{"id":5437,"date":"2021-12-08T13:35:35","date_gmt":"2021-12-08T13:35:35","guid":{"rendered":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/?page_id=5437"},"modified":"2022-01-03T07:41:26","modified_gmt":"2022-01-03T07:41:26","slug":"properties-of-whole-numbers-with-faqs","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/properties-of-whole-numbers-with-faqs\/","title":{"rendered":"Properties of Whole Numbers with FAQs"},"content":{"rendered":"

[et_pb_section fb_built=”1″ admin_label=”Section” module_class=”mainsec” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#e0f2fd” z_index=”1″ custom_padding=”5px||5px||true|false” locked=”off” collapsed=”off” global_colors_info=”{}”][et_pb_row column_structure=”3_5,2_5″ custom_padding_last_edited=”on|phone” _builder_version=”4.10.8″ _module_preset=”default” background_color=”#FFFFFF” width=”100%” max_width=”1310px” custom_padding=”|51px|40px|51px|false|true” custom_padding_tablet=”” custom_padding_phone=”|40px|30px|40px|false|true” border_radii=”on|10px|10px|10px|10px” global_colors_info=”{}”][et_pb_column type=”3_5″ admin_label=”Column L” _builder_version=”4.9.10″ _module_preset=”default” global_colors_info=”{}”][et_pb_text admin_label=”Acute Angles
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Properties of Whole Numbers with FAQs<\/h1>\n

[\/et_pb_text][et_pb_text admin_label=”Text” _builder_version=”4.13.1″ _module_preset=”default” text_font_size=”16px” header_2_font=”|600|||||||” header_2_text_color=”#a01414″ header_3_font=”|600|||||||” custom_padding=”15px|15px|54px|4px|false|false” global_colors_info=”{}”]<\/p>\n

Properties of Whole Numbers<\/b><\/h2>\n

Whole numbers include the set of natural numbers along with the number 0, i.e., the set of whole numbers is 0, 1, 2, 3, 4, 5,6, 7,\u00a0 \u2026 till infinity. The properties of whole numbers are described below with examples:<\/span><\/p>\n

<\/span><\/p>\n

1. Closure Property of Whole Numbers<\/b><\/h2>\n

<\/b><\/p>\n

This property states that when mathematical operations like addition and multiplication are applied on any two whole numbers then the result is also a whole number.<\/span><\/p>\n

For two Whole Numbers 4 and 7:<\/p>\n

Closure under Addition<\/strong>
4 + 7 = 11, 11 is a whole number.<\/p>\n

Hence, we say that whole numbers are closed under addition.<\/p>\n

Therefore, if a and b are whole numbers \\Rightarrow (a+b)<\/span> is also a whole number.<\/strong><\/p>\n

Closure under Multiplication<\/strong><\/p>\n

4 \\times 7=28<\/span>, 28 is a whole number.<\/p>\n

Hence, we say that whole numbers are closed under multiplication.<\/p>\n

Therefore, if a and b are whole numbers \\Rightarrow(\\mathbf{a} \\times \\mathbf{b})<\/span> is a whole number.<\/span><\/p>\n

Note:<\/strong><\/p>\n

Do you know why Subtraction and Division are not under Closure property?<\/strong><\/p>\n

Subtraction is not under closure property because for some numbers the subtraction result is not a whole number, for example, for two whole numbers 10 and 25:<\/span><\/p>\n

10 – 25 = -15,\u00a0 and ‘-15’ is not a whole number.<\/span><\/p>\n

The division is not under closure property because division by zero is not defined and for some numbers division result is not a whole number, for example, for two whole numbers 2 and 6,<\/span><\/p>\n

2 \u00f7 6 = 0.333,<\/span> which is not a whole number.\u00a0<\/span><\/p>\n

<\/span><\/p>\n

2. Commutative Property\u00a0<\/b><\/h2>\n

<\/b><\/p>\n

This property states that when two whole numbers are added or multiplied in any order the outcome of the operation is equal.<\/span><\/p>\n

For two whole numbers 11 and 17:<\/p>\n

Commutative under Addition<\/strong><\/p>\n

11 + 17 = 28<\/p>\n

17 + 11 = 28<\/p>\n

Hence we say that whole numbers are commutative under addition.<\/p>\n

Therefore, if a and b are whole numbers \\Rightarrow(a+b)=(b+a)<\/span>.\u00a0<\/p>\n

