PLS HELP i dont get distributive property

Answer 1

The distributive property is a mathematical and algebraic property that says that multiplying two numbers is the same as multiplying one of those numbers by the sum of the other number's parts. -- Wikipedia

So, here are two numbers: 2 and 3

Here are the "parts" of 3: 2 + 1

Here is what the distributive property of multiplication over addition says:

2 * 3 = 2*2 + 2*1 or we write 2*3 = 2*(2+1) and then "distribute the terms as 2*2 + 2*1

Using letters, it looks like this:

a*(b+c) = a*b + a*c

Here is an example of making a problem seem to be easier by using the distributive property:

What is 45*99?

Well, it is 45*(100-1) = 4500 - 45 = 4455 [note: this is addition of (-1)]

So, Bob bought 45 packs of pencils (enough for the whole class) that were on sale for 99 cents each. How much did Bob pay?

45*99 = 4455 cents = $44.55

Answer 2

Hi Reanna!

The distributive property prepares one for working with variables, and helps to solve expressions in the form of a(b + c) or a(b - c). Essentially, you can Distribute the number outside the parenthesis to everything inside, and then do your addition or subtraction. This is different than the Order of Operations you may have learned in the past with PEMDAS.

An example of a problem in the Distributive Property format using real numbers:

4(8+3)

Following Order of Operations method, evaluate what’s in the parentheses first, then multiply:

4(8+3) --> 4(11) = 44

1. We can use this method with real numbers, but it doesn't work with variables

Following the distributive property, multiply the 4 by each individual component in the parenthesis, then add:

4(8+3) --> 4(8) + 4(3) --> 32+12 = 44

1. We can use this method with variables AND real numbers

Imagine if the 8 was now a variable, X. You can not combine (x+3) before multiplication takes place, but by "distributing" the 4, we can still set our problem up to be solved.

4(x+3) --> 4(x) +4(3) --> 4x + 12

I hope this helps!