{"id":542,"date":"2022-01-13T10:16:19","date_gmt":"2022-01-13T10:16:19","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=542"},"modified":"2022-01-13T10:16:19","modified_gmt":"2022-01-13T10:16:19","slug":"multiplication","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/01\/13\/multiplication\/","title":{"rendered":"Multiplication"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">Multiplication :<\/h2>\n\n\n\n<p><\/p>\n\n\n\n<p><\/p>\n\n\n\n<p>In mathematics,&nbsp;<strong>multiplication<\/strong>&nbsp;is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life. The major application we can see in&nbsp;multiplication tables.<\/p>\n\n\n\n<p>In arithmetic, the multiplication of two numbers represents the&nbsp;repeated addition&nbsp;of one number with respect to another. These numbers can be whole numbers, natural numbers, integers, fractions, etc. If m is multiplied by n, then it means either m is added to itself \u2018n\u2019 number of times or vice versa.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p><\/p>\n\n\n\n<p>Multiplication&nbsp;(denoted by \u2018<strong>\u00d7<\/strong>\u2019) in Maths, is a mathematical operation, apart from addition, subtraction and division. Students learn the four basic&nbsp;arithmetic operations&nbsp;in their primary classes themselves. Here we will learn to solve multiplication problems in an easy and quick way.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">What is Multiplication?<\/h2>\n\n\n\n<p>Multiplication is the process of calculating the product of two or more numbers. The multiplication of numbers say, \u2018a\u2019 and \u2018b\u2019, is stated as \u2018a\u2019 multiplied by \u2018b\u2019.<\/p>\n\n\n\n<p>In Maths, the basic explanation of multiplication is adding a number, with respect to another number, repeatedly.<\/p>\n\n\n\n<p>For example, if we are multiplying 2 by 3, that means 3 is added to itself two times, i.e. 3 + 3 = 6. This is a simple technique for kids to multiply numbers.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"750\" height=\"252\" src=\"https:\/\/mdr.foobrdigital.com\/wp-content\/uploads\/2022\/01\/Addition-1-7.png\" alt=\"\" class=\"wp-image-543\" srcset=\"https:\/\/mudassirbackup.infinitycodestudio.com\/wp-content\/uploads\/2022\/01\/Addition-1-7.png 750w, https:\/\/mudassirbackup.infinitycodestudio.com\/wp-content\/uploads\/2022\/01\/Addition-1-7-300x101.png 300w\" sizes=\"(max-width: 750px) 100vw, 750px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Multiplication Examples<\/h3>\n\n\n\n<p>See few more examples of multiplication here:<\/p>\n\n\n\n<ul><li>Multiplication of 3 and 3 = 3 x 3 = 9<\/li><li>Multiplication of 4 by 4 = 4 + 4 + 4 + 4= 16<\/li><li>Multiplication of 5 by 5 = 5 + 5 + 5 + 5 + 5 = 25<\/li><li>Multiplication of 10 x 10 = 100<\/li><li>Multiplication of 8 by 9 = 8 x 9 = 72<\/li><\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Multiplication Symbol<\/h2>\n\n\n\n<p>The symbol of multiplication is denoted by a cross sign (\u00d7) and also sometimes by a dot (.).<\/p>\n\n\n\n<p>Examples:<\/p>\n\n\n\n<ul><li>3 \u00d7 11 = 33<\/li><li>5 \u00d7 9 = 45<\/li><li>8 \u00d7 2 \u00d7 10 = 160<\/li><li>(9).(10) = 90<\/li><li>(7).(8) = 56<\/li><\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Multiplication Formula<\/h2>\n\n\n\n<p>The multiplication formula is given by:<\/p>\n\n\n\n<p><strong>Multiplier \u00d7 Multiplicand = Product<\/strong><\/p>\n\n\n\n<ul><li>Multiplicand is the total number of objects in each group<\/li><li>Multiplier is the number of equal groups<\/li><li>Product is the result of multiplication of multiplier and multiplicand<\/li><\/ul>\n\n\n\n<p>Example: If Multiplier = 5 and Multiplicand = 8, then the product is:<\/p>\n\n\n\n<p>Product = 5 x 8 = 40<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Properties of Multiplication<\/h2>\n\n\n\n<p>The properties of multiplication are:<\/p>\n\n\n\n<ul><li>Closure Property<\/li><li>Commutative property<\/li><li>Associative property<\/li><li>Distributive property<\/li><li>Identity property<\/li><li>Zero property<\/li><\/ul>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Closure Property of Multiplication  :<\/h3>\n\n\n\n<p>According to closure property of multiplication,<\/p>\n\n\n\n<ul><li>Product of two integers is an integer (-4 x 3 = -12)<\/li><li>Product of two fractions is either a fraction or a whole number (1\/2 x 2 = 1)<\/li><\/ul>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Commutative Property of Multiplication<\/h3>\n\n\n\n<p>The commutative property of multiplication states, if A and B are any two integers, then:<\/p>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\"><table><tbody><tr><td><strong>A \u00d7 B = B \u00d7 A<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>For example: 2 \u00d7 3 = 3 \u00d7 2 = 6<br><a><\/a><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Associative Property of Multiplication<\/h3>\n\n\n\n<p>As per the associative property of multiplication, if A, B and C are any three integers, then:<\/p>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\"><table><tbody><tr><td><strong>A \u00d7 (B \u00d7 C) = (A \u00d7 B) \u00d7 C<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>For example: 2 \u00d7 (3 \u00d7 4) = (2 \u00d7 3) \u00d7 4 = 24<br><a><\/a><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Distributive Property of Multiplication<\/h3>\n\n\n\n<p>According to distributive property of multiplication, if A, B and C are any three integers, then:<\/p>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\"><table><tbody><tr><td><strong>A \u00d7 (B + C) = (A \u00d7 B) + (A \u00d7 C)<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>For example: 4 \u00d7 (2 + 3) = 4 \u00d7 2 + 4 \u00d7 3 \u2192 20<br><a><\/a><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Identity Property of Multiplication<\/h3>\n\n\n\n<p>As per the identity property of multiplication, if we multiply any value by 1, then its value remains unchanged, such that;<\/p>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\"><table><tbody><tr><td><strong>A \u00d7 1 = A<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>For example:<\/p>\n\n\n\n<ul><li>12 \u00d7 1 = 12<\/li><li>-3 \u00d7 1 = -3<\/li><\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Zero Property of Multiplication<\/h3>\n\n\n\n<p>Zero property of multiplication states that any number multiplied by 0 is equal to zero only.<\/p>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\"><table><tbody><tr><td><strong>A \u00d7 0 = 0<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>where A is any integer.<\/p>\n\n\n\n<p>For example: 9 \u00d7 0 = 0<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Rules of Multiplication (How to Multiply)<\/h2>\n\n\n\n<p>There are various rules to multiply numbers. They are:<\/p>\n\n\n\n<ul><li>Multiplication of two integers is an integer<\/li><li>Any number multiplied by 0 is 0<\/li><li>Any number multiplied by 1 is equal to the original number<\/li><li>If an integer is multiplied by multiples of 10, then the same number of 0s are added at the end of the original number. Example: 4 \u00d7 1000 = 4000<\/li><li>The order of the numbers, does not matter, when multiplied together. Example: 2 \u00d7 3 \u00d7 4 \u00d7 5 = 5 \u00d7 4 \u00d7 3 \u00d7 2 = 3 \u00d7 2 \u00d7 4 \u00d7 5 = 120<\/li><\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Multiplication Signs<\/h2>\n\n\n\n<p>When two or more numbers are multiplied with different sign (+ and -), then the output result varies, as per the sign rules given below:<\/p>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\"><table><tbody><tr><td><strong>S.No.<\/strong><\/td><td><strong>Operation<\/strong><\/td><td><strong>Result<\/strong><\/td><\/tr><tr><td>1.<\/td><td>(+ve) \u00d7 (+ve)<\/td><td>+ve<\/td><\/tr><tr><td>2.<\/td><td>(+ve) \u00d7 (-ve)<\/td><td>-ve<\/td><\/tr><tr><td>3.<\/td><td>(-ve) \u00d7 (+ve)<\/td><td>-ve<\/td><\/tr><tr><td>4.<\/td><td>(-ve) \u00d7 (-ve)<\/td><td>+ve<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Description:<\/strong><\/p>\n\n\n\n<ul><li>When two positive integers are multiplied, then the result is positive<\/li><li>When one positive integer and one negative integer is multiplied or vice versa, then the result is negative<\/li><li>When two negative integers are multiplied, then the result is a positive integer<\/li><\/ul>\n\n\n\n<p><strong>Facts:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\"><table><tbody><tr><td>Multiplication of even numbers of negative integers is always positive.