Verify the Equation: Is (3×7)/(7×4) + 4/3 = 1?

Determine if the simplification below is correct:

$\frac{3\cdot7}{7\cdot4}+\frac{4}{3}=1$

To determine the correctness of the simplification given by $\frac{3 \cdot 7}{7 \cdot 4} + \frac{4}{3} = 1$, we will follow these steps:

• Step 1: Simplify the first fraction.

The first fraction is $\frac{3 \cdot 7}{7 \cdot 4}$. We can cancel the common factor of 7 in the numerator and the denominator:

$\frac{3 \cdot 7}{7 \cdot 4} = \frac{3}{4}$.

• Step 2: Add the simplified first fraction to the second fraction.

Now we have $\frac{3}{4} + \frac{4}{3}$. To add these fractions, we need a common denominator. The least common denominator of 4 and 3 is 12.

Convert both fractions to have this common denominator:

$\frac{3}{4} = \frac{3 \cdot 3}{4 \cdot 3} = \frac{9}{12}$ and $\frac{4}{3} = \frac{4 \cdot 4}{3 \cdot 4} = \frac{16}{12}$.

Add these fractions:

$\frac{9}{12} + \frac{16}{12} = \frac{9 + 16}{12} = \frac{25}{12}$.

• Step 3: Compare the result with 1.

The result $\frac{25}{12}$ is not equal to 1. Therefore, the original expression does not simplify to 1.

Conclusion: The simplification is incorrect.