Verify if (5×3-4×2)/(2×4-3×5) = 0: Fraction Simplification Check

Determine if the simplification below is correct:

$\frac{5\cdot3-4\cdot2}{2\cdot4-3\cdot5}=0$

To determine if the given mathematical simplification is correct, we must evaluate both the numerator and the denominator separately and then divide the results. Let's work through this step by step.

The expression we are examining is:

$\frac{5\cdot3-4\cdot2}{2\cdot4-3\cdot5}$

First, let's calculate the numerator:

• Calculate $5 \cdot 3 = 15$.
• Calculate $4 \cdot 2 = 8$.
• Subtract these results: $15 - 8 = 7$.

The numerator simplifies to $7$.

Next, we calculate the denominator:

• Calculate $2 \cdot 4 = 8$.
• Calculate $3 \cdot 5 = 15$.
• Subtract these results: $8 - 15 = -7$.

The denominator simplifies to $-7$.

Now, we perform the division:

$\frac{7}{-7} = -1$

Thus, the value of the original expression is $-1$, not $0$, as stated in the problem.

Therefore, the statement that the original expression simplifies to $0$ is false.

Hence, the correct answer to this problem is False.