To solve the problem of adding the fractions [tex]\( \frac{2}{3} + \frac{5}{6} \)[/tex] and putting the answer in the simplest form, follow these steps:
1. Identify the fractions:
First, we have the fractions [tex]\( \frac{2}{3} \)[/tex] and [tex]\( \frac{5}{6} \)[/tex].
2. Find a common denominator:
To add these fractions, we need a common denominator. The denominators are 3 and 6. The least common multiple (LCM) of 3 and 6 is 6.
3. Convert the fractions to have the common denominator:
- For [tex]\( \frac{2}{3} \)[/tex], we need to convert it to a fraction with a denominator of 6. We can do this by multiplying both the numerator and the denominator by 2:
[tex]\[
\frac{2}{3} \times \frac{2}{2} = \frac{4}{6}
\][/tex]
- [tex]\( \frac{5}{6} \)[/tex] already has the denominator of 6, so it remains [tex]\( \frac{5}{6} \)[/tex].
4. Add the numerators:
Now that both fractions have the same denominator, we can add the numerators:
[tex]\[
\frac{4}{6} + \frac{5}{6} = \frac{4 + 5}{6} = \frac{9}{6}
\][/tex]
5. Simplify the fraction:
We need to simplify [tex]\( \frac{9}{6} \)[/tex]. To do this, we find the greatest common divisor (GCD) of 9 and 6, which is 3. Then we divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{9 \div 3}{6 \div 3} = \frac{3}{2}
\][/tex]
6. Conclusion:
The simplest form of [tex]\( \frac{9}{6} \)[/tex] is [tex]\( \frac{3}{2} \)[/tex].
Therefore, the answer to [tex]\( \frac{2}{3} + \frac{5}{6} \)[/tex] in simplest form is [tex]\( \frac{3}{2} \)[/tex].
