To add the fractions [tex]\(\frac{3}{6} + \frac{10}{12}\)[/tex], we need to follow these steps:
1. Simplify the fractions if possible:
The first fraction [tex]\(\frac{3}{6}\)[/tex] can be simplified. The greatest common divisor (GCD) of 3 and 6 is 3, so:
[tex]\[
\frac{3}{6} = \frac{3 \div 3}{6 \div 3} = \frac{1}{2}
\][/tex]
The second fraction [tex]\(\frac{10}{12}\)[/tex] can also be simplified. The GCD of 10 and 12 is 2, so:
[tex]\[
\frac{10}{12} = \frac{10 \div 2}{12 \div 2} = \frac{5}{6}
\][/tex]
2. Find a common denominator:
To add fractions, we need a common denominator. For [tex]\(\frac{1}{2}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex], the least common multiple (LCM) of 2 and 6 is 6.
3. Adjust the fractions to have the common denominator:
[tex]\(\frac{1}{2}\)[/tex] needs to be converted to a fraction with a denominator of 6:
[tex]\[
\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}
\][/tex]
The fraction [tex]\(\frac{5}{6}\)[/tex] already has the denominator of 6, so it remains:
[tex]\[
\frac{5}{6}
\][/tex]
4. Add the numerators:
Now, with the same denominators, we can add the fractions:
[tex]\[
\frac{3}{6} + \frac{5}{6} = \frac{3 + 5}{6} = \frac{8}{6}
\][/tex]
5. Simplify the resulting fraction:
The fraction [tex]\(\frac{8}{6}\)[/tex] can be simplified. The GCD of 8 and 6 is 2, so:
[tex]\[
\frac{8}{6} = \frac{8 \div 2}{6 \div 2} = \frac{4}{3}
\][/tex]
Therefore, the simplified result of adding [tex]\(\frac{3}{6} + \frac{10}{12}\)[/tex] is:
[tex]\[
\frac{4}{3}
\][/tex]
