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	<title>closures Archives &#8211; Mathemafia</title>
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	<title>closures Archives &#8211; Mathemafia</title>
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		<title>Closure property &#8211; Rational Numbers</title>
		<link>https://mathemafia.com/closure-property-rational-numbers/</link>
		
		<dc:creator><![CDATA[Sunil Syal]]></dc:creator>
		<pubDate>Sat, 15 Aug 2020 06:28:16 +0000</pubDate>
				<category><![CDATA[Number system]]></category>
		<category><![CDATA[Class 9 math tutorials]]></category>
		<category><![CDATA[closure property]]></category>
		<category><![CDATA[closures]]></category>
		<category><![CDATA[math]]></category>
		<category><![CDATA[mathemafia]]></category>
		<category><![CDATA[NCERT]]></category>
		<category><![CDATA[number system]]></category>
		<category><![CDATA[properties of numbers]]></category>
		<category><![CDATA[rational numbers]]></category>
		<guid isPermaLink="false">http://sh016.global.temp.domains/~mathemaf/?p=1369</guid>

					<description><![CDATA[<p>Concept: In this tutorial, you will learn about the closure property. It is discussed in detail for the following operations on rational numbers. Addition Subtraction Multiplication Division Closure property &#8211; Whole Numbers &#38; Integers Identity &#38; Inverse</p>
<p>The post <a href="https://mathemafia.com/closure-property-rational-numbers/">Closure property &#8211; Rational Numbers</a> appeared first on <a href="https://mathemafia.com">Mathemafia</a>.</p>
]]></description>
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									<p><b>Concept</b>: In this tutorial, you will learn about the closure property. It is discussed in detail for the following operations on rational numbers.</p><ul><li>Addition</li><li>Subtraction</li><li>Multiplication</li><li>Division</li></ul><div class="iframe-container"><iframe src="https://www.youtube.com/embed/fxt4yqhriK0?rel=0" width="560" height="315" frameborder="0" allowfullscreen="allowfullscreen"></iframe></div>								</div>
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					<a class="elementor-button elementor-button-link elementor-size-sm" href="/closure-property-whole-numbers-and-integers">
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									<span class="elementor-button-text"><span>Closure property - Whole Numbers &amp; Integers</span><span></span></span>
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					<a class="elementor-button elementor-button-link elementor-size-sm" href="/additive-identity-multiplicative-identity-additive-inverse-reciprocal">
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									<span class="elementor-button-text">Identity &amp; Inverse</span>
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									<div data-post-id="1333" class="insert-page insert-page-1333 ">		<div data-elementor-type="wp-page" data-elementor-id="1333" class="elementor elementor-1333">
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				<div class="elementor-widget-container">
					<h3 class="elementor-heading-title elementor-size-default">Number System<br></h3>				</div>
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					</div>
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				<section class="elementor-section elementor-top-section elementor-element elementor-element-a04c0dd elementor-section-boxed elementor-section-height-default elementor-section-height-default" data-id="a04c0dd" data-element_type="section" data-e-type="section">
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									<ul><li><a href="/number-system-best-explained-with-real-life-examples">Number System &#8211; Best explained with real life examples</a></li><li><a href="/distributive-property-of-multiplication-over-addition-and-subtraction">Distributive property of multiplication over addition and subtraction</a></li><li><a href="/associative-property-of-addition-and-multiplication">Associative property of addition and multiplication </a></li><li>Closure property<ul><li><a href="/closure-property-natural-numbers">Natural Numbers</a></li><li><a href="/closure-property-whole-numbers-and-integers">Whole Numbers &amp; Integers</a></li><li><a href="/closure-property-rational-numbers">Rational Numbers</a></li></ul></li><li><a href="/additive-identity-multiplicative-identity-additive-inverse-reciprocal">Additive Identity, Multiplicative identity, Additive inverse, Reciprocal</a></li><li><a style="background-color: #ffffff;" href="/commutative-law-explained-for-basic-arithmetic-operations">Commutative law explained for basic arithmetic operations</a></li><li>Rational Numbers<ul><li><a href="/find-a-rational-number-between-any-two-rational-numbers">Find a rational number between any two rational numbers</a></li><li><a style="background-color: #ffffff;" href="/rational-numbers-are-infinitely-many">Rational numbers are infinitely many</a></li><li><a href="/mean-method-infinitely-many-rational-numbers-between-any-two-rational-numbers">Mean method : Infinitely many rational numbers between any two rational numbers</a></li></ul></li><li>Integers<ul><li><a href="/proof-integers-are-infinitely-many">Integers are infinitely many</a></li></ul></li></ul>								</div>
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				<section class="elementor-section elementor-top-section elementor-element elementor-element-0dab545 elementor-section-boxed elementor-section-height-default elementor-section-height-default" data-id="0dab545" data-element_type="section" data-e-type="section">
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					<h3 class="elementor-heading-title elementor-size-default">Polynomials<br></h3>				</div>
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									<ul><li><a href="/class-9-chapter-2-polynomials-basics-of-polynomials">Basics of polynomials</a></li><li><a href="/class-9-chapter-2-polynomials-remainder-theorem">Remainder theorem</a></li><li><a href="/class-9-chapter-2-polynomials-factor-theorem">Factor theorem</a></li><li><a href="/class-9-chapter-2-polynomials-factorisation-by-splitting-the-middle-term/">Factorise &#8211; Splitting the middle term</a></li><li><a href="/class-9-chapter-2-polynomials-algebraic-identities">Algebraic Identities</a></li><li><a href="/rational-root-theorem">Rational root theorem</a></li></ul>								</div>
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					<h3 class="elementor-heading-title elementor-size-default">Important Concepts &#8211; Miscellaneous<br></h3>				</div>
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				<section class="elementor-section elementor-top-section elementor-element elementor-element-b41f83e elementor-section-boxed elementor-section-height-default elementor-section-height-default" data-id="b41f83e" data-element_type="section" data-e-type="section">
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									<ul><li><a href="/derivation-herons-formula">Derivation of Heron&#8217;s formula</a></li></ul>								</div>
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					<h3 class="elementor-heading-title elementor-size-default">Surface area and Volumes<br></h3>				</div>
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									<ul><li><a href="/area-surface-area-volume">Area / Surface area / Volume &#8211; Introduction</a></li><li><a href="/surface-area-of-cube-and-cuboid">Surface Area of Cube and Cuboid</a></li><li><a href="/volume-of-cuboid-and-cube">Volume Of Cuboid and Cube</a></li><li><a href="/surface-area-of-right-circular-cylinder">Surface Area of Right Circular Cylinder</a></li><li><a href="/volume-and-capacity-of-cylinder">Volume and capacity of Cylinder</a></li><li><a href="/right-circular-cone">Right circular Cone</a></li><li><a href="/surface-area-of-right-circular-cone">Surface Area of Right circular Cone</a></li><li><a href="/volume-of-cylinder-vs-cone">Volume of Cylinder vs Cone</a></li><li><a href="/litres-and-cubic-centimetre">Litres and Cubic centimetre (cm³)</a></li><li><a href="/cubic-meters-to-litres">Cubic meters to litres</a></li></ul>								</div>
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		<p>The post <a href="https://mathemafia.com/closure-property-rational-numbers/">Closure property &#8211; Rational Numbers</a> appeared first on <a href="https://mathemafia.com">Mathemafia</a>.</p>
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		<item>
		<title>Closure property &#8211; Whole Numbers and Integers</title>
		<link>https://mathemafia.com/closure-property-whole-numbers-and-integers/</link>
		
		<dc:creator><![CDATA[Sunil Syal]]></dc:creator>
		<pubDate>Sat, 15 Aug 2020 06:27:54 +0000</pubDate>
				<category><![CDATA[Number system]]></category>
		<category><![CDATA[Class 9 math tutorials]]></category>
		<category><![CDATA[closure property]]></category>
		<category><![CDATA[closures]]></category>
		<category><![CDATA[integers]]></category>
		<category><![CDATA[math]]></category>
		<category><![CDATA[mathemafia]]></category>
