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Evaluate the expression:

[tex]\(\frac{14}{15} - \frac{1}{3} =\)[/tex]

Answer :

To solve the problem [tex]\(\frac{14}{15} - \frac{1}{3}\)[/tex] and express your answer in simplest form, follow these steps:

1. Find a common denominator:
The denominators here are 15 and 3. The least common denominator (LCD) of 15 and 3 is 15.

2. Convert both fractions to have the common denominator:
[tex]\(\frac{14}{15}\)[/tex] already has the denominator 15.

Convert [tex]\(\frac{1}{3}\)[/tex] to a fraction with denominator 15. To do that, multiply both the numerator and the denominator by 5:
[tex]\[
\frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}
\][/tex]

3. Subtract the fractions:
Now, subtract [tex]\(\frac{5}{15}\)[/tex] from [tex]\(\frac{14}{15}\)[/tex]:
[tex]\[
\frac{14}{15} - \frac{5}{15} = \frac{14 - 5}{15} = \frac{9}{15}
\][/tex]

4. Simplify the result:
To simplify [tex]\(\frac{9}{15}\)[/tex], find the greatest common divisor (GCD) of 9 and 15, which is 3. Divide both the numerator and the denominator by 3:
[tex]\[
\frac{9}{15} = \frac{9 \div 3}{15 \div 3} = \frac{3}{5}
\][/tex]

5. Final Answer:
Therefore, [tex]\(\frac{14}{15} - \frac{1}{3} = \frac{3}{5}\)[/tex].

In decimal form, [tex]\(\frac{3}{5}\)[/tex] equals 0.6, which is consistent with our calculations.

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