Answer :
To add the mixed numbers [tex]\(5 \frac{2}{3} + 2 \frac{1}{5}\)[/tex] and write the answer as a mixed number, follow these steps:
1. Convert Mixed Numbers to Improper Fractions:
- For [tex]\(5 \frac{2}{3}\)[/tex], multiply the whole number 5 by the denominator 3, then add the numerator 2. This gives you an improper fraction:
[tex]\[
5 \times 3 + 2 = 15 + 2 = \frac{17}{3}
\][/tex]
- For [tex]\(2 \frac{1}{5}\)[/tex], multiply the whole number 2 by the denominator 5, then add the numerator 1. This gives you:
[tex]\[
2 \times 5 + 1 = 10 + 1 = \frac{11}{5}
\][/tex]
2. Find a Common Denominator:
- The denominators are 3 and 5. The least common denominator is 15.
3. Convert Fractions to the Same Denominator:
- Convert [tex]\(\frac{17}{3}\)[/tex] to a fraction with denominator 15:
[tex]\[
\frac{17 \times 5}{3 \times 5} = \frac{85}{15}
\][/tex]
- Convert [tex]\(\frac{11}{5}\)[/tex] to a fraction with denominator 15:
[tex]\[
\frac{11 \times 3}{5 \times 3} = \frac{33}{15}
\][/tex]
4. Add the Fractions:
- Add the numerators of the converted fractions:
[tex]\[
\frac{85}{15} + \frac{33}{15} = \frac{118}{15}
\][/tex]
5. Convert the Improper Fraction to a Mixed Number:
- Divide the numerator 118 by the denominator 15 to find the whole number part:
[tex]\[
118 \div 15 = 7 \quad \text{with a remainder of} \quad 13
\][/tex]
- This gives you a whole number 7 and a fractional part [tex]\(\frac{13}{15}\)[/tex].
Combining these gives you the mixed number:
[tex]\[
7 \frac{13}{15}
\][/tex]
So, the final answer for adding these mixed numbers is [tex]\(7 \frac{13}{15}\)[/tex].
1. Convert Mixed Numbers to Improper Fractions:
- For [tex]\(5 \frac{2}{3}\)[/tex], multiply the whole number 5 by the denominator 3, then add the numerator 2. This gives you an improper fraction:
[tex]\[
5 \times 3 + 2 = 15 + 2 = \frac{17}{3}
\][/tex]
- For [tex]\(2 \frac{1}{5}\)[/tex], multiply the whole number 2 by the denominator 5, then add the numerator 1. This gives you:
[tex]\[
2 \times 5 + 1 = 10 + 1 = \frac{11}{5}
\][/tex]
2. Find a Common Denominator:
- The denominators are 3 and 5. The least common denominator is 15.
3. Convert Fractions to the Same Denominator:
- Convert [tex]\(\frac{17}{3}\)[/tex] to a fraction with denominator 15:
[tex]\[
\frac{17 \times 5}{3 \times 5} = \frac{85}{15}
\][/tex]
- Convert [tex]\(\frac{11}{5}\)[/tex] to a fraction with denominator 15:
[tex]\[
\frac{11 \times 3}{5 \times 3} = \frac{33}{15}
\][/tex]
4. Add the Fractions:
- Add the numerators of the converted fractions:
[tex]\[
\frac{85}{15} + \frac{33}{15} = \frac{118}{15}
\][/tex]
5. Convert the Improper Fraction to a Mixed Number:
- Divide the numerator 118 by the denominator 15 to find the whole number part:
[tex]\[
118 \div 15 = 7 \quad \text{with a remainder of} \quad 13
\][/tex]
- This gives you a whole number 7 and a fractional part [tex]\(\frac{13}{15}\)[/tex].
Combining these gives you the mixed number:
[tex]\[
7 \frac{13}{15}
\][/tex]
So, the final answer for adding these mixed numbers is [tex]\(7 \frac{13}{15}\)[/tex].
