You could imagine you'reĪdding all of these. Thing over here? If you were to count all of this Times this expression, which is 8 plus 3. So this is literally what? Four times, right? Let me go back to theĭrawing tool. We have four, and we're going to add themĪll together. Whole thing, this whole thing times 4, whatĭoes that mean? Well, that means we're just That three of something, of maybe the same thing. Let's visualize justįour, five, six, seven, eight, right? And then we're going to add to The distributive law, you'd distribute the 4 first. 4 times 3 is 12 and 32 plusġ2 is equal to 44. But then when you evaluate it,Ĥ times 8- I'll do this in a different color- 4 times 8 isģ2, and then so we have 32 plus 4 times 3. And then when you evaluate it-Īnd I'm going to show you in kind of a visual way Is just to multiply the 4 times the 8, but no! You have to distribute the 4. So this is going to be equal toĤ times 8 plus 4 times 3. This will become, it'll become 4 times 8 plus 4 timesģ, and we're going to think about why that is in a second. And it's called the distributive lawīecause you distribute the 4, and we're going to thinkĪbout what that means. But they want us to use theĭistributive law of multiplication. Is going to be equal to- well, 4 times 11 is justĤ4, so you can evaluate it that way. What's outside of the parentheses, and we can do What's in the parentheses first and then worry about Parentheses, your inclination is, well, let me just evaluate Multiplication over addition, usually just called theĨ plus 8 plus 3. This or evaluate this expression, then we'll talkĪ little bit about the distributive law of Even if we do not really know the values of the variables, the notion is that c is being added by d, but you "add c b times more than before", and "add d b times more than before".Įxperiment with different values (but make sure whatever are marked as a same variable are equal values).Īnd then in parentheses we have 8 plus 3, using theĭistributive law of multiplication over addition. However, the distributive property lets us change b*(c+d) into bc+bd. c and d are not equal so we cannot combine them (in ways of adding like-variables and placing a coefficient to represent "how many times the variable was added". With variables, the distributive property provides an extra method in rewriting some annoying expressions, especially when more than 1 variable may be involved.įor example, if we have b*(c+d). Having 7(2+4) is just a different way to express it: we are adding 7 six times, except we first add the 7 two times, then add the 7 four times for a total of six 7s. You can think of 7*6 as adding 7 six times (7+7+7+7+7+7). There is of course more to why this works than of what I am showing, but the main thing is this: multiplication is repeated addition. If we split the 6 into two values, one added by another, we can get 7(2+4). Let's take 7*6 for an example, which equals 42. The literal definition of the distributive property is that multiplying a value by its sum or difference, you will get the same result. The commutative property means when the order of the values switched (still using the same operations) then the same result will be obtained.
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