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Lesson 50: The Distributive Property of Multiplication over Addition
This easy lesson introduces you to the distribute property of multiplication over addition. It comes up again and again in math.
Recall from Lesson 48 that we can use a middle dot to represent multiplication, or we can use no symbol at all. With that said, take a look at the problem below:
3 · (4 + 5) = ? In Lesson 53 you'll learn that we need to do what is in parentheses first. We would do 4 + 5 to get 9, and then multiply the 9 times 3 to get 27.
However, we could have used what is called the distributive property of multiplication over addition. You will use this property again and again, especially once you learn algebra. We can distribute the 3 over the addition as follows: (3 · 4) + (3 · 5). Instead of adding first and then multiplying, we can multiply each term in parentheses individually by 3, and then add together both results. We would get 12 + 15 = 27, the same answer as above.
We can represent this property using symbols like this: a ·
(b + c) = (a · b) + (a · c). The a has been distributed.
We can also omit the middle dots, which is even more common, and we
would write
a(b+c) = ab + ac.
Try these on your own. First rewrite them using the distributive property, then solve:
7 · (14 + 29)
25 · (31 + 46)
108 · (7 + 18)
Make sure that you memorize this lesson, since it comes up so frequently. Later you will have much more practice working with this property of math.
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