Answer :
Let's find the sum of the two numbers: [tex]\(-\frac{2}{5}\)[/tex] and [tex]\(1 \frac{1}{3}\)[/tex].
1. Convert the Mixed Number:
First, convert the mixed number [tex]\(1 \frac{1}{3}\)[/tex] into an improper fraction.
- The wholes are 1, and the fraction part is [tex]\(\frac{1}{3}\)[/tex].
- Convert it to an improper fraction:
[tex]\[ 1 \frac{1}{3} = \frac{3}{3} + \frac{1}{3} = \frac{4}{3} \][/tex]
2. Find a Common Denominator:
To add [tex]\(-\frac{2}{5}\)[/tex] and [tex]\(\frac{4}{3}\)[/tex], we need a common denominator.
- The denominators are 5 and 3. The least common denominator (LCD) is 15.
3. Convert Each Fraction:
Convert each fraction to have the denominator of 15.
- [tex]\(-\frac{2}{5}\)[/tex] can be converted by multiplying both the numerator and denominator by 3:
[tex]\[ -\frac{2}{5} = -\frac{2 \times 3}{5 \times 3} = -\frac{6}{15} \][/tex]
- [tex]\(\frac{4}{3}\)[/tex] can be converted by multiplying both the numerator and denominator by 5:
[tex]\[ \frac{4}{3} = \frac{4 \times 5}{3 \times 5} = \frac{20}{15} \][/tex]
4. Add the Fractions:
Now add the fractions:
[tex]\[ -\frac{6}{15} + \frac{20}{15} = \frac{-6 + 20}{15} = \frac{14}{15} \][/tex]
5. Select the Answer:
The result is [tex]\(\frac{14}{15}\)[/tex].
Therefore, the correct answer is C. [tex]\(\frac{14}{15}\)[/tex].
1. Convert the Mixed Number:
First, convert the mixed number [tex]\(1 \frac{1}{3}\)[/tex] into an improper fraction.
- The wholes are 1, and the fraction part is [tex]\(\frac{1}{3}\)[/tex].
- Convert it to an improper fraction:
[tex]\[ 1 \frac{1}{3} = \frac{3}{3} + \frac{1}{3} = \frac{4}{3} \][/tex]
2. Find a Common Denominator:
To add [tex]\(-\frac{2}{5}\)[/tex] and [tex]\(\frac{4}{3}\)[/tex], we need a common denominator.
- The denominators are 5 and 3. The least common denominator (LCD) is 15.
3. Convert Each Fraction:
Convert each fraction to have the denominator of 15.
- [tex]\(-\frac{2}{5}\)[/tex] can be converted by multiplying both the numerator and denominator by 3:
[tex]\[ -\frac{2}{5} = -\frac{2 \times 3}{5 \times 3} = -\frac{6}{15} \][/tex]
- [tex]\(\frac{4}{3}\)[/tex] can be converted by multiplying both the numerator and denominator by 5:
[tex]\[ \frac{4}{3} = \frac{4 \times 5}{3 \times 5} = \frac{20}{15} \][/tex]
4. Add the Fractions:
Now add the fractions:
[tex]\[ -\frac{6}{15} + \frac{20}{15} = \frac{-6 + 20}{15} = \frac{14}{15} \][/tex]
5. Select the Answer:
The result is [tex]\(\frac{14}{15}\)[/tex].
Therefore, the correct answer is C. [tex]\(\frac{14}{15}\)[/tex].
