![\"Properties](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Properties-of-Multiplication-1.png\")
<\/p>\nCheck out different properties of multiplication of whole numbers to solve the problems easily. We have given six properties of multiplication in the below article. They are Closure Property, Zero Property, Commutative Property, Associativity Property, Identity Property, and Distributive Property.<\/p>\n
The multiplication of whole numbers refers to the product of two or more whole numbers. Applying multiplication operation and the properties of multiplication are given clearly explained with the examples in this article for you. Have a look at the complete concept and improve your preparation level easily.<\/p>\n
<\/p>\n
According to Closure Property of Whole Numbers, if two whole numbers a and b are multiplied then their resultant a \u00d7 b is also a whole number. Therefore, whole numbers are closed under multiplication.<\/p>\n
a \u00d7 b is a whole number, for every whole number a and b.<\/p>\n
Verification:
\nIn order to verify the Closure Property of Whole Numbers, let us take a few pairs of whole numbers and multiply them.<\/p>\n
For example:
\nLet us take the whole numbers and multiply them to verify the Closure Property of Whole Numbers.
\n(i) 7 \u00d7 8 = 56
\n(ii) 0 \u00d7 15 = 0
\n(iii) 12 \u00d7 14 = 168
\n(iv) 21 \u00d7 1 = 21<\/p>\n
We find that the product is always a whole number.<\/p>\n
Also, Read:<\/p>\n
The commutative property of multiplication of whole numbers states that altering the order of operands or the whole numbers does not affect the result of the multiplication.<\/p>\n
a \u00d7 b = b \u00d7 a, for every whole number a and b.<\/p>\n
Verification:
\nIn order to verify the Commutativity of Whole Numbers property, let us take a few pairs of whole numbers and multiply the numbers in different orders as shown below.<\/p>\n
Examples:
\n(i) 7 \u00d7 8 = 56 and 8 \u00d7 7 = 56
\nBoth multiplications get the same output.
\nTherefore, 7 \u00d7 8 = 8 \u00d7 7
\n(ii) 30 \u00d7 10 = 300 and 10 \u00d7 30 = 300
\nBoth multiplications get the same output.
\nTherefore, 30 \u00d7 10 = 10 \u00d7 30
\n(iii) 14 \u00d7 13 = 182 and 13 \u00d7 14 = 182
\nBoth multiplications get the same output.
\nTherefore, 14 \u00d7 13 = 13 \u00d7 14
\n(iv) 16 \u00d7 17 = 272 and 17 \u00d7 16 = 272
\nBoth multiplications get the same output.
\nTherefore, 16 \u00d7 17 = 17 \u00d7 16
\n(V) 1235 \u00d7 334 = 412490 and 334 \u00d7 1235 = 412490
\nBoth multiplications get the same output.
\nTherefore, 1235 \u00d7 334 = 334 \u00d7 1235
\n(vi) 21534 \u00d7 1429 = 30772086 and 1429 \u00d7 21534 = 30772086
\nBoth multiplications get the same output.
\nTherefore, 21534 \u00d7 1429 = 1429 \u00d7 21534<\/p>\n
We find that in whatever order we multiply two whole numbers, the product remains the same.<\/p>\n
On multiplying any whole numbers by zero the result is always zero. In general, if a and b are two whole numbers then,
\na \u00d7 0 = 0 \u00d7 a = 0
\nThe product of any whole number and zero is always zero.<\/p>\n
Verification:
\nIn order to verify the Zero Property of Whole Numbers, we take some whole numbers and multiply them by zero as shown below<\/p>\n
Examples:
\n(i) 30 \u00d7 0 = 0 \u00d7 30 = 0
\n(ii) 2 \u00d7 0 = 0 \u00d7 2 = 0
\n(iii) 127 \u00d7 0 = 0 \u00d7 127 = 0
\n(iv) 0 \u00d7 0 = 0 \u00d7 0 = 0
\n(v) 144 \u00d7 0 = 0 \u00d7 144 = 0
