To solve the problem of adding the mixed fractions [tex]\(2 \frac{7}{8}\)[/tex] and [tex]\(1 \frac{11}{20}\)[/tex], follow these steps:
1. Convert mixed fractions to improper fractions:
- For [tex]\(2 \frac{7}{8}\)[/tex]:
- Convert the whole number to a fraction: [tex]\(2 = \frac{16}{8}\)[/tex]
- Add the fractional part: [tex]\(\frac{16}{8} + \frac{7}{8} = \frac{23}{8}\)[/tex]
- For [tex]\(1 \frac{11}{20}\)[/tex]:
- Convert the whole number to a fraction: [tex]\(1 = \frac{20}{20}\)[/tex]
- Add the fractional part: [tex]\(\frac{20}{20} + \frac{11}{20} = \frac{31}{20}\)[/tex]
2. Find the common denominator:
- The denominators are 8 and 20. The least common multiple (LCM) of 8 and 20 is 160.
3. Convert each fraction to have the common denominator:
- For [tex]\(\frac{23}{8}\)[/tex]:
- Multiply the numerator and denominator by 20 to get the new fraction: [tex]\(\frac{23 \times 20}{8 \times 20} = \frac{460}{160}\)[/tex]
- For [tex]\(\frac{31}{20}\)[/tex]:
- Multiply the numerator and denominator by 8 to get the new fraction: [tex]\(\frac{31 \times 8}{20 \times 8} = \frac{248}{160}\)[/tex]
4. Add the fractions:
- Now that both fractions have the same denominator, add the numerators:
[tex]\[
\frac{460}{160} + \frac{248}{160} = \frac{460 + 248}{160} = \frac{708}{160}
\][/tex]
5. Simplify the fraction if possible:
- Dividing both numerator and denominator by 4:
[tex]\[
\frac{708 \div 4}{160 \div 4} = \frac{177}{40}
\][/tex]
6. Convert the improper fraction to a mixed number:
- Divide 177 by 40:
[tex]\[
177 \div 40 = 4 \text{ remainder } 17
\][/tex]
- So, [tex]\(\frac{177}{40} = 4 \frac{17}{40}\)[/tex]
Thus, the sum of the given fractions [tex]\(2 \frac{7}{8} + 1 \frac{11}{20}\)[/tex] is [tex]\(4 \frac{17}{40}\)[/tex].
