Answer :
To subtract the fractions [tex]\(\frac{21}{25}\)[/tex] and [tex]\(\frac{14}{15}\)[/tex], follow these steps:
1. Find a common denominator:
The denominators are 25 and 15. Find the least common multiple (LCM) of these two numbers to use as a common denominator.
The LCM of 25 and 15 is 75.
2. Convert each fraction to an equivalent fraction with the common denominator:
- For [tex]\(\frac{21}{25}\)[/tex], multiply both the numerator and the denominator by 3 to convert it:
[tex]\[\frac{21}{25} = \frac{21 \times 3}{25 \times 3} = \frac{63}{75}\][/tex]
- For [tex]\(\frac{14}{15}\)[/tex], multiply both the numerator and the denominator by 5 to convert it:
[tex]\[\frac{14}{15} = \frac{14 \times 5}{15 \times 5} = \frac{70}{75}\][/tex]
3. Perform the subtraction:
With both fractions having a common denominator, subtract the numerators and keep the denominator the same:
[tex]\[\frac{63}{75} - \frac{70}{75} = \frac{63 - 70}{75} = \frac{-7}{75}\][/tex]
4. Simplify the resulting fraction:
In this case, [tex]\(\frac{-7}{75}\)[/tex] is already in its simplest form since 7 and 75 have no common factors other than 1.
Thus, the answer to the subtraction [tex]\(\frac{21}{25} - \frac{14}{15}\)[/tex] is [tex]\(\frac{-7}{75}\)[/tex].
1. Find a common denominator:
The denominators are 25 and 15. Find the least common multiple (LCM) of these two numbers to use as a common denominator.
The LCM of 25 and 15 is 75.
2. Convert each fraction to an equivalent fraction with the common denominator:
- For [tex]\(\frac{21}{25}\)[/tex], multiply both the numerator and the denominator by 3 to convert it:
[tex]\[\frac{21}{25} = \frac{21 \times 3}{25 \times 3} = \frac{63}{75}\][/tex]
- For [tex]\(\frac{14}{15}\)[/tex], multiply both the numerator and the denominator by 5 to convert it:
[tex]\[\frac{14}{15} = \frac{14 \times 5}{15 \times 5} = \frac{70}{75}\][/tex]
3. Perform the subtraction:
With both fractions having a common denominator, subtract the numerators and keep the denominator the same:
[tex]\[\frac{63}{75} - \frac{70}{75} = \frac{63 - 70}{75} = \frac{-7}{75}\][/tex]
4. Simplify the resulting fraction:
In this case, [tex]\(\frac{-7}{75}\)[/tex] is already in its simplest form since 7 and 75 have no common factors other than 1.
Thus, the answer to the subtraction [tex]\(\frac{21}{25} - \frac{14}{15}\)[/tex] is [tex]\(\frac{-7}{75}\)[/tex].
