Mathematics
Fill in the blanks to make each of the following a true statement:
(i) 375 × 57 = 57 × ….
(ii) (33 × 16) × 25 = 33 × (…. × 25)
(iii) 37 × 24 = 37 × 18 + 37 × ….
(iv) 7205 × 1 = …. = 1 × 7205
(v) 366 × 0 = ….
(vi) …. × 579 = 0
(vii) 473 × 108 = 473 × 100 + 473 × ….
(viii) 684 × 97 = 684 × 100 - …. × 3
(ix) 0 ÷ 5 = ….
(x) (14 - 14) ÷ 7 = ….
Whole Numbers
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Answer
(i) According to the Commutative Property of Multiplication: a × b = b × a.
375 × 57 = 57 × 375.
(ii) According to the Associative Law of Multiplication: (a × b) × c = a × (b × c).
(33 × 16) × 25 = 33 × (16 × 25).
(iii) Using the Distributive Law of Multiplication over Addition: a × (b + c) = a × b + a × c.
Since 24 = 18 + 6, we have:
37 × 24 = 37 × 18 + 37 × 6.
(iv) According to the Multiplicative Identity property, any number multiplied by 1 equals itself.
7205 × 1 = 7205 = 1 × 7205.
(v) According to the Multiplication by Zero property, any number multiplied by 0 equals 0.
366 × 0 = 0.
(vi) Any number multiplied by 0 gives 0.
0 × 579 = 0.
(vii) Using the Distributive Law of Multiplication over Addition.
Since 108 = 100 + 8, we have:
473 × 108 = 473 × 100 + 473 × 8.
(viii) Using the Distributive Law of Multiplication over Subtraction.
Since 97 = 100 - 3, we have:
684 × 97 = 684 × (100 - 3) = 684 × 100 - 684 × 3.
(ix) Zero divided by any non-zero whole number is 0.
0 ÷ 5 = 0.
(x) (14 - 14) ÷ 7 = 0 ÷ 7 = 0.
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