		<category><![CDATA[NCERT]]></category>
		<category><![CDATA[number system]]></category>
		<category><![CDATA[properties of numbers]]></category>
		<category><![CDATA[whole numbers]]></category>
		<guid isPermaLink="false">http://sh016.global.temp.domains/~mathemaf/?p=1368</guid>

					<description><![CDATA[<p>Concept: In this tutorial, you will learn about the closure property. It is discussed in detail for the following operations on Whole numbers and Integers. Addition Subtraction Multiplication Division Closure property &#8211; Natural numbers Closure property &#8211; Rational numbers</p>
<p>The post <a href="https://mathemafia.com/closure-property-whole-numbers-and-integers/">Closure property &#8211; Whole Numbers and Integers</a> appeared first on <a href="https://mathemafia.com">Mathemafia</a>.</p>
]]></description>
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									<p><b>Concept</b>: In this tutorial, you will learn about the closure property. It is discussed in detail for the following operations on Whole numbers and Integers.</p><ul><li>Addition</li><li>Subtraction</li><li>Multiplication</li><li>Division</li></ul><div class="iframe-container"><iframe src="https://www.youtube.com/embed/4L8Jc_g_SWs?rel=0" width="560" height="315" frameborder="0" allowfullscreen="allowfullscreen"></iframe></div>								</div>
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					<a class="elementor-button elementor-button-link elementor-size-sm" href="/closure-property-natural-numbers">
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									<span class="elementor-button-text"><span>Closure property - Natural numbers</span></span>
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					<a class="elementor-button elementor-button-link elementor-size-sm" href="/closure-property-rational-numbers">
						<span class="elementor-button-content-wrapper">
									<span class="elementor-button-text">Closure property - Rational numbers</span>
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					</div>
		</section>
				<section class="elementor-section elementor-top-section elementor-element elementor-element-87e16f2 elementor-section-boxed elementor-section-height-default elementor-section-height-default" data-id="87e16f2" data-element_type="section" data-e-type="section">
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						<section class="elementor-section elementor-top-section elementor-element elementor-element-78f40ce elementor-section-boxed elementor-section-height-default elementor-section-height-default" data-id="78f40ce" data-element_type="section" data-e-type="section">
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				<div class="elementor-widget-container">
					<h3 class="elementor-heading-title elementor-size-default">Number System<br></h3>				</div>
				</div>
					</div>
		</div>
					</div>
		</section>
				<section class="elementor-section elementor-top-section elementor-element elementor-element-a04c0dd elementor-section-boxed elementor-section-height-default elementor-section-height-default" data-id="a04c0dd" data-element_type="section" data-e-type="section">
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									<ul><li><a href="/number-system-best-explained-with-real-life-examples">Number System &#8211; Best explained with real life examples</a></li><li><a href="/distributive-property-of-multiplication-over-addition-and-subtraction">Distributive property of multiplication over addition and subtraction</a></li><li><a href="/associative-property-of-addition-and-multiplication">Associative property of addition and multiplication </a></li><li>Closure property<ul><li><a href="/closure-property-natural-numbers">Natural Numbers</a></li><li><a href="/closure-property-whole-numbers-and-integers">Whole Numbers &amp; Integers</a></li><li><a href="/closure-property-rational-numbers">Rational Numbers</a></li></ul></li><li><a href="/additive-identity-multiplicative-identity-additive-inverse-reciprocal">Additive Identity, Multiplicative identity, Additive inverse, Reciprocal</a></li><li><a style="background-color: #ffffff;" href="/commutative-law-explained-for-basic-arithmetic-operations">Commutative law explained for basic arithmetic operations</a></li><li>Rational Numbers<ul><li><a href="/find-a-rational-number-between-any-two-rational-numbers">Find a rational number between any two rational numbers</a></li><li><a style="background-color: #ffffff;" href="/rational-numbers-are-infinitely-many">Rational numbers are infinitely many</a></li><li><a href="/mean-method-infinitely-many-rational-numbers-between-any-two-rational-numbers">Mean method : Infinitely many rational numbers between any two rational numbers</a></li></ul></li><li>Integers<ul><li><a href="/proof-integers-are-infinitely-many">Integers are infinitely many</a></li></ul></li></ul>								</div>
