The Distributive Property Associative Property and Commutative Property Explained Clearly

foreign property let's first read kind of definition and then think once you see the examples this will make sense it says multiplying the sum of two or more add-ins by number produces the same result as when each add-in is Multiplied individually by the number and the products are added what it does it does allow you to break number apart and then distribute let's first look at what it means okay basically it's saying this you can either add these two numbers together if they're like terms and then multiply it by the three and that's 24 8 16 24 and that's going to be the same as if you distribute the three three times two is six three times six is eighteen eighteen plus six is 24. so basically it's saying these two are equal this does allow you to break number apart let me show you what mean okay we have 45 times 2 45 times 2 is 90. but the distributive property says you can break this 45 apart let's call it plus 5 to put parentheses around it times 2 and then we can distribute the two 2 times 40 is 80. plus 2 times 5 is 10 and that equals tiny so that allows you to break number apart and distribute now let's look at an algebra example okay in algebra it's going to be the same but remember you cannot combine these together because they're unlike terms so we can distribute 5 times 3 is 15 plus 5 times 6 is 30. in this video let's talk about the associative property of addition and subtraction call it the parentheses property because it's associated with parentheses couple ways you can look at it one rearranging the parentheses in an additional multiplication problem will not change the result also think of the name associative who the numbers are associated with will not change the results just to help me remember it because Lots there's lots of other rules is think the two s's as parentheses in the name and it does not work for subtraction and division let's look at couple examples okay the first example obviously is addition notice here the 4 is associated with the three on this side the four is associated with the six but they're equal four times three is excuse me not 12. it's addition four plus three is seven Plus six is thirteen okay on this side four plus six remember your order up operations always parentheses first is ten plus 3 is 13. notice that they are equal now let's look at multiplication okay same thing this side the four is associated with the five this side it's associated with the two but it's not going to impact it because we have all multiplication five times four it's not addition this time so I'll try not to make that mistake four times five is twenty times two is forty but it's going to equal the same as this side four times two is eight eight times five is 40. they are equal now let me show you something that it does not work for in this example the 6 is associated with the four on this side the six is associated with three but you have addition you have addition but they are not equal let me show you what six times four is twenty four six twelve eighteen twenty four plus three equals twenty six twenty seven but now if you multiply on this side six times three is eighteen and eighteen plus four is twenty two so they are not equal interesting if this was multiplication they would be equal six times four is twenty four twenty four times three is seventy two okay six times three is eighteen eighteen times four is also seventy two thanks in this video let's take look at the commutative property think commuting remember when you commute you change your location the community property states that changing the order of the operands does not change the result the commutative property for addition is plus equals plus and for multiplication it's times equals times please note it does not work for subtraction and Division let's look at couple examples okay let's take this addition we have five plus six but now the six is commuted to the front now but five plus six is eleven and six plus five easy is also eleven let's look at multiplication let's move this up we have five times six the six has commuted to the front the five is moved to the back five times six is thirty six times five is 30. it also works for more than one number let's take look at this two plus three is five five plus four is nine now we have three plus two is five five plus four is nine and now let's look at division excuse me not division of multiplication problems remember it doesn't work for subtraction or division okay let's go two times three is six six times four is six twelve eighteen twenty four now we've changed the order the 4 is at the front now four times two is eight eight times three is twenty four so there's the commutative property remember changing the order of the operands does not change the results think foreign