$3 \frac{5}{6}+2 \frac{7}{8}$

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05-11-2026
Mathematics

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$3 \frac{5}{6}+2 \frac{7}{8}$

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-05T18:56:47-05:00

Separate each mixed number into its integer and fractional parts: $3 + \frac{5}{6}$ and $2 + \frac{7}{8}$.
Find the least common denominator of 6 and 8, which is 24, to combine the fractions: $\frac{20}{24} + \frac{21}{24} = \frac{41}{24}$.
Convert the improper fraction $\frac{41}{24}$ to the mixed number $1 \frac{17}{24}$.
Add the integer parts and the mixed fraction to get the total: $5 + 1 \frac{17}{24} = \boxed{6 \frac{17}{24}}$.

Explanation

Representing mixed numbers as sums

To add the two mixed numbers $3 \frac{5}{6}$ and $2 \frac{7}{8}$, we first express each mixed number as the sum of its integer part and its fractional part.
A mixed number $A \frac{B}{C}$ is defined as $A + \frac{B}{C}$.
Thus, we have:
\[3 \frac{5}{6} = 3 + \frac{5}{6}\]
\[2 \frac{7}{8} = 2 + \frac{7}{8}\]

Grouping terms and finding a common denominator

Now, we group the integer parts and the fractional parts together:
\[\left(3 + \frac{5}{6}\right) + \left(2 + \frac{7}{8}\right) = (3 + 2) + \left(\frac{5}{6} + \frac{7}{8}\right) = 5 + \left(\frac{5}{6} + \frac{7}{8}\right)\]
To add the fractions $\frac{5}{6}$ and $\frac{7}{8}$, we need to find a common denominator. The least common multiple (LCM) of 6 and 8 is 24.

Converting and adding fractions

We convert each fraction to have a denominator of 24:
\[\frac{5}{6} = \frac{5 \times 4}{6 \times 4} = \frac{20}{24}\]
\[\frac{7}{8} = \frac{7 \times 3}{8 \times 3} = \frac{21}{24}\]
Adding these fractions together:
\[\frac{20}{24} + \frac{21}{24} = \frac{20 + 21}{24} = \frac{41}{24}\]

Final result calculation

The resulting fraction $\frac{41}{24}$ is an improper fraction. We convert it back into a mixed number by dividing 41 by 24:
\[41 \div 24 = 1 \text{ with a remainder of } 17\]
So, $\frac{41}{24} = 1 \frac{17}{24}$.
Finally, add this to our integer sum from step 2:
\[5 + 1 \frac{17}{24} = 6 \frac{17}{24}\]
Thus, the sum is $\boxed{6 \frac{17}{24}}$.

Examples

Adding mixed numbers is essential for many practical measurements, such as in construction or cooking. For example, if you are building a small shelf and have two pieces of wood measuring $3 \frac{5}{6}$ feet and $2 \frac{7}{8}$ feet long, joining them gives a total length of $6 \frac{17}{24}$ feet. This math ensures that you can combine different materials precisely to reach the desired total dimension for your project.