Question

Use properties of operations and rules for multiplying signed numbers to multiply by Write the answer in

simplest form.

-6/5

-3/25

-6/50

3/5

Answer 1

To multiply the fractions \(-\frac{6}{5} \times -\frac{3}{25} \times -\frac{6}{50} \times \frac{3}{5}\), we will follow these steps:

1. **Multiply the numerators together.**
2. **Multiply the denominators together.**
3. **Simplify the resulting fraction.**
4. **Consider the signs.**

### Step 1: Multiply the Numerators
Numerators:
- \(-6\)
- \(-3\)
- \(-6\)
- \(3\)

\[
-6 \times -3 \times -6 \times 3
\]

Calculate:
\[
(-6) \times (-3) = 18 \quad (\text{negative times negative is positive})
\]
\[
18 \times (-6) = -108 \quad (\text{positive times negative is negative})
\]
\[
-108 \times 3 = -324 \quad (\text{negative times positive is negative})
\]

So, the product of the numerators is \(-324\).

### Step 2: Multiply the Denominators
Denominators:
- \(5\)
- \(25\)
- \(50\)
- \(5\)

\[
5 \times 25 \times 50 \times 5
\]

Calculate:
\[
5 \times 25 = 125
\]
\[
125 \times 50 = 6250
\]
\[
6250 \times 5 = 31250
\]

So, the product of the denominators is \(31250\).

### Step 3: Combine the Results
Now we combine our results from the numerators and denominators:

\[
-\frac{324}{31250}
\]

### Step 4: Simplify
To simplify \(-\frac{324}{31250}\), we find the greatest common divisor (GCD) of \(324\) and \(31250\).

- \(324 = 2^2 \times 3^4\)
- \(31250 = 2 \times (5^5)\)

Since their only common factor is \(2\), we can divide both the numerator and the denominator by \(2\):

\[
-\frac{324 \div 2}{31250 \div 2} = -\frac{162}{15625}
\]

### Final Answer
The final answer in simplest form is:

\[
-\frac{162}{15625}
\]