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Answer :
To subtract the fractions [tex]\(\frac{13}{15}\)[/tex] and [tex]\(\frac{1}{6}\)[/tex], we'll follow these steps:
1. Find a common denominator:
To subtract fractions, you need to have the same denominator. The denominators we have are 15 and 6. The least common multiple (LCM) of 15 and 6 is 30.
2. Convert each fraction to have the common denominator:
- Convert [tex]\(\frac{13}{15}\)[/tex] to a fraction with a denominator of 30:
[tex]\[
\frac{13}{15} = \frac{13 \times 2}{15 \times 2} = \frac{26}{30}
\][/tex]
- Convert [tex]\(\frac{1}{6}\)[/tex] to a fraction with a denominator of 30:
[tex]\[
\frac{1}{6} = \frac{1 \times 5}{6 \times 5} = \frac{5}{30}
\][/tex]
3. Subtract the fractions:
Now that both fractions have the same denominator, you can subtract the numerators:
[tex]\[
\frac{26}{30} - \frac{5}{30} = \frac{26 - 5}{30} = \frac{21}{30}
\][/tex]
4. Simplify the result:
Finally, simplify [tex]\(\frac{21}{30}\)[/tex] by finding the greatest common divisor (GCD) of 21 and 30, which is 3.
[tex]\[
\frac{21}{30} = \frac{21 \div 3}{30 \div 3} = \frac{7}{10}
\][/tex]
So, the simplified result of [tex]\(\frac{13}{15} - \frac{1}{6}\)[/tex] is [tex]\(\frac{7}{10}\)[/tex].
1. Find a common denominator:
To subtract fractions, you need to have the same denominator. The denominators we have are 15 and 6. The least common multiple (LCM) of 15 and 6 is 30.
2. Convert each fraction to have the common denominator:
- Convert [tex]\(\frac{13}{15}\)[/tex] to a fraction with a denominator of 30:
[tex]\[
\frac{13}{15} = \frac{13 \times 2}{15 \times 2} = \frac{26}{30}
\][/tex]
- Convert [tex]\(\frac{1}{6}\)[/tex] to a fraction with a denominator of 30:
[tex]\[
\frac{1}{6} = \frac{1 \times 5}{6 \times 5} = \frac{5}{30}
\][/tex]
3. Subtract the fractions:
Now that both fractions have the same denominator, you can subtract the numerators:
[tex]\[
\frac{26}{30} - \frac{5}{30} = \frac{26 - 5}{30} = \frac{21}{30}
\][/tex]
4. Simplify the result:
Finally, simplify [tex]\(\frac{21}{30}\)[/tex] by finding the greatest common divisor (GCD) of 21 and 30, which is 3.
[tex]\[
\frac{21}{30} = \frac{21 \div 3}{30 \div 3} = \frac{7}{10}
\][/tex]
So, the simplified result of [tex]\(\frac{13}{15} - \frac{1}{6}\)[/tex] is [tex]\(\frac{7}{10}\)[/tex].
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