Commutative under Multiplication<\/strong><\/p>\n

11 \\times 17=187 <\/span>
17 \\times 11=187<\/span><\/p>\n

Hence we say that whole numbers are commutative under multiplication.<\/p>\n

Therefore, if a and b are whole numbers \\Rightarrow(a \\times b)=(b \\times a)<\/span>.<\/p>\n

 <\/p>\n

3. Associative Property<\/b><\/h2>\n

<\/b><\/p>\n

This property states that when any three whole numbers are added or multiplied by grouping in any manner the outcome is equal.<\/span><\/p>\n

For three whole numbers 6, 10 and 15:<\/p>\n

Associative under Addition<\/strong><\/p>\n

(6 + 10) + 15 = 16 + 15 = 31<\/p>\n

6 + (10 + 15) = 6 + 25 = 31<\/p>\n

Hence we say that whole numbers are associative under addition.<\/p>\n

Therefore, if a, b and c are whole numbers \\Rightarrow(\\mathbf{a}+\\mathbf{b})+\\mathbf{c}=\\mathbf{a}+(\\mathbf{b}+\\mathbf{c})<\/span>.\u00a0<\/p>\n

Associative under Multiplication<\/strong><\/p>\n

(6 \\times 10) \\times 15=60 \\times 15=900 <\/span>
6 \\times(10 \\times 15)=6 \\times 150=900<\/span><\/p>\n

Hence we say that whole numbers are associative under multiplication.<\/p>\n

Therefore if a, b and c are whole numbers \\Rightarrow(a \\times b) \\times c=a \\times(b \\times c)<\/span>.<\/p>\n

 <\/p>\n

4. Distributive Property<\/b><\/h2>\n

<\/b><\/p>\n

This property states that i<\/span>f a, b and c are whole numbers then:<\/p>\n

Distributive Property of Multiplication under Addition<\/strong><\/p>\na \\times(b+c)=(a \\times b)+(a \\times c)<\/span>\n

Distributive Property of Multiplication under Subtraction<\/strong><\/p>\na \\times(b-c)=(a \\times b)-(a \\times c)<\/span>\n

Note:<\/strong> Distributive property of multiplication under subtraction holds true only if b \\geq c<\/span>.<\/p>\n

 <\/p>\n

For three whole numbers 3, 6 and 8:<\/p>\n

3 \\times(6+8)=3 \\times 14=42 <\/span>
(3 \\times 6)+(3 \\times 8)=18+24=42 <\/span>
\\therefore 3 \\times(6+8)=(3 \\times 6)+(3 \\times 8)<\/span><\/p>\n

Hence the distributive property of multiplication under addition holds true.<\/p>\n

Similarly for three whole numbers 4, 11 and 5:<\/p>\n

4 \\times(11-5)=4 \\times 6=24 <\/span>
(4 \\times 11)-(4 \\times 5)=44-20=24 <\/span>
\\therefore 4 \\times(11-5)=(4 \\times 11)-(4 \\times 5)<\/span><\/p>\n

Hence the distributive property of multiplication under subtraction holds true.<\/p>\n

 <\/p>\n

5. Identity Property<\/b><\/h2>\n

<\/b><\/p>\n

For any whole number that exists the additive identity is 0 and the multiplicative identity is 1. When 0 is added to a whole number the result is the number itself and when 1 is multiplied to a whole number again the result is the number itself.\u00a0<\/span><\/p>\n

For the whole number <\/span>11<\/span>,<\/span><\/p>\n

\u00a0\u00a0\u00a0<\/span>11 + 0 = 11<\/span>\u00a0<\/span><\/p>\n

\u21d2<\/span> \u20180\u2019 is the additive identity.<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>11 \u00d7 1 = 11<\/span>\u00a0<\/span><\/p>\n