(-) \u00d7 (-) \u00d7 (-) \u00d7 (-) = (+)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Multiplication Table<\/h2>\n\n\n\n<p>The table of multiplication for numbers 1 to 10, row-wise and column-wise is given below. With the help of these tables, we can easily find the product of two numbers from 1 to 10 in a quick manner.<\/p>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\"><table><tbody><tr><td><strong>\u00d7<\/strong><\/td><td><strong>1<\/strong><\/td><td><strong>2<\/strong><\/td><td><strong>3<\/strong><\/td><td><strong>4<\/strong><\/td><td><strong>5<\/strong><\/td><td><strong>6<\/strong><\/td><td><strong>7<\/strong><\/td><td><strong>8<\/strong><\/td><td><strong>9<\/strong><\/td><td><strong>10<\/strong><\/td><\/tr><tr><td><strong>1<\/strong><\/td><td>1<\/td><td>2<\/td><td>3<\/td><td>4<\/td><td>5<\/td><td>6<\/td><td>7<\/td><td>8<\/td><td>9<\/td><td>10<\/td><\/tr><tr><td><strong>2<\/strong><\/td><td>2<\/td><td>4<\/td><td>6<\/td><td>8<\/td><td>10<\/td><td>12<\/td><td>14<\/td><td>16<\/td><td>18<\/td><td>20<\/td><\/tr><tr><td><strong>3<\/strong><\/td><td>3<\/td><td>6<\/td><td>9<\/td><td>12<\/td><td>15<\/td><td>18<\/td><td>21<\/td><td>24<\/td><td>27<\/td><td>30<\/td><\/tr><tr><td><strong>4<\/strong><\/td><td>4<\/td><td>8<\/td><td>12<\/td><td>16<\/td><td>20<\/td><td>24<\/td><td>28<\/td><td>32<\/td><td>36<\/td><td>40<\/td><\/tr><tr><td><strong>5<\/strong><\/td><td>5<\/td><td>10<\/td><td>15<\/td><td>20<\/td><td>25<\/td><td>30<\/td><td>35<\/td><td>40<\/td><td>45<\/td><td>50<\/td><\/tr><tr><td><strong>6<\/strong><\/td><td>6<\/td><td>12<\/td><td>18<\/td><td>24<\/td><td>30<\/td><td>36<\/td><td>42<\/td><td>48<\/td><td>54<\/td><td>60<\/td><\/tr><tr><td><strong>7<\/strong><\/td><td>7<\/td><td>14<\/td><td>21<\/td><td>28<\/td><td>35<\/td><td>42<\/td><td>49<\/td><td>56<\/td><td>63<\/td><td>70<\/td><\/tr><tr><td><strong>8<\/strong><\/td><td>8<\/td><td>16<\/td><td>24<\/td><td>32<\/td><td>40<\/td><td>48<\/td><td>56<\/td><td>64<\/td><td>72<\/td><td>80<\/td><\/tr><tr><td><strong>9<\/strong><\/td><td>9<\/td><td>18<\/td><td>27<\/td><td>36<\/td><td>45<\/td><td>54<\/td><td>63<\/td><td>72<\/td><td>81<\/td><td>90<\/td><\/tr><tr><td><strong>10<\/strong><\/td><td>10<\/td><td>20<\/td><td>30<\/td><td>40<\/td><td>50<\/td><td>60<\/td><td>70<\/td><td>80<\/td><td>90<\/td><td>100<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Multiplication of Fractions<\/h2>\n\n\n\n<p>When two or more fractions are multiplied then the numerators and denominators are multiplied together, such that:<\/p>\n\n\n\n<p>(a\/b) \u00d7 (c\/d) = (a\u00d7c)\/(b\u00d7d)<\/p>\n\n\n\n<ul><li>Example 1: Multiply \u00be and 5\/2.<\/li><\/ul>\n\n\n\n<p>(\u00be) \u00d7 (5\/2)<\/p>\n\n\n\n<p>= (3\u00d75)\/(4\u00d72)<\/p>\n\n\n\n<p>= 15\/8<\/p>\n\n\n\n<ul><li>Example 2: Multiply 4\/7 and 21\/2<\/li><\/ul>\n\n\n\n<p>(4\/7) \u00d7 (21\/2)<\/p>\n\n\n\n<p>= 2 \u00d7 3<\/p>\n\n\n\n<p>= 6<br><a><\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Multiplication of Decimals<\/h2>\n\n\n\n<p>The method of finding the product of decimals is the same as multiplying the integers. We need to take care here of the position of decimal (.), after multiplication. Let us understand by example.<\/p>\n\n\n\n<ul><li>Example 1: Find the product of 1.2 and 3.<\/li><\/ul>\n\n\n\n<p>Sol: 1.2 \u00d7 3 = 3.6<\/p>\n\n\n\n<ul><li>Example 2: Multiply 4.2 and 1.5<\/li><\/ul>\n\n\n\n<p>Sol: Let us multiply 4.2 and 1.5 by removing the decimals here and considering them as whole numbers. Hence,<\/p>\n\n\n\n<p>42 \u00d7 15<\/p>\n\n\n\n<p>= 630<\/p>\n\n\n\n<p>Now, if we put the decimal back, then the product of the two decimal numbers will have decimal up to two positions from right to left, such that;<\/p>\n\n\n\n<p>4.2 \u00d7 1.5 = 6.30<br><a><\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Multiplication Tricks<\/h2>\n\n\n\n<p>Multiplication of single-digit numbers is an easy task. But multiplying two or more digit numbers can be a difficult and time-consuming task. Here are few multiplication tricks that students can remember while finding the product.