Answer :
Certainly! Let's simplify the expression [tex]\(\frac{49}{60} - \frac{1}{4}\)[/tex].
To subtract these fractions, we first need a common denominator. The least common multiple (LCM) of 60 and 4 is 60. We'll convert each fraction to have this common denominator.
1. The fraction [tex]\(\frac{49}{60}\)[/tex] already has the denominator 60, so we can leave it as it is.
2. For the fraction [tex]\(\frac{1}{4}\)[/tex], we need to convert it to a fraction with the denominator 60.
[tex]\[
\frac{1}{4} \times \frac{15}{15} = \frac{15}{60}
\][/tex]
Now we have:
[tex]\[
\frac{49}{60} - \frac{15}{60}
\][/tex]
Both fractions now have the same denominator, so we can subtract the numerators:
[tex]\[
\frac{49 - 15}{60} = \frac{34}{60}
\][/tex]
Next, we simplify [tex]\(\frac{34}{60}\)[/tex]. We find the greatest common divisor (GCD) of 34 and 60, which is 2:
[tex]\[
\frac{34 \div 2}{60 \div 2} = \frac{17}{30}
\][/tex]
So, the simplified form is [tex]\(\frac{17}{30}\)[/tex].
Thus, the answer is:
D. [tex]\(\frac{17}{30}\)[/tex]
To subtract these fractions, we first need a common denominator. The least common multiple (LCM) of 60 and 4 is 60. We'll convert each fraction to have this common denominator.
1. The fraction [tex]\(\frac{49}{60}\)[/tex] already has the denominator 60, so we can leave it as it is.
2. For the fraction [tex]\(\frac{1}{4}\)[/tex], we need to convert it to a fraction with the denominator 60.
[tex]\[
\frac{1}{4} \times \frac{15}{15} = \frac{15}{60}
\][/tex]
Now we have:
[tex]\[
\frac{49}{60} - \frac{15}{60}
\][/tex]
Both fractions now have the same denominator, so we can subtract the numerators:
[tex]\[
\frac{49 - 15}{60} = \frac{34}{60}
\][/tex]
Next, we simplify [tex]\(\frac{34}{60}\)[/tex]. We find the greatest common divisor (GCD) of 34 and 60, which is 2:
[tex]\[
\frac{34 \div 2}{60 \div 2} = \frac{17}{30}
\][/tex]
So, the simplified form is [tex]\(\frac{17}{30}\)[/tex].
Thus, the answer is:
D. [tex]\(\frac{17}{30}\)[/tex]