				</div>
					</div>
		</div>
					</div>
		</section>
				<section class="elementor-section elementor-top-section elementor-element elementor-element-0dab545 elementor-section-boxed elementor-section-height-default elementor-section-height-default" data-id="0dab545" data-element_type="section" data-e-type="section">
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					<h3 class="elementor-heading-title elementor-size-default">Polynomials<br></h3>				</div>
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					</div>
		</section>
				<section class="elementor-section elementor-top-section elementor-element elementor-element-d43dfba elementor-section-boxed elementor-section-height-default elementor-section-height-default" data-id="d43dfba" data-element_type="section" data-e-type="section">
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									<ul><li><a href="/class-9-chapter-2-polynomials-basics-of-polynomials">Basics of polynomials</a></li><li><a href="/class-9-chapter-2-polynomials-remainder-theorem">Remainder theorem</a></li><li><a href="/class-9-chapter-2-polynomials-factor-theorem">Factor theorem</a></li><li><a href="/class-9-chapter-2-polynomials-factorisation-by-splitting-the-middle-term/">Factorise &#8211; Splitting the middle term</a></li><li><a href="/class-9-chapter-2-polynomials-algebraic-identities">Algebraic Identities</a></li><li><a href="/rational-root-theorem">Rational root theorem</a></li></ul>								</div>
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					</div>
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				<div class="elementor-widget-container">
					<h3 class="elementor-heading-title elementor-size-default">Important Concepts &#8211; Miscellaneous<br></h3>				</div>
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					</div>
		</div>
					</div>
		</section>
				<section class="elementor-section elementor-top-section elementor-element elementor-element-b41f83e elementor-section-boxed elementor-section-height-default elementor-section-height-default" data-id="b41f83e" data-element_type="section" data-e-type="section">
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									<ul><li><a href="/derivation-herons-formula">Derivation of Heron&#8217;s formula</a></li></ul>								</div>
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					</div>
		</section>
				<section class="elementor-section elementor-top-section elementor-element elementor-element-a849333 elementor-section-boxed elementor-section-height-default elementor-section-height-default" data-id="a849333" data-element_type="section" data-e-type="section">
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					<h3 class="elementor-heading-title elementor-size-default">Surface area and Volumes<br></h3>				</div>
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		</div>
					</div>
		</section>
				<section class="elementor-section elementor-top-section elementor-element elementor-element-1ba149d elementor-section-boxed elementor-section-height-default elementor-section-height-default" data-id="1ba149d" data-element_type="section" data-e-type="section">
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									<ul><li><a href="/area-surface-area-volume">Area / Surface area / Volume &#8211; Introduction</a></li><li><a href="/surface-area-of-cube-and-cuboid">Surface Area of Cube and Cuboid</a></li><li><a href="/volume-of-cuboid-and-cube">Volume Of Cuboid and Cube</a></li><li><a href="/surface-area-of-right-circular-cylinder">Surface Area of Right Circular Cylinder</a></li><li><a href="/volume-and-capacity-of-cylinder">Volume and capacity of Cylinder</a></li><li><a href="/right-circular-cone">Right circular Cone</a></li><li><a href="/surface-area-of-right-circular-cone">Surface Area of Right circular Cone</a></li><li><a href="/volume-of-cylinder-vs-cone">Volume of Cylinder vs Cone</a></li><li><a href="/litres-and-cubic-centimetre">Litres and Cubic centimetre (cm³)</a></li><li><a href="/cubic-meters-to-litres">Cubic meters to litres</a></li></ul>								</div>
				</div>
					</div>
		</div>
					</div>
		</section>
				</div>
		</div>								</div>
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					</div>
		</section>
