$4 \frac{5}{8}+2 \frac{2}{3}$

Question

05-11-2026
Mathematics

Answered

$4 \frac{5}{8}+2 \frac{2}{3}$

Verified Answer :

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-05T18:54:26-05:00

Convert the mixed numbers $4 \frac{5}{8}$ and $2 \frac{2}{3}$ to improper fractions: $\frac{37}{8}$ and $\frac{8}{3}$.
Find a common denominator, which is 24, and rewrite the fractions as $\frac{111}{24}$ and $\frac{64}{24}$.
Sum the fractions to get $\frac{175}{24}$.
Convert the result back to a mixed number to get $\boxed{7 \frac{7}{24}}$.

Explanation

Analysis of the Problem

To calculate the sum of two mixed numbers $4 \frac{5}{8}$ and $2 \frac{2}{3}$, we first analyze the structure of mixed numbers. A mixed number is composed of a whole number part and a fractional part. For example, $A \frac{B}{C}$ is equivalent to the sum $A + \frac{B}{C}$. Our objective is to find the total sum, simplify it, and express it back as a mixed number. We will use the common denominator method to perform the addition.

Converting to Improper Fractions

First, we convert both mixed numbers into improper fractions.
For $4 \frac{5}{8}$:
\[4 \frac{5}{8} = 4 + \frac{5}{8} = \frac{4 \times 8 + 5}{8} = \frac{32 + 5}{8} = \frac{37}{8}\]
For $2 \frac{2}{3}$:
\[2 \frac{2}{3} = 2 + \frac{2}{3} = \frac{2 \times 3 + 2}{3} = \frac{6 + 2}{3} = \frac{8}{3}\]

Adding Fractions with a Common Denominator

To add the fractions $\frac{37}{8}$ and $\frac{8}{3}$, we find a common denominator. The least common multiple of the denominators 8 and 3 is 24.
We rewrite each fraction with 24 as the denominator:
\[\frac{37}{8} = \frac{37 \times 3}{8 \times 3} = \frac{111}{24}\]
\[\frac{8}{3} = \frac{8 \times 8}{3 \times 8} = \frac{64}{24}\]
Now, we add the two fractions together:
\[\frac{111}{24} + \frac{64}{24} = \frac{111 + 64}{24} = \frac{175}{24}\]

Final Conversion and Conclusion

Finally, we convert the improper fraction $\frac{175}{24}$ back into a mixed number. We divide 175 by 24:
\[175 \div 24 = 7 \text{ with a remainder of } 175 - (24 \times 7) = 175 - 168 = 7\]
Thus, the improper fraction is equivalent to $7 \frac{7}{24}$.
Therefore, $4 \frac{5}{8} + 2 \frac{2}{3} = \boxed{7 \frac{7}{24}}$.

Examples

In daily life, such calculations are frequent in culinary arts or construction. For instance, if a recipe calls for $4 \frac{5}{8}$ cups of flour for one batch of cookies and $2 \frac{2}{3}$ cups for another smaller batch, you can add them to determine that you need $7 \frac{7}{24}$ cups in total to combine the batches. This mathematical skill is essential for managing resources efficiently in various practical tasks.