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Answer :
To solve the subtraction problem [tex]\(\frac{9}{10} - \frac{1}{12}\)[/tex], we need to perform fraction subtraction by first finding a common denominator.
### Step 1: Find the Least Common Denominator (LCD)
The denominators in our fractions are 10 and 12. The least common multiple of these two numbers is 60. So, 60 will be our common denominator.
### Step 2: Convert Fractions to Have the Common Denominator
Convert each fraction to have the denominator of 60:
1. [tex]\(\frac{9}{10}\)[/tex]:
- To convert [tex]\(\frac{9}{10}\)[/tex] to a fraction with a denominator of 60, multiply both the numerator and the denominator by 6.
- [tex]\(\frac{9 \times 6}{10 \times 6} = \frac{54}{60}\)[/tex].
2. [tex]\(\frac{1}{12}\)[/tex]:
- To convert [tex]\(\frac{1}{12}\)[/tex] to a fraction with a denominator of 60, multiply both the numerator and the denominator by 5.
- [tex]\(\frac{1 \times 5}{12 \times 5} = \frac{5}{60}\)[/tex].
### Step 3: Subtract the Fractions
Now subtract the two fractions:
[tex]\[
\frac{54}{60} - \frac{5}{60} = \frac{54 - 5}{60} = \frac{49}{60}
\][/tex]
### Step 4: Simplify the Result
The fraction [tex]\(\frac{49}{60}\)[/tex] is already in its simplest form because 49 and 60 have no common factors other than 1.
Therefore, the result of [tex]\(\frac{9}{10} - \frac{1}{12}\)[/tex] is [tex]\(\frac{49}{60}\)[/tex].
In the options provided, [tex]\(\frac{49}{60}\)[/tex] matches one of the given answers.
### Step 1: Find the Least Common Denominator (LCD)
The denominators in our fractions are 10 and 12. The least common multiple of these two numbers is 60. So, 60 will be our common denominator.
### Step 2: Convert Fractions to Have the Common Denominator
Convert each fraction to have the denominator of 60:
1. [tex]\(\frac{9}{10}\)[/tex]:
- To convert [tex]\(\frac{9}{10}\)[/tex] to a fraction with a denominator of 60, multiply both the numerator and the denominator by 6.
- [tex]\(\frac{9 \times 6}{10 \times 6} = \frac{54}{60}\)[/tex].
2. [tex]\(\frac{1}{12}\)[/tex]:
- To convert [tex]\(\frac{1}{12}\)[/tex] to a fraction with a denominator of 60, multiply both the numerator and the denominator by 5.
- [tex]\(\frac{1 \times 5}{12 \times 5} = \frac{5}{60}\)[/tex].
### Step 3: Subtract the Fractions
Now subtract the two fractions:
[tex]\[
\frac{54}{60} - \frac{5}{60} = \frac{54 - 5}{60} = \frac{49}{60}
\][/tex]
### Step 4: Simplify the Result
The fraction [tex]\(\frac{49}{60}\)[/tex] is already in its simplest form because 49 and 60 have no common factors other than 1.
Therefore, the result of [tex]\(\frac{9}{10} - \frac{1}{12}\)[/tex] is [tex]\(\frac{49}{60}\)[/tex].
In the options provided, [tex]\(\frac{49}{60}\)[/tex] matches one of the given answers.
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