1Cademy - Adding $$\frac{13}{15} + \frac{17}{20}$$

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Adding $\frac{7}{12} + \frac{5}{18}$

Example

Adding $\frac{13}{15} + \frac{17}{20}$

Add two fractions with different denominators by finding their least common denominator (LCD) and converting them to equivalent fractions:

$\frac{13}{15} + \frac{17}{20}$

Step 1 — Find the LCD and rewrite: Find the prime factorizations of the denominators: $15 = 3 \cdot 5$ and $20 = 2 \cdot 2 \cdot 5$ . The LCD is $2 \cdot 2 \cdot 3 \cdot 5 = 60$ . To rewrite the fractions, multiply the first fraction by $\frac{4}{4}$ and the second fraction by $\frac{3}{3}$ :

$\frac{13 \cdot 4}{15 \cdot 4} + \frac{17 \cdot 3}{20 \cdot 3} = \frac{52}{60} + \frac{51}{60}$

Step 2 — Add: Add the numerators together while keeping the denominator the same:

$\frac{52 + 51}{60} = \frac{103}{60}$

Step 3 — Simplify: The numerator $103$ is a prime number and shares no common factors with $60$ , meaning the fraction is already in simplest form. The result is $\frac{103}{60}$ .

Updated 2026-05-02

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OpenStax Intermediate Algebra

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