et's find \( \frac{2}{5}+\frac{1}{3} \). First write the addition with a common denominator. Then add. \[ \frac{2}{5}+\frac{1}{3}=\frac{\square}{\square}+\frac{\square}{\square}=\frac{\square}{\square} \]
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The Deep Dive
To add the fractions \( \frac{2}{5} \) and \( \frac{1}{3} \), we need to find a common denominator. The least common multiple of 5 and 3 is 15. Now, we can convert each fraction: 1. For \( \frac{2}{5} \), multiply the numerator and denominator by 3: \( \frac{2 \times 3}{5 \times 3} = \frac{6}{15} \). 2. For \( \frac{1}{3} \), multiply the numerator and denominator by 5: \( \frac{1 \times 5}{3 \times 5} = \frac{5}{15} \). Now we can add them together with the common denominator: \[ \frac{2}{5} + \frac{1}{3} = \frac{6}{15} + \frac{5}{15} = \frac{11}{15} \] So, the completed equation looks like this: \[ \frac{2}{5}+\frac{1}{3}=\frac{6}{15}+\frac{5}{15}=\frac{11}{15} \]
