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Answer :
To solve the problem [tex]\(\frac{14}{15} - \frac{5}{6}\)[/tex], follow these steps:
1. Find a common denominator for the fractions:
- The denominators here are 15 and 6. The least common multiple (LCM) of these two numbers is 30.
2. Convert each fraction to have the common denominator:
- For [tex]\(\frac{14}{15}\)[/tex], multiply both the numerator and the denominator by 2 to get [tex]\(\frac{28}{30}\)[/tex].
- For [tex]\(\frac{5}{6}\)[/tex], multiply both the numerator and the denominator by 5 to get [tex]\(\frac{25}{30}\)[/tex].
3. Subtract the fractions:
- Now, subtract the second fraction from the first: [tex]\(\frac{28}{30} - \frac{25}{30} = \frac{3}{30}\)[/tex].
4. Simplify the result:
- The fraction [tex]\(\frac{3}{30}\)[/tex] can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3: [tex]\(\frac{3}{30} = \frac{1}{10}\)[/tex].
Therefore, [tex]\(\frac{14}{15} - \frac{5}{6} = \frac{1}{10}\)[/tex], which is approximately equal to 0.1. However, due to the nature of floating-point arithmetic in computers, when calculating the exact numerical result, it can be represented as 0.09999999999999998.
1. Find a common denominator for the fractions:
- The denominators here are 15 and 6. The least common multiple (LCM) of these two numbers is 30.
2. Convert each fraction to have the common denominator:
- For [tex]\(\frac{14}{15}\)[/tex], multiply both the numerator and the denominator by 2 to get [tex]\(\frac{28}{30}\)[/tex].
- For [tex]\(\frac{5}{6}\)[/tex], multiply both the numerator and the denominator by 5 to get [tex]\(\frac{25}{30}\)[/tex].
3. Subtract the fractions:
- Now, subtract the second fraction from the first: [tex]\(\frac{28}{30} - \frac{25}{30} = \frac{3}{30}\)[/tex].
4. Simplify the result:
- The fraction [tex]\(\frac{3}{30}\)[/tex] can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3: [tex]\(\frac{3}{30} = \frac{1}{10}\)[/tex].
Therefore, [tex]\(\frac{14}{15} - \frac{5}{6} = \frac{1}{10}\)[/tex], which is approximately equal to 0.1. However, due to the nature of floating-point arithmetic in computers, when calculating the exact numerical result, it can be represented as 0.09999999999999998.
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