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Simplify the expression below. \(3 \frac{\mathrm{2} }{\mathrm{5}} + 1 \frac{\mathrm{4} }{\mathrm{7}} \) . Which of the following is correct?

A \(\frac{\mathrm{174} }{\mathrm{35}}\)

To add mixed number fractions, first convert them to improper fractions, then find a common denominator and add the numerators, placing them over the common denominator. Reduce the final fraction if necessary. \(3 \frac{\mathrm{2} }{\mathrm{5}} = \frac{\mathrm{17} }{\mathrm{5}} \) , \(1 \frac{\mathrm{4} }{\mathrm{7}} = \frac{\mathrm{11} }{\mathrm{7}}\)
Now find the lowest common denominator between 5 and 7. Since they are both prime numbers, their lowest common denominator is their product, 35. We can rewrite both fractions: \(\frac{\mathrm{17} }{\mathrm{5}} = \frac{\mathrm{119} }{\mathrm{35}}\) , \(\frac{\mathrm{11} }{\mathrm{7}} = \frac{\mathrm{55} }{\mathrm{35}}\)
Now that the denominators are the same, we can add the numerators: \(\frac{\mathrm{119+55} }{\mathrm{35}}=\frac{\mathrm{174} }{\mathrm{35}}\)