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

Question

elotito11 elotito11

31-10-2026
Mathematics

Answered

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

Verified Answer :

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-10-31T13:49:46-04:00

Identify the least common multiple of the denominators 3 and 5, which is 15.
Convert each fraction to an equivalent fraction with a denominator of 15: $\frac{1}{3} = \frac{5}{15}$ and $\frac{2}{5} = \frac{6}{15}$.
Sum the converted fractions: $\frac{5}{15} + \frac{6}{15} = \frac{11}{15}$.
The final result is $\boxed{\frac{11}{15}}$.

Explanation

Analyzing the Problem

To compute the sum $\frac{1}{3} + \frac{2}{5}$, we need to add two fractions with different denominators. The first fraction is $\frac{1}{3}$ and the second is $\frac{2}{5}$. To add fractions, they must share a common denominator. The least common multiple (LCM) of the denominators 3 and 5 is 15.

Converting to a Common Denominator

To express $\frac{1}{3}$ with the denominator 15, we multiply both the numerator and denominator by 5:
\[\frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}.\]
Next, to express $\frac{2}{5}$ with the denominator 15, we multiply both the numerator and denominator by 3:
\[\frac{2}{5} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15}.\]

Performing the Addition

Now that the fractions have the same denominator, we can add them by summing their numerators:
\[\frac{5}{15} + \frac{6}{15} = \frac{5 + 6}{15} = \frac{11}{15}.\]
Thus, the sum is $\frac{11}{15}$.

Examples

In daily life, fractions are often used for cooking. If a recipe calls for $1/3$ of a cup of flour and then adds $2/5$ of a cup more, you need to find the total amount of flour used. By finding a common denominator, you determine that the total amount is $11/15$ of a cup, allowing you to measure the ingredients accurately.