Sure, let's solve the problem:
You need to add two mixed fractions: [tex]\(9 \frac{1}{3}\)[/tex] and [tex]\(3 \frac{2}{4}\)[/tex].
Step-by-Step Solution:
1. Convert the mixed fractions to improper fractions:
- For [tex]\(9 \frac{1}{3}\)[/tex]:
The whole number part is 9, and the fractional part is [tex]\(\frac{1}{3}\)[/tex].
To convert a mixed fraction to an improper fraction, we use the formula:
[tex]\[
\text{Improper Fraction} = \text{Whole Part} \times \text{Denominator} + \text{Numerator}
\][/tex]
So for [tex]\(9 \frac{1}{3}\)[/tex]:
[tex]\[
9 \times 3 + 1 = 27 + 1 = 28
\][/tex]
Therefore, [tex]\(9 \frac{1}{3} = \frac{28}{3}\)[/tex].
- For [tex]\(3 \frac{2}{4}\)[/tex]:
The whole number part is 3, and the fractional part is [tex]\(\frac{2}{4}\)[/tex].
Simplify [tex]\(\frac{2}{4}\)[/tex] to [tex]\(\frac{1}{2}\)[/tex].
Now, convert [tex]\(3 \frac{1}{2}\)[/tex] to an improper fraction:
[tex]\[
3 \times 2 + 1 = 6 + 1 = 7
\][/tex]
Therefore, [tex]\(3 \frac{1}{2} = \frac{7}{2}\)[/tex].
2. Convert the improper fractions to a common denominator:
- Fractions [tex]\(\frac{28}{3}\)[/tex] and [tex]\(\frac{7}{2}\)[/tex] need a common denominator to be added. The least common multiple of 3 and 2 is 6.
Convert [tex]\(\frac{28}{3}\)[/tex] to a denominator of 6:
[tex]\[
\frac{28}{3} \times \frac{2}{2} = \frac{56}{6}
\][/tex]
Convert [tex]\(\frac{7}{2}\)[/tex] to a denominator of 6:
[tex]\[
\frac{7}{2} \times \frac{3}{3} = \frac{21}{6}
\][/tex]
3. Add the fractions:
Now that both fractions have a common denominator, we can add them:
[tex]\[
\frac{56}{6} + \frac{21}{6} = \frac{77}{6}
\][/tex]
4. Convert the resulting improper fraction back to a mixed number:
Divide 77 by 6:
[tex]\[
77 \div 6 = 12 \, \text{remainder} \, 5
\][/tex]
So,
[tex]\[
\frac{77}{6} = 12 \frac{5}{6}
\][/tex]
Therefore, the result of adding [tex]\(9 \frac{1}{3}\)[/tex] and [tex]\(3 \frac{2}{4}\)[/tex] is [tex]\(12 \frac{5}{6}\)[/tex].
When we approximate these fractions/calculations to the decimal form, we get:
[tex]\[ 9 \frac{1}{3} \approx 9.333333333333334 \][/tex]
[tex]\[ 3 \frac{2}{4} \approx 3.5 \][/tex]
Adding these gives us:
[tex]\[ 12.833333333333334 \][/tex]
So, numerically approximated, the sum is approximately [tex]\(12.833333333333334\)[/tex].
