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$Evaluate the expression shown below and write your answer as a fraction in simplest form. (2)/(7)+(7)/(9) Answer:$

Evaluate the expression shown below and write your answer as a fraction in simplest form. $\newline$ $\frac{2}{7}+\frac{7}{9}$ $\newline$ Answer:

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Roots of rational numbers

Full solution

Q. Evaluate the expression shown below and write your answer as a fraction in simplest form.

\newline

\frac{2}{7}+\frac{7}{9}

\newline

Answer:

Identify Common Denominator: Identify a common denominator for the fractions $(\frac{2}{7})$ and $(\frac{7}{9})$ . The denominators are $7$ and $9$ , which are both prime numbers. Therefore, the least common denominator (LCD) is their product, which is $7 \times 9 = 63$ .
Convert to Equivalent Fractions: Convert each fraction to an equivalent fraction with the common denominator of $63$ . For $(\frac{2}{7})$ , multiply both the numerator and the denominator by $9$ to get $(\frac{2\times9}{7\times9}) = \frac{18}{63}$ . For $(\frac{7}{9})$ , multiply both the numerator and the denominator by $7$ to get $(\frac{7\times7}{9\times7}) = \frac{49}{63}$ .
Add Fractions: Add the fractions with the common denominator. $\newline$ $(\frac{18}{63}) + (\frac{49}{63}) = (\frac{18 + 49}{63}) = \frac{67}{63}$ .
Check for Simplification: Check if the fraction can be simplified. $\newline$ The fraction $\frac{67}{63}$ cannot be simplified further because $67$ and $63$ have no common factors other than $1$ .

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