\u21d2<\/span> \u20181\u2019 is the multiplicative identity.<\/span><\/p>\n

[\/et_pb_text][\/et_pb_column][et_pb_column type=”2_5″ module_id=”stickysideR” admin_label=”Column R” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#fdefe0″ custom_padding=”25px|25px|25px|25px|true|true” sticky_position=”top” sticky_offset_top=”-280px” sticky_limit_top=”row” sticky_limit_bottom=”row” sticky_position_tablet=”none” sticky_position_phone=”none” sticky_position_last_edited=”on|desktop” sticky_limit_bottom_tablet=”” sticky_limit_bottom_phone=”” sticky_limit_bottom_last_edited=”on|phone” border_radii=”on|15px|15px|15px|15px” box_shadow_style=”preset3″ global_colors_info=”{}”][et_pb_image src=”https:\/\/eistudymaterial.s3.amazonaws.com\/1080×1080.png” alt=”Free Trial banner” title_text=”Mindspark Free Trial Banner” url=”https:\/\/mindspark.in\/free-trial” align=”center” module_class=”adsimg” _builder_version=”4.11.1″ _module_preset=”default” custom_padding=”||||false|false” border_radii=”on|10px|10px|10px|10px” global_colors_info=”{}” transform_styles__hover_enabled=”on|hover” transform_scale__hover_enabled=”on|hover” transform_translate__hover_enabled=”on|desktop” transform_rotate__hover_enabled=”on|desktop” transform_skew__hover_enabled=”on|desktop” transform_origin__hover_enabled=”on|desktop” transform_scale__hover=”102%|102%”][\/et_pb_image][et_pb_text admin_label=”Explore Other Topics
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Explore Other Topics<\/h1>\n

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\n
Geometry<\/a><\/div>\n
Trigonometry<\/a><\/div>\n
Operations<\/a><\/div>\n
Numbers<\/a><\/div>\n<\/div>\n

[\/et_pb_text][et_pb_text admin_label=”Related Concepts
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Related Concepts<\/h1>\n

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\n
Types of Numbers<\/a><\/div>\n
Properties of Rational numbers<\/a><\/div>\n
Difference between Rational and Irrational numbers<\/a><\/a><\/div>\n<\/div>\n

[\/et_pb_text][\/et_pb_column][\/et_pb_row][et_pb_row admin_label=”Row for space” _builder_version=”4.10.6″ _module_preset=”default” locked=”off” global_colors_info=”{}”][et_pb_column type=”4_4″ _builder_version=”4.9.11″ _module_preset=”default” global_colors_info=”{}”][et_pb_divider show_divider=”off” _builder_version=”4.10.4″ _module_preset=”default” global_colors_info=”{}”][\/et_pb_divider][\/et_pb_column][\/et_pb_row][\/et_pb_section][et_pb_section fb_built=”1″ admin_label=”banner and faq Section” module_class=”mainsec2″ _builder_version=”4.10.4″ _module_preset=”default” custom_padding=”40px||0px||false|false” global_colors_info=”{}”][et_pb_row use_custom_gutter=”on” gutter_width=”1″ make_equal=”on” disabled_on=”on|on|off” admin_label=”banner Row” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#fff7d6″ width=”100%” max_width=”1310px” height=”134px” custom_margin=”||50px||false|false” custom_padding=”12px||12px||true|false” border_radii=”on|11px|11px|11px|11px” locked=”off” collapsed=”off” global_colors_info=”{}”][et_pb_column type=”4_4″ _builder_version=”4.9.10″ _module_preset=”default” global_colors_info=”{}”][et_pb_image src=”https:\/\/stgwebsite.mindspark.in\/wordpress\/wp-content\/uploads\/2021\/08\/calloutImage.png” title_text=”calloutImage” show_bottom_space=”off” admin_label=”Image” module_class=”img1″ _builder_version=”4.10.8″ _module_preset=”default” width=”25px” height=”60px” custom_padding=”2px||2px||true|false” global_colors_info=”{}”][\/et_pb_image][et_pb_text module_class=”ftstyle” _builder_version=”4.9.10″ _module_preset=”default” text_orientation=”center” global_colors_info=”{}”]<\/p>\n

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Frequently Asked Questions\u00a0<\/span><\/span><\/h1>\n
    <\/ol>\n

    Q1: What are the Properties of Whole Numbers?
    <\/strong><\/h3>\n

    Ans: <\/strong>The major properties of rational numbers are:
    (1) Closure Property, (2) Commutative Property, (3) Associative Property, (4) Distributive Property and (5) Identity Property.
    <\/strong><\/span><\/span><\/p>\n

    Q2. Show how whole numbers are closed under addition?
    <\/strong><\/h3>\n

    Ans: <\/strong>By closure property of addition when two whole numbers are added the result is also a whole number.
    For example, 21 + 32 = 53, 53 is a whole number.
    Note:<\/strong><\/em> When 0 is added to a whole number the result is the number itself, hence following the additive identity property of whole numbers.

    <\/strong><\/p>\n

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