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Answer :
To subtract the fractions [tex]\(\frac{9}{10}\)[/tex] and [tex]\(\frac{1}{12}\)[/tex], we first need to find a common denominator. The denominators here are 10 and 12, so we find the least common multiple (LCM) of these numbers.
1. Find the Least Common Multiple (LCM):
- List the multiples of each denominator:
- Multiples of 10: 10, 20, 30, 40, 50, 60, ...
- Multiples of 12: 12, 24, 36, 48, 60, ...
- The smallest common multiple is 60, so 60 is the LCM.
2. Convert each fraction to have the common denominator:
- For [tex]\(\frac{9}{10}\)[/tex]:
- To convert [tex]\(\frac{9}{10}\)[/tex] to a denominator of 60, multiply both the numerator and denominator by 6:
[tex]\[
\frac{9}{10} \times \frac{6}{6} = \frac{54}{60}
\][/tex]
- For [tex]\(\frac{1}{12}\)[/tex]:
- To convert [tex]\(\frac{1}{12}\)[/tex] to a denominator of 60, multiply both the numerator and denominator by 5:
[tex]\[
\frac{1}{12} \times \frac{5}{5} = \frac{5}{60}
\][/tex]
3. Subtract the converted fractions:
- Now that both fractions have the same denominator, we can subtract the numerators:
[tex]\[
\frac{54}{60} - \frac{5}{60} = \frac{54 - 5}{60} = \frac{49}{60}
\][/tex]
Therefore, the result of [tex]\(\frac{9}{10} - \frac{1}{12}\)[/tex] is [tex]\(\frac{49}{60}\)[/tex].
1. Find the Least Common Multiple (LCM):
- List the multiples of each denominator:
- Multiples of 10: 10, 20, 30, 40, 50, 60, ...
- Multiples of 12: 12, 24, 36, 48, 60, ...
- The smallest common multiple is 60, so 60 is the LCM.
2. Convert each fraction to have the common denominator:
- For [tex]\(\frac{9}{10}\)[/tex]:
- To convert [tex]\(\frac{9}{10}\)[/tex] to a denominator of 60, multiply both the numerator and denominator by 6:
[tex]\[
\frac{9}{10} \times \frac{6}{6} = \frac{54}{60}
\][/tex]
- For [tex]\(\frac{1}{12}\)[/tex]:
- To convert [tex]\(\frac{1}{12}\)[/tex] to a denominator of 60, multiply both the numerator and denominator by 5:
[tex]\[
\frac{1}{12} \times \frac{5}{5} = \frac{5}{60}
\][/tex]
3. Subtract the converted fractions:
- Now that both fractions have the same denominator, we can subtract the numerators:
[tex]\[
\frac{54}{60} - \frac{5}{60} = \frac{54 - 5}{60} = \frac{49}{60}
\][/tex]
Therefore, the result of [tex]\(\frac{9}{10} - \frac{1}{12}\)[/tex] is [tex]\(\frac{49}{60}\)[/tex].
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