<\/p>\n\n\n\n<ul><li>Multiplication of numbers can be done in any order. (3 x 4 = 4 x 3)<\/li><li>While multiplying a number by multiples of 10, just put the number of zeros equal to multiples of 10, next to the multiplier (Eg. 6 x 100 = 600)<\/li><li>If there are three numbers to be multiplied, multiply the small numbers first for quick calculation and then multiply to the third number<\/li><li>If the multiplication includes two-digits or three-digit numbers, then write such numbers in expanded form and then multiply. (Eg: 45 x 9 = (40 + 5) x 9 = 40 x 9 + 5 x 9 = 360 + 45 = 405)<\/li><li>Follow the sign rule given in the above section<\/li><\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Word Problems on Multiplication<\/h2>\n\n\n\n<p>Q. 1: If Sita has 10 baskets and each basket has 5 apples. Then find the total number of apples Sita has.<\/p>\n\n\n\n<p>Sol: Number of baskets Sita has = 10<\/p>\n\n\n\n<p>Number of apples each basket has = 5<\/p>\n\n\n\n<p>Total number of apples = (Number of baskets) \u00d7 (Number of apples in each basket)<\/p>\n\n\n\n<p>= 10 \u00d7 5 = 50<\/p>\n\n\n\n<p>Therefore, Sita has 50 apples.<\/p>\n\n\n\n<p>Q.2: Sam brings 3 boxes of chocolates from the market. If each box contains 50 chocolates, then how many total chocolates did he has?<\/p>\n\n\n\n<p>Solution: Number of boxes = 3<\/p>\n\n\n\n<p>Number of chocolates in each box = 50<\/p>\n\n\n\n<p>Total number of chocolates = 3 x 50 = 150<\/p>\n\n\n\n<p>Hence, Sam has 150 chocolates.<\/p>\n\n\n\n<p>Q.3: Find the product of 13.99 \u00d7 10000.<\/p>\n\n\n\n<p>Sol: 13.99 \u00d7 10000<\/p>\n\n\n\n<p>= 139900.00<\/p>\n\n\n\n<p>= 139900<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Practice Questions on Multiplication<\/h2>\n\n\n\n<p>Students can practice these multiplication sums here:<\/p>\n\n\n\n<ol><li>Find: 45 \u00d7 10<\/li><li>Multiply 1.2 \u00d7 90<\/li><li>Find 8 \u00d7 11<\/li><li>Find the product of 10 and 78<\/li><li>Find the product of 900 and 70<\/li><li>Find 0.5 \u00d7 100<\/li><\/ol>\n\n\n\n<h2 class=\"wp-block-heading\">Frequently Asked Questions on Multiplication<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">What is multiplication in Maths?<\/h3>\n\n\n\n<p>Multiplication is an arithmetic operation, where we find the product of two or more numbers. A times B means, B is repeatedly added A number of times. For example, 5 times of 4 = 4 + 4 + 4 + 4 + 4 = 20<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">What is the symbol for multiplication?<\/h3>\n\n\n\n<p>The symbol used to represent multiplication is a cross sign (\u00d7). Also, sometimes we use a dot (.) to represent a product of numbers.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">What is basic multiplication?<\/h3>\n\n\n\n<p>Basic multiplication is simply explained for kids, where we find the product of two or more whole numbers by repeated addition.<\/p>\n\n\n\n<p>2 \u00d7 3 = 3 + 3 + 3= 6<\/p>\n\n\n\n<p>8 \u00d7 4 = 8 + 8 + 8 + 8 = 32<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">What are the rules of multiplication?<\/h3>\n\n\n\n<p>The major rules for multiplication are:<\/p>\n\n\n\n<p>Two integers when multiplied by each other results in an integer value<\/p>\n\n\n\n<p>When a value is multiplied by 0, then result is zero<\/p>\n\n\n\n<p>When a value is multiplied by 1, then the result is the same<\/p>\n\n\n\n<p>Order of multiplication of two or more numbers does not matter<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">What are the properties of multiplication?<\/h3>\n\n\n\n<p>The properties of multiplication are closure property, commutative property, associative property, distributive property, identity property.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Multiplication : In mathematics,&nbsp;multiplication&nbsp;is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life. The major application we can see in&nbsp;multiplication tables. In arithmetic, the multiplication of two numbers represents the&nbsp;repeated addition&nbsp;of one number with respect to another. These numbers [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[870],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/542"}],"collection":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/comments?post=542"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/542\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=542"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=542"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=542"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}