Answer :
To simplify the expression [tex]\(\frac{-3}{4} \div \frac{1}{-2} \times \frac{-2}{-5}\)[/tex], we'll break the problem down into steps:
### Step 1: Dividing Fractions
First, we handle the division part of the expression [tex]\(\frac{-3}{4} \div \frac{1}{-2}\)[/tex].
Dividing by a fraction is equivalent to multiplying by its reciprocal. So, we rewrite the division as a multiplication:
[tex]\[ \frac{-3}{4} \div \frac{1}{-2} = \frac{-3}{4} \times \frac{-2}{1} \][/tex]
### Step 2: Multiplying Fractions
Next, we multiply these fractions:
[tex]\[ \frac{-3}{4} \times \frac{-2}{1} = \frac{(-3) \cdot (-2)}{4 \cdot 1} = \frac{6}{4} = \frac{3}{2} \][/tex]
The result of the division is [tex]\(\frac{3}{2}\)[/tex].
### Step 3: Multiplying the Result by Another Fraction
Now, we take the result from the division ([tex]\(\frac{3}{2}\)[/tex]) and multiply it by the remaining fraction [tex]\(\frac{-2}{-5}\)[/tex].
Since [tex]\(\frac{-2}{-5} = \frac{2}{5}\)[/tex] (negative signs cancel each other out), we perform the multiplication:
[tex]\[ \frac{3}{2} \times \frac{2}{5} = \frac{3 \cdot 2}{2 \cdot 5} = \frac{6}{10} = \frac{3}{5} \][/tex]
The simplified expression is [tex]\(\frac{3}{5}\)[/tex].
### Choice Selection
Comparing this result with the options provided:
(a) [tex]\(\frac{-15}{4}\)[/tex]
(b) [tex]\(-\frac{3}{5}\)[/tex]
(c) [tex]\(\frac{3}{5}\)[/tex]
(d) [tex]\(\frac{15}{4}\)[/tex]
The correct answer is:
(c) [tex]\(\frac{3}{5}\)[/tex].
### Step 1: Dividing Fractions
First, we handle the division part of the expression [tex]\(\frac{-3}{4} \div \frac{1}{-2}\)[/tex].
Dividing by a fraction is equivalent to multiplying by its reciprocal. So, we rewrite the division as a multiplication:
[tex]\[ \frac{-3}{4} \div \frac{1}{-2} = \frac{-3}{4} \times \frac{-2}{1} \][/tex]
### Step 2: Multiplying Fractions
Next, we multiply these fractions:
[tex]\[ \frac{-3}{4} \times \frac{-2}{1} = \frac{(-3) \cdot (-2)}{4 \cdot 1} = \frac{6}{4} = \frac{3}{2} \][/tex]
The result of the division is [tex]\(\frac{3}{2}\)[/tex].
### Step 3: Multiplying the Result by Another Fraction
Now, we take the result from the division ([tex]\(\frac{3}{2}\)[/tex]) and multiply it by the remaining fraction [tex]\(\frac{-2}{-5}\)[/tex].
Since [tex]\(\frac{-2}{-5} = \frac{2}{5}\)[/tex] (negative signs cancel each other out), we perform the multiplication:
[tex]\[ \frac{3}{2} \times \frac{2}{5} = \frac{3 \cdot 2}{2 \cdot 5} = \frac{6}{10} = \frac{3}{5} \][/tex]
The simplified expression is [tex]\(\frac{3}{5}\)[/tex].
### Choice Selection
Comparing this result with the options provided:
(a) [tex]\(\frac{-15}{4}\)[/tex]
(b) [tex]\(-\frac{3}{5}\)[/tex]
(c) [tex]\(\frac{3}{5}\)[/tex]
(d) [tex]\(\frac{15}{4}\)[/tex]
The correct answer is:
(c) [tex]\(\frac{3}{5}\)[/tex].
