Distributive property over addition

rewrite the expression four times than in parentheses we have eight plus three using the distributive law of multiplication over addition then simplify the expression so let's just try to solve this or evaluate this expression and then we'll talk a little bit about the distributive law of multiplication over addition usually just called the distributive law so we have 4 times 8 4 times 8 plus 8 plus 3 8 plus 3 now there's two ways to do it normally when you have parentheses your inclination is well let me just evaluate what's in the parentheses first and then worry about what's outside of the parentheses and we can do that fairly easily here we can evaluate what 8 plus 3 is 8 plus 3 is 11 so if we do that let me do that in this direction so if we do that we get 4 times we get 4 times and in parentheses we have an 1183 is 11 and then this is going to be equal to well 4 times 11 is just 44 so you can evaluate it that way but they want us to use the distributive law of multiplication we did not use the distributive law just now we just evaluated the expression maybe use the parentheses first then multiplied by 4 and the distributive law we multiply by 4 first and it's called the distributive law because you distribute the 4 and we're going to think about what that means so in the distributive law what this will become it'll become 4 times 8 plus 4 times 3 and we're going to think about why that is in a second so this is going to be equal to 4 times 8 4 times 8 plus 4 times 4 times 3 4 times 3 a lot of people's first instinct is just to multiply the 4 times the 8 but know you have to distribute the 4 you have to multiply it times times the 8 and times the 3 this is right here this is the distributive property in action right here distributive property in action and then when you evaluate I'm going to show you in kind of a visual way why this word but then when you evaluate it four times eight this in a different color 4 times 8 is 32 and then so we have 32 plus 4 times 3 4 times 3 is 12 and 32 plus 12 is equal to 44 that is also equal to 44 so you can get it either way but when they want us to use the distributive law you would multiply it you distribute the 4 first now let's think about why that happens let's let's visualize just what 8 plus 3 is so let me draw 8 of something so 1 2 3 4 5 6 let me draw it this well 6 7 8 right 1 2 3 4 5 6 7 8 and then we're going to add to that we're going to add to that 3 of something of them maybe the same thing 1 2 3 so you could imagine this is what we have inside of the parentheses we have 8 circles plus 3 circles now when we're multiplying this whole thing this whole thing times 4 what does that mean well that means we're just going to add this to itself 4 times so let me do that with the copy and paste copy and paste let me copy and then let me paste there you go that's 2 that's 1 2 3 and then we have 4 and we're going to add them all together so this is literally what 4 times right we have it let me go back to the drawing tool we have it 1 2 3 4 times this expression which is 8 plus 3 now what is this thing over here what is this thing over here what is this thing over here if you were to count all of this stuff you would get 44 but what is this thing over here well that's 8 add it to itself 4 times you could imagine you're adding all of these so what's 8 add it to itself 4 times that is 4 times 8 so this is 4 times 8 and what is this over here in the orange we have 1 2 3 4 times well each time we have three so it's got four times this right here this right here is four times three so you see why the distributive property works if you do four times eight plus three you have to multiply what when you I guess you could imagine duplicate the thing four times both the eight and the three is getting duplicated four times or it's being added to itself four times and that's why we distribute the four