Algebra (Combining coefficients (Decimals))

Question

My question is why the math is done differently on these 2 problems.

1.3b + 7.8 - 3.2b

To solve, I know to subtract 1.3 from 3.2 to get -1.9, but my question lies in the order of operations.

(1.3 - 3.2)b + 7.8

Because 1.3 is first in this expression I must place it first, right? But, when I do the math I get left with -2.1 so, my confusion is why when solving this equation is -2.1 incorrect if I am following the order of operations?

This is also my struggle with the next expression:

-3.6 - 1.9t + 1.2 + 5.1t

When I solve this I combine my like terms the same (-1.9 + 5.1) however I am unable to solve this expression without first flipping the numbers around. Now, let me ask again.

Why, when following the order of operations, can I not solve this expression correctly? i.e. (-1.9 + 5.1) to get -4.8? What makes that answer incorrect?

Answer 1

1.3b +7.8 -3.2b

7.8 - 1.9b

use pemdas

-3.6 -1.9t + 1.2 +5.1t

=-2.4 +3.2t

-(1.9+5.2)= -7.1, but there are no parentheses

no way to get -4.8

unless you insert parentheses

-(3.6+1.4)=-4.8, but there are no parentheses

think of -3.2 as (-1)(3.2) and m in pemdas is the 1st in the pemdas order of operations, before a or s