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Answer :
Let's add the mixed numbers [tex]\(6 \frac{38}{45}\)[/tex] and [tex]\(2 \frac{5}{9}\)[/tex] together step-by-step:
1. Convert Mixed Numbers to Improper Fractions:
- For [tex]\(6 \frac{38}{45}\)[/tex]:
- Multiply the whole number by the denominator: [tex]\(6 \times 45 = 270\)[/tex].
- Add the numerator: [tex]\(270 + 38 = 308\)[/tex].
- The improper fraction is [tex]\(\frac{308}{45}\)[/tex].
- For [tex]\(2 \frac{5}{9}\)[/tex]:
- Multiply the whole number by the denominator: [tex]\(2 \times 9 = 18\)[/tex].
- Add the numerator: [tex]\(18 + 5 = 23\)[/tex].
- The improper fraction is [tex]\(\frac{23}{9}\)[/tex].
2. Find a Common Denominator:
- The denominators are 45 and 9. The least common multiple (LCM) of 45 and 9 is 45.
3. Convert Fractions to Have a Common Denominator:
- The fraction [tex]\(\frac{308}{45}\)[/tex] already has the denominator 45.
- Convert [tex]\(\frac{23}{9}\)[/tex] to have a denominator of 45:
- Multiply both the numerator and the denominator by 5: [tex]\(\frac{23 \times 5}{9 \times 5} = \frac{115}{45}\)[/tex].
4. Add the Fractions:
- Add the numerators: [tex]\(308 + 115 = 423\)[/tex].
- The resulting fraction is [tex]\(\frac{423}{45}\)[/tex].
5. Convert the Improper Fraction Back to a Mixed Number:
- Divide the numerator by the denominator: [tex]\(423 \div 45 = 9\)[/tex] with a remainder of [tex]\(18\)[/tex].
- The mixed number is [tex]\(9 \frac{18}{45}\)[/tex].
6. Simplify the Fraction:
- Find the greatest common divisor (GCD) of 18 and 45, which is 9.
- Simplify the fraction: [tex]\(\frac{18 \div 9}{45 \div 9} = \frac{2}{5}\)[/tex].
Therefore, the sum of [tex]\(6 \frac{38}{45} + 2 \frac{5}{9}\)[/tex] is [tex]\(9 \frac{2}{5}\)[/tex].
1. Convert Mixed Numbers to Improper Fractions:
- For [tex]\(6 \frac{38}{45}\)[/tex]:
- Multiply the whole number by the denominator: [tex]\(6 \times 45 = 270\)[/tex].
- Add the numerator: [tex]\(270 + 38 = 308\)[/tex].
- The improper fraction is [tex]\(\frac{308}{45}\)[/tex].
- For [tex]\(2 \frac{5}{9}\)[/tex]:
- Multiply the whole number by the denominator: [tex]\(2 \times 9 = 18\)[/tex].
- Add the numerator: [tex]\(18 + 5 = 23\)[/tex].
- The improper fraction is [tex]\(\frac{23}{9}\)[/tex].
2. Find a Common Denominator:
- The denominators are 45 and 9. The least common multiple (LCM) of 45 and 9 is 45.
3. Convert Fractions to Have a Common Denominator:
- The fraction [tex]\(\frac{308}{45}\)[/tex] already has the denominator 45.
- Convert [tex]\(\frac{23}{9}\)[/tex] to have a denominator of 45:
- Multiply both the numerator and the denominator by 5: [tex]\(\frac{23 \times 5}{9 \times 5} = \frac{115}{45}\)[/tex].
4. Add the Fractions:
- Add the numerators: [tex]\(308 + 115 = 423\)[/tex].
- The resulting fraction is [tex]\(\frac{423}{45}\)[/tex].
5. Convert the Improper Fraction Back to a Mixed Number:
- Divide the numerator by the denominator: [tex]\(423 \div 45 = 9\)[/tex] with a remainder of [tex]\(18\)[/tex].
- The mixed number is [tex]\(9 \frac{18}{45}\)[/tex].
6. Simplify the Fraction:
- Find the greatest common divisor (GCD) of 18 and 45, which is 9.
- Simplify the fraction: [tex]\(\frac{18 \div 9}{45 \div 9} = \frac{2}{5}\)[/tex].
Therefore, the sum of [tex]\(6 \frac{38}{45} + 2 \frac{5}{9}\)[/tex] is [tex]\(9 \frac{2}{5}\)[/tex].
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