Answer :
To solve the problem of adding the fractions [tex]\(\frac{3}{5}\)[/tex] and [tex]\(\frac{1}{6}\)[/tex], follow these steps:
1. Find a Common Denominator:
- The denominators of the fractions are 5 and 6.
- To add these fractions, we need a common denominator. The least common multiple (LCM) of 5 and 6 is 30.
2. Convert Each Fraction to Have the Common Denominator:
- For [tex]\(\frac{3}{5}\)[/tex], convert it to a fraction with a denominator of 30.
- Multiply both the numerator and the denominator by 6: [tex]\[ \frac{3}{5} = \frac{3 \times 6}{5 \times 6} = \frac{18}{30} \][/tex]
- For [tex]\(\frac{1}{6}\)[/tex], convert it to a fraction with a denominator of 30.
- Multiply both the numerator and the denominator by 5: [tex]\[ \frac{1}{6} = \frac{1 \times 5}{6 \times 5} = \frac{5}{30} \][/tex]
3. Add the Fractions:
- Now that both fractions have the same denominator, add the numerators: [tex]\[ \frac{18}{30} + \frac{5}{30} = \frac{18 + 5}{30} = \frac{23}{30} \][/tex]
4. Simplify if Necessary:
- The fraction [tex]\(\frac{23}{30}\)[/tex] is already in its simplest form because 23 and 30 have no common factors other than 1.
So, the sum of [tex]\(\frac{3}{5}\)[/tex] and [tex]\(\frac{1}{6}\)[/tex] is [tex]\(\frac{23}{30}\)[/tex].
1. Find a Common Denominator:
- The denominators of the fractions are 5 and 6.
- To add these fractions, we need a common denominator. The least common multiple (LCM) of 5 and 6 is 30.
2. Convert Each Fraction to Have the Common Denominator:
- For [tex]\(\frac{3}{5}\)[/tex], convert it to a fraction with a denominator of 30.
- Multiply both the numerator and the denominator by 6: [tex]\[ \frac{3}{5} = \frac{3 \times 6}{5 \times 6} = \frac{18}{30} \][/tex]
- For [tex]\(\frac{1}{6}\)[/tex], convert it to a fraction with a denominator of 30.
- Multiply both the numerator and the denominator by 5: [tex]\[ \frac{1}{6} = \frac{1 \times 5}{6 \times 5} = \frac{5}{30} \][/tex]
3. Add the Fractions:
- Now that both fractions have the same denominator, add the numerators: [tex]\[ \frac{18}{30} + \frac{5}{30} = \frac{18 + 5}{30} = \frac{23}{30} \][/tex]
4. Simplify if Necessary:
- The fraction [tex]\(\frac{23}{30}\)[/tex] is already in its simplest form because 23 and 30 have no common factors other than 1.
So, the sum of [tex]\(\frac{3}{5}\)[/tex] and [tex]\(\frac{1}{6}\)[/tex] is [tex]\(\frac{23}{30}\)[/tex].