\n(vi) 54791 \u00d7 0 = 0 \u00d7 54791 = 0
\n(vii) 62888 \u00d7 0 = 0 \u00d7 62888 = 0<\/p>\n
From the above examples, the product of any whole number and zero is zero.<\/p>\n
On multiplying any whole number by 1 the result obtained is the whole number itself. In general, if a and b are two whole numbers then,
\na \u00d7 1 = 1 \u00d7 a = a
\nTherefore 1 is the Multiplicative Identity of Integers.<\/p>\n
Verification:
\nIn order to verify Multiplicative Identity of Whole Numbers, we find the product of different whole numbers with 1 as shown below<\/p>\n
Examples:
\n(i) 16 \u00d7 1 = 16 = 1 \u00d7 16
\n(ii) 1 \u00d7 1 = 1 = 1 \u00d7 1
\n(iii) 27 \u00d7 1 = 27 = 1 \u00d7 27
\n(iv) 127 \u00d7 1 = 127 = 1 \u00d7 127
\n(v) 3518769 \u00d7 1 = 3518769
\n(vi) 257394 \u00d7 1 = 257394
\nWe see that in each case a \u00d7 1 = a = 1 \u00d7 a.<\/p>\n
The number 1 is called the multiplication identity or the identity element for multiplication of whole numbers because it does not change the value of the numbers during the operation of multiplication.<\/p>\n
The result of the product of three or more whole numbers is irrespective of the grouping of these whole numbers. In general, if a, b and c are three whole numbers then, a \u00d7 (b \u00d7 c) = (a \u00d7 b) \u00d7 c.<\/p>\n
Verification:
\nIn order to verify the Associativity Property of Multiplication of Whole Numbers, we take three whole numbers say a, b, c, and find the values of the expression (a \u00d7 b) \u00d7 c and a \u00d7 (b \u00d7 c) as shown below :<\/p>\n
Examples:
\n(i) (3 \u00d7 4) \u00d7 5 = 12 \u00d7 5 = 60 and 3 \u00d7 (4 \u00d7 5) = 3 \u00d7 20 = 60
\nBoth multiplications get the same output.
\nTherefore, (3 \u00d7 4) \u00d7 5 = 3 \u00d7 (4 \u00d7 5)
\n(ii) (1 \u00d7 7) \u00d7 2 = 7 \u00d7 2 = 14 and 1 \u00d7 (7 \u00d7 2) = 1 \u00d7 14 = 14
\nBoth multiplications get the same output.
\nTherefore, (1 \u00d7 7) \u00d7 2 = 1 \u00d7 (7 \u00d7 2)
\n(iii) (2 \u00d7 9) \u00d7 3 = 18 \u00d7 3 = 54 and 2 \u00d7 (9 \u00d7 3) = 2 \u00d7 27 = 54
\nBoth multiplications get the same output.
\nTherefore, (2 \u00d7 9) \u00d7 3 = 2 \u00d7 (9 \u00d7 3).
\n(iv) (2 \u00d7 1) \u00d7 3 = 2 \u00d7 3 = 6 and 2 \u00d7 (1 \u00d7 3) = 2 \u00d7 3 = 6
\nBoth multiplications get the same output.
\nTherefore, (2 \u00d7 1) \u00d7 3 = 2 \u00d7 (1 \u00d7 3).
\n(v) (221 \u00d7 142) \u00d7 421 = 221 \u00d7 (142 \u00d7 421)
\nBoth multiplications get the same output.
\n(vi) (2504 \u00d7 547) \u00d7 1379 = 2504 \u00d7 (547 \u00d7 1379)
\nBoth multiplications get the same output.
\nWe find that in each case (a \u00d7 b) \u00d7 c = a \u00d7 (b \u00d7 c).
\nThus, the multiplication of whole numbers is associative.<\/p>\n
According to the distributive property of multiplication of whole numbers, if a, b and c are three whole numbers then, a\u00d7 (b + c) = (a \u00d7 b) + (a \u00d7 c) and (b + c) \u00d7 a = b \u00d7 a + c \u00d7 a<\/p>\n
Verification:
\nIn order to verify the Distributive Property of Multiplication of Whole Numbers, we take any three whole numbers a, b, c and find the values of the expressions a \u00d7 (b + c) and a \u00d7 b + a \u00d7 c as shown below<\/p>\n
Examples:
\n(i) 3 \u00d7 (2 + 5) = 3 \u00d7 7 = 21 and 3 \u00d7 2 + 3 \u00d7 5 = 6 + 15 =21
\nTherefore, 3 \u00d7 (2 + 5) = 3 \u00d7 2 + 3 \u00d7 5
\n(ii) 1 \u00d7 (5 + 9) = 1 \u00d7 14 = 15 and 1 \u00d7 5 + 1 \u00d7 9 = 5 + 9 = 14
\nTherefore, 1 \u00d7 (5 + 9) = 1 \u00d7 5 + 1 \u00d7 9.
