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Original
2026-01-01
Modified
2026-02-28
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<p>The basic<a>arithmetic operations</a>are applicable on whole numbers, resulting in five main properties:<a>closure property</a>,<a>commutative property</a>,<a>associative property</a>, and<a>distributive property</a>.</p>
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<p>The basic<a>arithmetic operations</a>are applicable on whole numbers, resulting in five main properties:<a>closure property</a>,<a>commutative property</a>,<a>associative property</a>, and<a>distributive property</a>.</p>
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<h3><strong>Closure Property</strong></h3>
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<h3><strong>Closure Property</strong></h3>
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<p>The Closure property of numbers states that when you add or multiply any two whole numbers, the result will always be a whole number.</p>
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<p>The Closure property of numbers states that when you add or multiply any two whole numbers, the result will always be a whole number.</p>
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<p>For example, 4 × 6 = 24</p>
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<p>For example, 4 × 6 = 24</p>
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<p>When we multiply 4 and 6, the<a>product</a>is 24, which is also a whole number. </p>
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<p>When we multiply 4 and 6, the<a>product</a>is 24, which is also a whole number. </p>
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<p>The closure property is not applicable to the subtraction and division of whole numbers.</p>
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<p>The closure property is not applicable to the subtraction and division of whole numbers.</p>
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<p><strong>Commutative Property of Addition and Multiplication</strong></p>
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<p><strong>Commutative Property of Addition and Multiplication</strong></p>
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<p>The commutative property says that the<a>sum</a>and product of whole numbers will not change even if you change the order of the numbers. </p>
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<p>The commutative property says that the<a>sum</a>and product of whole numbers will not change even if you change the order of the numbers. </p>
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<p>For example, consider that ‘a’ and ‘b’ are two whole numbers. According to this property </p>
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<p>For example, consider that ‘a’ and ‘b’ are two whole numbers. According to this property </p>
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<p>\(a + b = b + a \)</p>
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<p>\(a + b = b + a \)</p>
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<p>\(a × b = b × a\)</p>
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<p>\(a × b = b × a\)</p>
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<p>Example: Consider a = 13 and b = 2</p>
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<p>Example: Consider a = 13 and b = 2</p>
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<p>\(13 + 2 = 2 + 13\)</p>
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<p>\(13 + 2 = 2 + 13\)</p>
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<p>\(13 × 2 = 2 × 13\)</p>
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<p>\(13 × 2 = 2 × 13\)</p>
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<h3> <strong>Associative Property of Addition and Multiplication</strong></h3>
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<h3> <strong>Associative Property of Addition and Multiplication</strong></h3>
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<p>The associative property refers to the grouping of three or more whole numbers in addition or multiplication without changing the result. </p>
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<p>The associative property refers to the grouping of three or more whole numbers in addition or multiplication without changing the result. </p>
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<p>For example, consider a, b, c are three whole numbers. According to the associative property:</p>
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<p>For example, consider a, b, c are three whole numbers. According to the associative property:</p>
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<p>a + (b + c) = (a + b) + c a × (b × c) = (a × b) × c </p>
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<p>a + (b + c) = (a + b) + c a × (b × c) = (a × b) × c </p>
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<p> Example: For Addition</p>
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<p> Example: For Addition</p>
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<p>\(4 + (3 + 5) = (4 + 3) + 5\)</p>
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<p>\(4 + (3 + 5) = (4 + 3) + 5\)</p>
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<p>\(4 + 8 = 7 + 5\)</p>
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<p>\(4 + 8 = 7 + 5\)</p>
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<p>12 = 12 </p>
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<p>12 = 12 </p>
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<p>For Multiplication</p>
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<p>For Multiplication</p>
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<p>\(2 × (3 × 4) = (2 × 3) × 4\)</p>
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<p>\(2 × (3 × 4) = (2 × 3) × 4\)</p>
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<p>\(2 × 12 = 6 × 4 \)</p>
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<p>\(2 × 12 = 6 × 4 \)</p>
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<p>24 = 24 </p>
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<p>24 = 24 </p>
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<h3><strong>Distributive Property of Multiplication Over Addition</strong></h3>
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<h3><strong>Distributive Property of Multiplication Over Addition</strong></h3>
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<p>It states that when you multiply a number by a sum, it is the same as multiplying that same number by each part of the sum separately. It can be written as :</p>
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<p>It states that when you multiply a number by a sum, it is the same as multiplying that same number by each part of the sum separately. It can be written as :</p>
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<p>\(a × (b + c) = (a × b) + (a × c)\)</p>
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<p>\(a × (b + c) = (a × b) + (a × c)\)</p>
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<p>For example, a = 3, b = 4, c = 5</p>
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<p>For example, a = 3, b = 4, c = 5</p>
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<p>\(3 × (4 + 5) = (3 × 4) + (3 × 5)\)</p>
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<p>\(3 × (4 + 5) = (3 × 4) + (3 × 5)\)</p>
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<p>\(3 × 9 = 12 + 15\)</p>
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<p>\(3 × 9 = 12 + 15\)</p>
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<p>27 = 27</p>
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<p>27 = 27</p>
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<h3><strong>Identity Property</strong> </h3>
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<h3><strong>Identity Property</strong> </h3>
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<ul><li><strong>Additive Identity:</strong> <p>The property states that when you add 0 to any whole number, the answer will be the whole number itself. </p>
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<ul><li><strong>Additive Identity:</strong> <p>The property states that when you add 0 to any whole number, the answer will be the whole number itself. </p>
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<p>For example, consider ‘a’ as a whole number </p>
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<p>For example, consider ‘a’ as a whole number </p>
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<p>a + 0 = a</p>
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<p>a + 0 = a</p>
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</li>
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</li>
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</ul><ul><li><strong>Multiplicative Identity</strong>:<p>This property states that when we multiply a whole number by 1 then it results in the whole number itself. </p>
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</ul><ul><li><strong>Multiplicative Identity</strong>:<p>This property states that when we multiply a whole number by 1 then it results in the whole number itself. </p>
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<p>For example, consider ‘b’ as a whole number 1 × b = b</p>
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<p>For example, consider ‘b’ as a whole number 1 × b = b</p>
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</li>
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</li>
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</ul>
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</ul>