Answer :

Sure! Let's solve the expression [tex]\(4 \frac{1}{3} + 3 \frac{2}{5} - 2 \frac{14}{15}\)[/tex] by converting each mixed number into improper fractions and then evaluating the expression.

1. Convert Mixed Numbers to Improper Fractions:

- For [tex]\(4 \frac{1}{3}\)[/tex]:
[tex]\[
4 \frac{1}{3} = \frac{4 \times 3 + 1}{3} = \frac{13}{3}
\][/tex]

- For [tex]\(3 \frac{2}{5}\)[/tex]:
[tex]\[
3 \frac{2}{5} = \frac{3 \times 5 + 2}{5} = \frac{17}{5}
\][/tex]

- For [tex]\(2 \frac{14}{15}\)[/tex]:
[tex]\[
2 \frac{14}{15} = \frac{2 \times 15 + 14}{15} = \frac{44}{15}
\][/tex]

2. Find a Common Denominator:

The denominators are 3, 5, and 15. The least common multiple of these numbers is 15.

3. Convert Fractions to Have a Common Denominator of 15:

- For [tex]\(\frac{13}{3}\)[/tex]:
[tex]\[
\frac{13}{3} = \frac{13 \times 5}{3 \times 5} = \frac{65}{15}
\][/tex]

- For [tex]\(\frac{17}{5}\)[/tex]:
[tex]\[
\frac{17}{5} = \frac{17 \times 3}{5 \times 3} = \frac{51}{15}
\][/tex]

- [tex]\(\frac{44}{15}\)[/tex] already has the common denominator of 15.

4. Perform the Addition and Subtraction:

Combine the fractions:
[tex]\[
\frac{65}{15} + \frac{51}{15} - \frac{44}{15} = \frac{65 + 51 - 44}{15} = \frac{72}{15}
\][/tex]

5. Simplify the Result:

Simplify [tex]\(\frac{72}{15}\)[/tex] by dividing the numerator and the denominator by their greatest common divisor, which is 3:
[tex]\[
\frac{72}{15} = \frac{72 \div 3}{15 \div 3} = \frac{24}{5}
\][/tex]

As a mixed number, this is [tex]\(4 \frac{4}{5}\)[/tex].

So, the result of the expression [tex]\(4 \frac{1}{3} + 3 \frac{2}{5} - 2 \frac{14}{15}\)[/tex] is [tex]\(4 \frac{4}{5}\)[/tex].

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