\n(iii) 2 \u00d7 (7 + 15) = 2 \u00d7 22 = 44 and 2 \u00d7 7 + 2 \u00d7 15 = 14 + 30 = 44.
\nTherefore, 2 \u00d7 (7 + 15) = 2 \u00d7 7 + 2 \u00d7 15.
\n(iv) 50 \u00d7 (325 + 175) = 50 \u00d7 3250 + 50 \u00d7 175
\n(v) 1007 \u00d7 (310 + 798) = 1007 \u00d7 310 + 1007 \u00d7 798<\/p>\n
(i) Number \u00d7 0 = __________
\n(ii) 64 \u00d7 __________ = 64000
\n(iii) Number \u00d7 __________ = Number itself
\n(iv) 3 \u00d7 (7 \u00d7 9) = (3 \u00d7 7) \u00d7 __________
\n(v) 4 \u00d7 _________ = 8 \u00d7 4
\n(vi) 7 \u00d7 6 \u00d7 11 = 11 \u00d7 __________
\n(vii) 72 \u00d7 10 = __________
\n(viii) 6 \u00d7 48 \u00d7 100 = 6 \u00d7 100 \u00d7 __________<\/p>\n
Solutions:
\n(i) Number \u00d7 0 = __________
\nAny number multiplied with 0 gives 0 output.
\nTherefore, the answer is 0 \u00d7 Number.
\n(ii) 64 \u00d7 __________ = 64000
\nThe given numbers are 64 \u00d7 __________ = 64000
\nTo get the answer multiply 64 with 1000.
\n64 \u00d7 1000.
\nTherefore, the answer is 1000.
\n(iii) Number \u00d7 __________ = Number itself
\nAny number multiplied with 1 gives Number itself.
\nTherefore, the answer is Number \u00d7 1 = Number itself.
\n(iv) 3 \u00d7 (7 \u00d7 9) = (3 \u00d7 7) \u00d7 __________
\nThe given numbers are 3 \u00d7 (7 \u00d7 9) = (3 \u00d7 7) \u00d7 __________
\nFrom the Associativity Property of Multiplication of Whole Numbers, 3 \u00d7 (7 \u00d7 9) = (3 \u00d7 7) \u00d7 9 gives the same output.
\nTherefore, the answer is 9.
\n(v) 4 \u00d7 _________ = 8 \u00d7 4
\nThe given numbers are 4 \u00d7 _________ = 8 \u00d7 4
\nFrom the Commutativity of Whole Numbers, 4 \u00d7 8 = 8 \u00d7 4 gives the same output.
\nTherefore, the answer is 8.
\n(vi) 7 \u00d7 6 \u00d7 11 = 11 \u00d7 __________
\nThe given numbers are 7 \u00d7 6 \u00d7 11 = 11 \u00d7
\nFrom the Associativity Property of Multiplication of Whole Numbers, 7 \u00d7 (6 \u00d7 11) = 11 \u00d7 (7 \u00d7 6) gives the same output.
\nTherefore, the answer is 7 \u00d7 6.
\n(vii) 72 \u00d7 10 = __________
\nThe given numbers are 72 \u00d7 10 = __________
\nFrom the Commutativity of Whole Numbers, 72 \u00d7 10 = 10 \u00d7 72 gives the same output.
\nTherefore, the answer is 10 \u00d7 72.
\n(viii) 6 \u00d7 48 \u00d7 100 = 6 \u00d7 100 \u00d7 __________
\nThe given numbers are 6 \u00d7 48 \u00d7 100 = 6 \u00d7 100 \u00d7
\nFrom the Associativity Property of Multiplication of Whole Numbers, 6 \u00d7 48 \u00d7 100 = 6 \u00d7 100 \u00d7 48 gives the same output.
\nTherefore, the answer is 48.<\/p>\n","protected":false},"excerpt":{"rendered":"
Check out different properties of multiplication of whole numbers to solve the problems easily. We have given six properties of multiplication in the below article. They are Closure Property, Zero Property, Commutative Property, Associativity Property, Identity Property, and Distributive Property. The multiplication of whole numbers refers to the product of two or more whole numbers. … Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":79442,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Properties-of-Multiplication.png","_links":{"self":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/79441"}],"collection":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/comments?post=79441"}],"version-history":[{"count":1,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/79441\/revisions"}],"predecessor-version":[{"id":137728,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/79441\/revisions\/137728"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media\/79442"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=79441"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=79441"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=79441"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}