				</div>
		<p>The post <a href="https://mathemafia.com/closure-property-whole-numbers-and-integers/">Closure property &#8211; Whole Numbers and Integers</a> appeared first on <a href="https://mathemafia.com">Mathemafia</a>.</p>
]]></content:encoded>
					
		
		
			</item>
		<item>
		<title>Closure property &#8211; Natural Numbers</title>
		<link>https://mathemafia.com/closure-property-natural-numbers/</link>
		
		<dc:creator><![CDATA[Sunil Syal]]></dc:creator>
		<pubDate>Sat, 15 Aug 2020 06:18:15 +0000</pubDate>
				<category><![CDATA[Number system]]></category>
		<category><![CDATA[Class 9 math tutorials]]></category>
		<category><![CDATA[closure property]]></category>
		<category><![CDATA[closures]]></category>
		<category><![CDATA[math]]></category>
		<category><![CDATA[mathemafia]]></category>
		<category><![CDATA[natural numbers]]></category>
		<category><![CDATA[NCERT]]></category>
		<category><![CDATA[number system]]></category>
		<category><![CDATA[properties of numbers]]></category>
		<guid isPermaLink="false">http://sh016.global.temp.domains/~mathemaf/?p=1361</guid>

					<description><![CDATA[<p>Concept: In this tutorial, you will learn about the closure property. It is discussed in detail for the following operations on natural numbers. Addition Subtraction Multiplication Division Associative property Closure property &#8211; Whole Numbers &#38; Integers</p>
<p>The post <a href="https://mathemafia.com/closure-property-natural-numbers/">Closure property &#8211; Natural Numbers</a> appeared first on <a href="https://mathemafia.com">Mathemafia</a>.</p>
]]></description>
										<content:encoded><![CDATA[		<div data-elementor-type="wp-post" data-elementor-id="1361" class="elementor elementor-1361">
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				<div class="elementor-widget-container">
									<p><b>Concept</b>: In this tutorial, you will learn about the closure property. It is discussed in detail for the following operations on natural numbers.</p><ul><li>Addition</li><li>Subtraction</li><li>Multiplication</li><li>Division</li></ul><div class="iframe-container"><iframe src="https://www.youtube.com/embed/nKuVzwDPxms?rel=0" width="560" height="315" frameborder="0" allowfullscreen="allowfullscreen"></iframe></div>								</div>
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		</section>
				<section class="elementor-section elementor-top-section elementor-element elementor-element-3197b0d post-nav-container elementor-section-boxed elementor-section-height-default elementor-section-height-default" data-id="3197b0d" data-element_type="section" data-e-type="section">
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					<a class="elementor-button elementor-button-link elementor-size-sm" href="/associative-property-of-addition-and-multiplication">
						<span class="elementor-button-content-wrapper">
									<span class="elementor-button-text">Associative property</span>
					</span>
					</a>
				</div>
								</div>
				</div>
					</div>
		</div>
				<div class="elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-8fffdd9" data-id="8fffdd9" data-element_type="column" data-e-type="column">
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					<a class="elementor-button elementor-button-link elementor-size-sm" href="/closure-property-whole-numbers-and-integers">
						<span class="elementor-button-content-wrapper">
									<span class="elementor-button-text">Closure property - Whole Numbers &amp; Integers</span>
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					</a>
				</div>
								</div>
				</div>
					</div>
		</div>
					</div>
		</section>
				<section class="elementor-section elementor-top-section elementor-element elementor-element-87e16f2 elementor-section-boxed elementor-section-height-default elementor-section-height-default" data-id="87e16f2" data-element_type="section" data-e-type="section">
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									<div data-post-id="1333" class="insert-page insert-page-1333 ">		<div data-elementor-type="wp-page" data-elementor-id="1333" class="elementor elementor-1333">
						<section class="elementor-section elementor-top-section elementor-element elementor-element-78f40ce elementor-section-boxed elementor-section-height-default elementor-section-height-default" data-id="78f40ce" data-element_type="section" data-e-type="section">
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					<div class="elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-8948fd3" data-id="8948fd3" data-element_type="column" data-e-type="column">
