Distributive property of multiplication

In summary, the conversation discusses the equation 48 / 2(9 + 3) = 2 and the ambiguity of its notation. The distributive property is mentioned as a possible explanation, but it is ultimately determined that the ambiguity can be resolved by using parentheses to clarify the intended order of operations. The thread is then locked.
  • #1
drkent3
1
0
OK - this one has been argued to death in several different threads, but the answers have been less than satisfactory... so someone provide a reason why I am wrong here:

48 / 2(9 + 3) = 2.

Why? Because the distributive property of multiplication means that 2(9+3) = (2*9+2*3).

For example, what if we replace (9+3) with x? 48 / 2x = ?

Yes? No?

(Apologies in advance for posting yet again that which everyone thinks has been put to rest).
 
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  • #2
That is NOT a matter of the "distributive property", it is just a matter of your notation being ambiguous. That could be interpreted as either
[tex]48/(2(9+3))= \frac{48}{2(9+ 3)}= \frac{48}{2(12)}= \frac{48}{24}= 2[/tex]
or as
[tex](48/2)(9+ 3)= \frac{48}{2}\left(9+ 3\right)= 24(12)= 288[/tex]

Use parentheses to make your meaning clear.
 

What is the distributive property of multiplication?

The distributive property of multiplication is a mathematical property that states that when multiplying a number by a sum, the result will be the same as multiplying each addend by the number individually and then adding the products together. This property is often written as a(b + c) = ab + ac, where a, b, and c are any numbers.

How do you use the distributive property of multiplication?

To use the distributive property of multiplication, you simply need to distribute the number outside the parentheses to each term inside the parentheses. For example, if you have the expression 3(4 + 5), you would distribute the 3 to both the 4 and 5, resulting in 3(4) + 3(5) = 12 + 15 = 27.

Why is the distributive property of multiplication important?

The distributive property of multiplication is important because it allows us to simplify complex algebraic expressions and solve equations more easily. It also helps us to understand the relationship between multiplication and addition.

What is an example of using the distributive property of multiplication in real life?

An example of using the distributive property of multiplication in real life is when calculating the cost of a purchase with a discount. For example, if a shirt originally costs $20, but is on sale for 20% off, we can use the distributive property to calculate the final cost as 0.8(20) = $16.

Can the distributive property of multiplication be used with variables?

Yes, the distributive property of multiplication can be used with variables. For example, if you have the expression x(2 + 3), you can distribute the x to both the 2 and 3, resulting in x(2) + x(3) = 2x + 3x = 5x.

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