Identify LCD: Identify the least common denominator (LCD) for the fractions 1/3 and 2/5. The denominators are 3 and 5, so the LCD is the least common multiple of these two numbers. The least common multiple of 3 and 5 is 15.Convert fractions: Convert each fraction to an equivalent fraction with the LCD as the denominator. For 1/3, multiply the numerator and denominator by 5 to get 5/15. For 2/5, multiply the numerator and denominator by 3 to get 6/15.Add equivalent fractions: Add the two equivalent fractions with the common denominator. 5/15 + 6/15 = (5 + 6)/15Perform addition: Perform the addition of the numerators. 5 + 6 = 11 So, 5/15 + 6/15 = 11/15Check for simplification: Check if the resulting fraction can be simplified. The fraction 11/15 cannot be simplified further because 11 and 15 have no common factors other than 1.

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$\frac{1}{3}+\frac{2}{5}$ = `?`

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Algebra 1

Multiplication with rational exponents

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\frac{1}{3}+\frac{2}{5}

= `?`

Identify LCD: Identify the least common denominator (LCD) for the fractions $\frac{1}{3}$ and $\frac{2}{5}$ . The denominators are $3$ and $5$ , so the LCD is the least common multiple of these two numbers. The least common multiple of $3$ and $5$ is $15$ .
Convert fractions: Convert each fraction to an equivalent fraction with the LCD as the denominator. $\newline$ For $\frac{1}{3}$ , multiply the numerator and denominator by $5$ to get $\frac{5}{15}$ . $\newline$ For $\frac{2}{5}$ , multiply the numerator and denominator by $3$ to get $\frac{6}{15}$ .
Add equivalent fractions: Add the two equivalent fractions with the common denominator. $\newline$ $\frac{5}{15} + \frac{6}{15} = \frac{(5 + 6)}{15}$
Perform addition: Perform the addition of the numerators. $\newline$ $5 + 6 = 11$ $\newline$ So, $\frac{5}{15} + \frac{6}{15} = \frac{11}{15}$
Check for simplification: Check if the resulting fraction can be simplified. $\newline$ The fraction $\frac{11}{15}$ cannot be simplified further because $11$ and $15$ have no common factors other than $1$ .