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				<div class="elementor-widget-container">
					<h3 class="elementor-heading-title elementor-size-default">Number System<br></h3>				</div>
				</div>
					</div>
		</div>
					</div>
		</section>
				<section class="elementor-section elementor-top-section elementor-element elementor-element-a04c0dd elementor-section-boxed elementor-section-height-default elementor-section-height-default" data-id="a04c0dd" data-element_type="section" data-e-type="section">
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				<div class="elementor-widget-container">
									<ul><li><a href="/number-system-best-explained-with-real-life-examples">Number System &#8211; Best explained with real life examples</a></li><li><a href="/distributive-property-of-multiplication-over-addition-and-subtraction">Distributive property of multiplication over addition and subtraction</a></li><li><a href="/associative-property-of-addition-and-multiplication">Associative property of addition and multiplication </a></li><li>Closure property<ul><li><a href="/closure-property-natural-numbers">Natural Numbers</a></li><li><a href="/closure-property-whole-numbers-and-integers">Whole Numbers &amp; Integers</a></li><li><a href="/closure-property-rational-numbers">Rational Numbers</a></li></ul></li><li><a href="/additive-identity-multiplicative-identity-additive-inverse-reciprocal">Additive Identity, Multiplicative identity, Additive inverse, Reciprocal</a></li><li><a style="background-color: #ffffff;" href="/commutative-law-explained-for-basic-arithmetic-operations">Commutative law explained for basic arithmetic operations</a></li><li>Rational Numbers<ul><li><a href="/find-a-rational-number-between-any-two-rational-numbers">Find a rational number between any two rational numbers</a></li><li><a style="background-color: #ffffff;" href="/rational-numbers-are-infinitely-many">Rational numbers are infinitely many</a></li><li><a href="/mean-method-infinitely-many-rational-numbers-between-any-two-rational-numbers">Mean method : Infinitely many rational numbers between any two rational numbers</a></li></ul></li><li>Integers<ul><li><a href="/proof-integers-are-infinitely-many">Integers are infinitely many</a></li></ul></li></ul>								</div>
				</div>
					</div>
		</div>
					</div>
		</section>
				<section class="elementor-section elementor-top-section elementor-element elementor-element-0dab545 elementor-section-boxed elementor-section-height-default elementor-section-height-default" data-id="0dab545" data-element_type="section" data-e-type="section">
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				<div class="elementor-widget-container">
					<h3 class="elementor-heading-title elementor-size-default">Polynomials<br></h3>				</div>
				</div>
					</div>
		</div>
					</div>
		</section>
				<section class="elementor-section elementor-top-section elementor-element elementor-element-d43dfba elementor-section-boxed elementor-section-height-default elementor-section-height-default" data-id="d43dfba" data-element_type="section" data-e-type="section">
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				<div class="elementor-widget-container">
									<ul><li><a href="/class-9-chapter-2-polynomials-basics-of-polynomials">Basics of polynomials</a></li><li><a href="/class-9-chapter-2-polynomials-remainder-theorem">Remainder theorem</a></li><li><a href="/class-9-chapter-2-polynomials-factor-theorem">Factor theorem</a></li><li><a href="/class-9-chapter-2-polynomials-factorisation-by-splitting-the-middle-term/">Factorise &#8211; Splitting the middle term</a></li><li><a href="/class-9-chapter-2-polynomials-algebraic-identities">Algebraic Identities</a></li><li><a href="/rational-root-theorem">Rational root theorem</a></li></ul>								</div>
				</div>
					</div>
		</div>
					</div>
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				<section class="elementor-section elementor-top-section elementor-element elementor-element-b41f83e elementor-section-boxed elementor-section-height-default elementor-section-height-default" data-id="b41f83e" data-element_type="section" data-e-type="section">
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		<p>The post <a href="https://mathemafia.com/closure-property-natural-numbers/">Closure property &#8211; Natural Numbers</a> appeared first on <a href="https://mathemafia.com">Mathemafia</a>.</p>
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