Answer :
To solve the problem [tex]\(\frac{2}{5} + 1 \frac{4}{9}\)[/tex], we'll follow these steps:
1. Convert the Mixed Number to an Improper Fraction:
The mixed number [tex]\(1 \frac{4}{9}\)[/tex] can be converted to an improper fraction.
Steps:
- Multiply the whole number by the denominator: [tex]\(1 \times 9 = 9\)[/tex].
- Add the result to the numerator: [tex]\(9 + 4 = 13\)[/tex].
- So, [tex]\(1 \frac{4}{9} = \frac{13}{9}\)[/tex].
2. Add the Fractions:
Now add [tex]\(\frac{2}{5}\)[/tex] to [tex]\(\frac{13}{9}\)[/tex].
To add fractions, we first find a common denominator.
3. Find a Common Denominator:
The denominators are 5 and 9.
- The least common multiple (LCM) of 5 and 9 is 45.
4. Convert Each Fraction to Have the Common Denominator:
- [tex]\(\frac{2}{5} = \frac{2 \times 9}{5 \times 9} = \frac{18}{45}\)[/tex]
- [tex]\(\frac{13}{9} = \frac{13 \times 5}{9 \times 5} = \frac{65}{45}\)[/tex]
5. Add the New Fractions:
[tex]\(\frac{18}{45} + \frac{65}{45} = \frac{18 + 65}{45} = \frac{83}{45}\)[/tex]
6. Convert the Improper Fraction to a Mixed Number:
Divide the numerator by the denominator:
- [tex]\(83 \div 45 = 1\)[/tex] with a remainder of 38.
- So, [tex]\(\frac{83}{45}\)[/tex] is equivalent to the mixed number [tex]\(1 \frac{38}{45}\)[/tex].
Thus, the correct answer to the addition [tex]\(\frac{2}{5} + 1 \frac{4}{9}\)[/tex] is [tex]\(1 \frac{38}{45}\)[/tex].
Therefore, the correct option is:
d. [tex]\(1 \frac{38}{45}\)[/tex]
1. Convert the Mixed Number to an Improper Fraction:
The mixed number [tex]\(1 \frac{4}{9}\)[/tex] can be converted to an improper fraction.
Steps:
- Multiply the whole number by the denominator: [tex]\(1 \times 9 = 9\)[/tex].
- Add the result to the numerator: [tex]\(9 + 4 = 13\)[/tex].
- So, [tex]\(1 \frac{4}{9} = \frac{13}{9}\)[/tex].
2. Add the Fractions:
Now add [tex]\(\frac{2}{5}\)[/tex] to [tex]\(\frac{13}{9}\)[/tex].
To add fractions, we first find a common denominator.
3. Find a Common Denominator:
The denominators are 5 and 9.
- The least common multiple (LCM) of 5 and 9 is 45.
4. Convert Each Fraction to Have the Common Denominator:
- [tex]\(\frac{2}{5} = \frac{2 \times 9}{5 \times 9} = \frac{18}{45}\)[/tex]
- [tex]\(\frac{13}{9} = \frac{13 \times 5}{9 \times 5} = \frac{65}{45}\)[/tex]
5. Add the New Fractions:
[tex]\(\frac{18}{45} + \frac{65}{45} = \frac{18 + 65}{45} = \frac{83}{45}\)[/tex]
6. Convert the Improper Fraction to a Mixed Number:
Divide the numerator by the denominator:
- [tex]\(83 \div 45 = 1\)[/tex] with a remainder of 38.
- So, [tex]\(\frac{83}{45}\)[/tex] is equivalent to the mixed number [tex]\(1 \frac{38}{45}\)[/tex].
Thus, the correct answer to the addition [tex]\(\frac{2}{5} + 1 \frac{4}{9}\)[/tex] is [tex]\(1 \frac{38}{45}\)[/tex].
Therefore, the correct option is:
d. [tex]\(1 \frac{38}{45}\)[/tex]
