Because that’s how it works.
It’s NOT THE SAME as having a multiplication sign between them
His could also be written as
48/6(3+1)
I’ll quote this again, as you dont get it
Distributive property of multiplication. Early Algebra.
The distributive property of multiplication CLEARLY states that the 2(9+3) is an entire term and CANNOT be broken up. 2(9+3) follows the distributive property which can be rewritten as (29+23). Let me repeat the 2 outside of the parenthesis follows the distributive property of multiplication and must be factored and simplified before performing any other operations on it.
So this can be rewritten as:
48 / (29 + 23)
Which leaves us with
48 / 24 = 2
Answer = 2.
Lastly for those using Google or any other online calculator. These do not understand many theorems or properties so you must explicitly explain what you mean. There is a difference between 48 / 2 (9+3) and 48 / 2(9+3). The first notation reads 48 / 2 * 1(9+3) while the second reads 48 / (29+2*3). Be very careful with your signs.
Ill also copy this from math.edu
Link works Better than quote
http://www.math.unt.edu/mathlab/emathlab/distributive_property_of_multipl.htm
The distributive property of multiplication over addition is simply this:* it makes no difference whether you add two or more terms together first, and then multiply the results by a factor, or whether you multiply each term alone by the factor first, and then add up the results.
That is,
*** adding up the term first; then multiplying by the factor** =* multiplying each term by the factor first, then adding up the resulting terms
That is:****** Factor(Term1 + Term2 + … + TermN)* =** Factor(Term1) + Factor(Term2) + … + Factor(TermN)
If we call the Factor “a,”* and we call the terms “b”, “c,”…“t”, then this statement begins to look like a mathematical statement:
************************************************* a(b + c + … + t)*** = a(b) + a(c) + … +a(t)
** EXAMPLE:*** (The factor is 3, and the three terms* are 2, 7, -5)
************************************************************ 3(2 + 7 - 5)* =** 3(2) + 3(7) + (3)(-5)
**************************************************************** 3(4) ******* =**** 6*** +* 21*** -* 15
****************************************************************** 12******** =** 12
This is kinda cool, but you might wonder* what possible use it might be.* I mean, really, why wouldn’t you ALWAYS add the terms together first, and avoid all that yukky multiplication?** Well, the answer is:** It comes in very useful when you have terms that cannot be added together first, because they are not like terms.
Case in point:*** 3(2x + 4).*** We can’t combine the 2x and the 4, because the first is x’s and the second is 1’s (four of them).* But, suppose this expression showed up in an equation like:
**************************** 3(2x + 4) = 5
and we were asked to solve for x?* What to do?* We have to get the x’s untied from the 1’s, right?* Using the distributive property of multiplication over addition is what is going to let us solve this equation:
************************** 3(2x) + 3(4) = 5****** Ta-da!** Now the x’s are unhooked from the 1’s
***************************** 6x + 12** =* 5
*************************************** 6x =* 5 - 12
******************************************** =* -7
*************************************** x* =* -7/6