A Simple Math Problem? - Page 53

Since we have 48, 2, 9, and 3, I will assume we're working within the field of real numbers (if we were working in the ring of integers, this problem gets ugly), which I will denote as R.

We know a few things about R.
R is equipped with the binary operations addition and multiplication, + and * respectively. Let a, b, and c be arbitrary elements in R.
The following properties hold:
1) For any a and b within R, a+b is still within R
2) For any a, b, and c in R, a+(b+c)=(a+b)+c
3) For any a in R, there exists a 0, which we will call the identity unit, such that a+0=0+a=a
4) For any a in R, there exists an inverse element -a, such that a+(-a)=0=(-a)+a
5) For any a and b in R, a+b=b+a
Note: These first five axioms are equivalent to saying that R is an abelian group with respect to addition, denoted as (R,+)
6) For any a and b in R, a*b is still contained in R
7) For any a, b, and c in R, a*(b*c)=(a*b)*c
8) For any nonzero element a in R, there exists an inverse element a^(-1), such that a*a^(-1)=1=a^(-1)*a
9) For any a, b in R, a*b=b*a
10) For any a in R, there exists an identity element, which we will call 1, such that a*1=1*a
Note: Axioms 6-10 are equivalent to saying that R minus the 0 element is an abelian group with respect to multiplication, denoted (R\{0}, *).
11) For any a, b, and c in R, a*(b+c)=a*c+a*c and (a+b)*c=a*c+b*c. This is called the distributive property.

Note: The notation ÷ is equivalent to multiplying the number to its immediate right by it's inverse.
e.g. a÷b=a*b^(-1)
Additional Note: When multiplying, the * symbol is sometimes removed for convenience.
e.g. a*b=ab or a(b+c)=ab+ac=a*b+a*c=a*(b+c)



48÷2(9+3)
=48*2^(-1)*(9+3)
=24*(9+3)
=24*9+24*3
=216+72
=288