To verify the equality [tex]\(\frac{a}{b} \times \frac{c}{d} = \frac{c}{d} \times \frac{a}{b}\)[/tex] given [tex]\(a = -1\)[/tex], [tex]\(b = 2\)[/tex], [tex]\(c = 3\)[/tex], and some value for [tex]\(d\)[/tex], let's perform the step-by-step calculation for both sides of the equation.
### Step 1: Assign values to the variables
We are given:
- [tex]\(a = -1\)[/tex]
- [tex]\(b = 2\)[/tex]
- [tex]\(c = 3\)[/tex]
We still need a value for [tex]\(d\)[/tex]. Let's assume [tex]\(d = 4\)[/tex] as an arbitrary example.
### Step 2: Calculate the left side of the equation
The left side of the equation is:
[tex]\[
\frac{a}{b} \times \frac{c}{d}
\][/tex]
Substituting the values:
[tex]\[
\frac{-1}{2} \times \frac{3}{4}
\][/tex]
### Step 3: Perform the multiplication
Multiply the fractions:
[tex]\[
\frac{-1 \times 3}{2 \times 4} = \frac{-3}{8}
\][/tex]
### Step 4: Calculate the right side of the equation
The right side of the equation is:
[tex]\[
\frac{c}{d} \times \frac{a}{b}
\][/tex]
Substituting the values:
[tex]\[
\frac{3}{4} \times \frac{-1}{2}
\][/tex]
### Step 5: Perform the multiplication
Multiply the fractions:
[tex]\[
\frac{3 \times -1}{4 \times 2} = \frac{-3}{8}
\][/tex]
### Step 6: Compare the results
The left side of the equation is:
[tex]\[
\frac{-3}{8}
\][/tex]
The right side of the equation is:
[tex]\[
\frac{-3}{8}
\][/tex]
### Conclusion
Both sides of the equation yield the same result:
[tex]\[
\frac{-3}{8}
\][/tex]
Therefore, we have verified that:
[tex]\[
\frac{a}{b} \times \frac{c}{d} = \frac{c}{d} \times \frac{a}{b}
\][/tex]
if [tex]\(a = -1\)[/tex], [tex]\(b = 2\)[/tex], [tex]\(c = 3\)[/tex], and [tex]\(d = 4\)[/tex].
