What am I doing wrrong here that violates the rule that "order doesn't matter when multiplying and dividing?"

Question

5 / 1 * 4

if I do the 5/1 first: (5 / 1) * 4 = 5 * 4 = 20 (final answer is 20)

if I do the 1 * 4 first: 5/ (1 * 4) = 5/4 (final answer is 5/4)

What am I doing wrong?

Answer 1

When you divide by 4, you are multiplying by 1/4.

Multiplication is commutative, which means that A.B = B.A, so 5*(1/4) = (1/4)*5. However, division is clearly diferent, for 1/4 ≠ 4/1. So in the first line you are multiplying (5/1)*4 = 5*4 = 20 In the second line its diferent, 5/ (1 * 4) = 5*(1/(1*4)) = 5*(1/4) = 5/4

Also, parentheses do matter a lot, for they clear what operations come first (operation priority). Multiplication and division have priority over sum and subtraction, but if you have a sum with parentheses , that comes first. For example: A*(B+C) ≠ AB+C, because the first one is A(B+C) = AB+AC (Distributive property)

I hope I have helped. Saclyr.