1Cademy - Adding $$\frac{7}{12} + \frac{11}{15}$$

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

Example

Adding $\frac{7}{12} + \frac{11}{15}$

Add two fractions with unlike denominators by first determining their least common denominator (LCD):

$\frac{7}{12} + \frac{11}{15}$

Step 1 — Find the LCD and rewrite: Factor the denominators: $12 = 2 \cdot 2 \cdot 3$ and $15 = 3 \cdot 5$ . The LCD is $2 \cdot 2 \cdot 3 \cdot 5 = 60$ . Multiply the numerator and denominator of the first fraction by $5$ and the second fraction by $4$ to convert them to equivalent fractions:

$\frac{7 \cdot 5}{12 \cdot 5} + \frac{11 \cdot 4}{15 \cdot 4} = \frac{35}{60} + \frac{44}{60}$

Step 2 — Add: Combine the numerators over the common denominator:

$\frac{35 + 44}{60} = \frac{79}{60}$

Step 3 — Simplify: Because $79$ is a prime number and does not divide evenly into $60$ , the fraction cannot be simplified further. The final result is $\frac{79}{60}$ .

Updated 2026-05-02

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OpenStax Intermediate Algebra

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