for 2/5 and 3/7.
(b) 3/8, -2/9:
The product of 3/8 and -2/9 is (3/8) × (-2/9) = -6/72 = -1/12, which is a fraction.
Swapping the order, (-2/9) × (3/8) = -6/72 = -1/12, which is the same result.
Hence, the closure property and commutative property of multiplication hold for 3/8 and -2/9.
(c) -4/11, 22/13:
The product of -4/11 and 22/13 is (-4/11) × (22/13) = -88/143, which is a fraction.
Swapping the order, (22/13) × (-4/11) = -88/143, which is the same result.
Therefore, the closure property and commutative property of multiplication hold for -4/11 and 22/13.
(d) -5/8, 4/-3:
The product of -5/8 and 4/-3 is (-5/8) × (4/-3) = 20/24 = 5/6, which is a fraction.
Swapping the order, (4/-3) × (-5/8) = 20/24 = 5/6, which is the same result.
Therefore, the closure property and commutative property of multiplication hold for -5/8 and 4/-3.
Therefore,
The closure property and commutative property of multiplication hold for all the given pairs of fractions.
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