To add the fractions [tex]\(\frac{5}{10}\)[/tex] and [tex]\(\frac{1}{3}\)[/tex], follow these steps:
1. Identify the Fractions:
- The first fraction is [tex]\(\frac{5}{10}\)[/tex].
- The second fraction is [tex]\(\frac{1}{3}\)[/tex].
2. Find a Common Denominator:
- The denominator of [tex]\(\frac{5}{10}\)[/tex] is 10.
- The denominator of [tex]\(\frac{1}{3}\)[/tex] is 3.
- A common denominator for these fractions can be found by taking the least common multiple (LCM) of 10 and 3, which is 30.
3. Convert Each Fraction to the Common Denominator:
- [tex]\(\frac{5}{10}\)[/tex] needs to be converted to a fraction with a denominator of 30. To do this, multiply both the numerator and the denominator by 3:
[tex]\[
\frac{5}{10} = \frac{5 \times 3}{10 \times 3} = \frac{15}{30}
\][/tex]
- [tex]\(\frac{1}{3}\)[/tex] needs to be converted to a fraction with a denominator of 30. To do this, multiply both the numerator and the denominator by 10:
[tex]\[
\frac{1}{3} = \frac{1 \times 10}{3 \times 10} = \frac{10}{30}
\][/tex]
4. Add the Fractions:
- Now that both fractions have the same denominator, you can add the numerators:
[tex]\[
\frac{15}{30} + \frac{10}{30} = \frac{15 + 10}{30} = \frac{25}{30}
\][/tex]
5. Simplify the Result:
- The fraction [tex]\(\frac{25}{30}\)[/tex] can be simplified by finding the greatest common divisor (GCD) of 25 and 30, which is 5:
[tex]\[
\frac{25 \div 5}{30 \div 5} = \frac{5}{6}
\][/tex]
- So, the simplified form of the sum of the fractions is [tex]\(\frac{5}{6}\)[/tex].
6. Convert the Result to Decimal:
- To express the fraction [tex]\(\frac{5}{6}\)[/tex] as a decimal, perform the division [tex]\(5 \div 6\)[/tex]:
[tex]\[
\frac{5}{6} \approx 0.8333333\ldots
\][/tex]
- This can be rounded to approximately 0.8333333333333334.
Final Answer:
[tex]\[
\frac{5}{10} + \frac{1}{3} = \frac{5}{6} \approx 0.8333333333333334
\][/tex]
