Absolutely! Let's go through the process step-by-step to add the fractions [tex]\(\frac{10}{6}\)[/tex] and [tex]\(\frac{3}{6}\)[/tex] and then convert the result to a mixed number.
### Step 1: Add the Fractions
Since the denominators of the fractions are the same, we can directly add the numerators:
[tex]\[
\frac{10}{6} + \frac{3}{6} = \frac{10 + 3}{6} = \frac{13}{6}
\][/tex]
So, the sum of the fractions [tex]\(\frac{10}{6}\)[/tex] and [tex]\(\frac{3}{6}\)[/tex] is [tex]\(\frac{13}{6}\)[/tex].
### Step 2: Simplify the Fraction (if needed)
First, check if the fraction [tex]\(\frac{13}{6}\)[/tex] can be simplified. To simplify, we find the greatest common divisor (GCD) of 13 and 6.
The GCD of 13 and 6 is 1, so [tex]\(\frac{13}{6}\)[/tex] cannot be simplified further and remains [tex]\(\frac{13}{6}\)[/tex].
### Step 3: Convert to a Mixed Number
To convert the improper fraction [tex]\(\frac{13}{6}\)[/tex] to a mixed number, we perform the division of the numerator by the denominator:
[tex]\[
13 \div 6 = 2 \text{ R } 1
\][/tex]
Here, 13 divided by 6 gives a quotient of 2 and a remainder of 1. This can be written as a mixed number:
[tex]\[
\frac{13}{6} = 2 \frac{1}{6}
\][/tex]
### Final Answer
Combining all the steps, the fractions [tex]\(\frac{10}{6} + \frac{3}{6} = \frac{13}{6}\)[/tex] can be expressed as the mixed number [tex]\(2 \frac{1}{6}\)[/tex].
To summarize the steps clearly:
1. [tex]\(\frac{10}{6} + \frac{3}{6} = \frac{13}{6}\)[/tex]
2. Simplified form: [tex]\(\frac{13}{6}\)[/tex]
3. Mixed number: [tex]\(2 \frac{1}{6}\)[/tex]
With these steps, the final result of adding [tex]\(\frac{10}{6}\)[/tex] and [tex]\(\frac{3}{6}\)[/tex] and converting it to a mixed number is [tex]\(2 \frac{1}{6}\)[/tex].
