Answer:
-7/40
Explanation:
always remember about the signs :
+ + = +
+ - = -
- + = -
- - = +
+ × + = +
- × + = -
+ × - = -
- × - = +
and the absolute value is always the positive value of the interval value (no matter if it is already positive or not).
oh, and the priority of arithmetic functions :
1. brackets
2. exponents (does not apply here)
3. multiplications and divisions
4. additions and subtractions
so, we have here
(2 - |-¼ - 2(-⅗)|) ÷ (-6)
let's start with the innermost multiplication with a bracket :
2(-⅗) = 2 × -⅗ = (2 × -3)/5 = -6/5
combining this with the rest of the argument of the absolute value function (we also need to bring the 2 fractions to the same denominator)
-¼ - -6/5 = -¼ + 6/5 = -(5×1)/20 + (4×6)/20 =
= -5/20 + 24/20 = 19/20
|19/20| = 19/20
based on the brackets we have to combine this with the first term (2), which we also need to bring to 1/20 form :
2 - 19/20 = (20×2)/20 - 19/20 = 40/20 - 19/20 = 21/20
what is left is the final division by -6 :
21/20 ÷ -6 = 21/20 / -6/1
remember :
a/b / c/d = (a×d)/(b×c)
so,
21/20 / -6/1 = (21×1)/(20×-6) = 21/-120 = -21/120 = -7/40