What is $\frac{5}{6}-\frac{2}{5}$?

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06-11-2026
Mathematics

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What is $\frac{5}{6}-\frac{2}{5}$?

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-06T20:46:05-05:00

Determine the least common multiple (LCM) of the denominators 6 and 5, which is 30.
Rewrite both fractions using the common denominator: $\frac{5}{6} = \frac{25}{30}$ and $\frac{2}{5} = \frac{12}{30}$.
Subtract the numerators while keeping the common denominator: $\frac{25}{30} - \frac{12}{30} = \frac{13}{30}$.
The final result is $\boxed{\frac{13}{30}}$.

Explanation

Analyzing the problem

To find the value of the expression $\frac{5}{6} - \frac{2}{5}$, we need to perform the subtraction of two rational numbers (fractions) that have different denominators. In this case, the denominators are 6 and 5. To subtract fractions, we must first express them with a common denominator, which is typically the least common multiple (LCM) of the original denominators.

Finding a common denominator and converting fractions

To subtract $\frac{5}{6}$ and $\frac{2}{5}$, we find the least common multiple of their denominators, 6 and 5. Since 6 and 5 have no common factors other than 1, their least common multiple is their product: $6 \times 5 = 30$. We then convert both fractions to equivalent ones with a denominator of 30:

For $\frac{5}{6}$, we multiply both the numerator and denominator by 5: $\frac{5 \times 5}{6 \times 5} = \frac{25}{30}$.
For $\frac{2}{5}$, we multiply both the numerator and denominator by 6: $\frac{2 \times 6}{5 \times 6} = \frac{12}{30}$.

Performing the subtraction and simplifying the result

Now that the fractions have the same denominator, we can subtract the second numerator from the first:
\[\frac{25}{30} - \frac{12}{30} = \frac{25 - 12}{30} = \frac{13}{30}.\]
The result $\frac{13}{30}$ cannot be simplified further because 13 is a prime number and does not divide 30. Therefore, the subtraction is complete.

Examples

In everyday life, knowing how to subtract fractions is essential for tasks like baking or measuring. For example, if a recipe calls for $\frac{5}{6}$ of a cup of flour, but you have already used $\frac{2}{5}$ of a cup for another portion of the recipe, you need to calculate how much flour is left. Performing the subtraction $\frac{5}{6} - \frac{2}{5} = \frac{13}{30}$ tells you exactly how much flour remains, helping you manage your ingredients efficiently.