To evaluate the expression -3/4 × -1/5 ÷ -1/4 + -2/5, we will follow the order of operations carefully. Let's break it down step by step.
- Evaluate the multiplication:
-3/4 × -1/5.
When multiplying two negative fractions, the result is positive.
Calculation:
(-3 × -1) / (4 × 5) = 3/20. - Next, we have the division:
Now, we need to divide the result by -1/4.
Dividing by a fraction is the same as multiplying by its reciprocal:
(3/20) ÷ (-1/4) = (3/20) × (-4/1) = -12/20. - Simplify the fraction:
-12/20 can be simplified. Both numbers can be divided by 4.
Final result after simplification:
-12/20 = -3/5. - Now, add -2/5:
We need to add -3/5 and -2/5.
Since they have the same denominator, we can add the numerators directly:
-3 + (-2) = -5, so:
-3/5 + -2/5 = -5/5. - Simplify the final fraction:
-5/5 = -1.
Therefore, the final answer of the expression is -1.