Questions: Add the rational numbers. Express the sum as a rational number in lowest terms. 5/9 + 3/7 5/9 + 3/7 = (Type an integer or a simplified fraction.)

Solution Steps

To add the fractions \(\frac{5}{9}\) and \(\frac{3}{7}\), first find the least common denominator (LCD) of the denominators 9 and 7. The LCD of 9 and 7 is \(63\).

Rewrite each fraction so that they have the denominator \(63\): \[ \frac{5}{9} = \frac{5 \times 7}{9 \times 7} = \frac{35}{63} \] \[ \frac{3}{7} = \frac{3 \times 9}{7 \times 9} = \frac{27}{63} \]

Add the two fractions: \[ \frac{35}{63} + \frac{27}{63} = \frac{35 + 27}{63} = \frac{62}{63} \]

Check if the fraction \(\frac{62}{63}\) can be simplified. Since 62 and 63 have no common factors other than 1, the fraction is already in its lowest terms.

Final Answer