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Answer :
Sure, let's tackle this step-by-step.
1. Finding the Least Common Denominator (LCD):
We have two fractions: [tex]\(\frac{14}{15}\)[/tex] and [tex]\(\frac{8}{25}\)[/tex].
To find the least common denominator (LCD) of the fractions, we need to find the least common multiple (LCM) of the denominators 15 and 25.
- The prime factorization of 15 is [tex]\(3 \times 5\)[/tex].
- The prime factorization of 25 is [tex]\(5 \times 5\)[/tex].
To find the LCM, we take each prime number the greatest number of times it occurs in any of the factorizations:
- The number 3 appears once in 15.
- The number 5 appears twice (as [tex]\(5 \times 5\)[/tex]) in 25.
Therefore, the LCM of 15 and 25 is [tex]\(3 \times 5 \times 5 = 75\)[/tex].
So, the least common denominator is 75.
2. Adding the Fractions:
We need to add the fractions [tex]\(\frac{14}{15}\)[/tex], [tex]\(\frac{11}{15}\)[/tex], and [tex]\(\frac{1}{15}\)[/tex].
Since the denominators are the same (15), we can directly add the numerators:
- Add the numerators: [tex]\(14 + 11 + 1 = 26\)[/tex].
- The denominator remains the same, which is 15.
Therefore, [tex]\(\frac{14}{15} + \frac{11}{15} + \frac{1}{15} = \frac{26}{15}\)[/tex].
In summary, the LCD for the fractions [tex]\(\frac{14}{15}\)[/tex] and [tex]\(\frac{8}{25}\)[/tex] is 75, and the result of adding the fractions [tex]\(\frac{14}{15}\)[/tex], [tex]\(\frac{11}{15}\)[/tex], and [tex]\(\frac{1}{15}\)[/tex] is [tex]\(\frac{26}{15}\)[/tex].
1. Finding the Least Common Denominator (LCD):
We have two fractions: [tex]\(\frac{14}{15}\)[/tex] and [tex]\(\frac{8}{25}\)[/tex].
To find the least common denominator (LCD) of the fractions, we need to find the least common multiple (LCM) of the denominators 15 and 25.
- The prime factorization of 15 is [tex]\(3 \times 5\)[/tex].
- The prime factorization of 25 is [tex]\(5 \times 5\)[/tex].
To find the LCM, we take each prime number the greatest number of times it occurs in any of the factorizations:
- The number 3 appears once in 15.
- The number 5 appears twice (as [tex]\(5 \times 5\)[/tex]) in 25.
Therefore, the LCM of 15 and 25 is [tex]\(3 \times 5 \times 5 = 75\)[/tex].
So, the least common denominator is 75.
2. Adding the Fractions:
We need to add the fractions [tex]\(\frac{14}{15}\)[/tex], [tex]\(\frac{11}{15}\)[/tex], and [tex]\(\frac{1}{15}\)[/tex].
Since the denominators are the same (15), we can directly add the numerators:
- Add the numerators: [tex]\(14 + 11 + 1 = 26\)[/tex].
- The denominator remains the same, which is 15.
Therefore, [tex]\(\frac{14}{15} + \frac{11}{15} + \frac{1}{15} = \frac{26}{15}\)[/tex].
In summary, the LCD for the fractions [tex]\(\frac{14}{15}\)[/tex] and [tex]\(\frac{8}{25}\)[/tex] is 75, and the result of adding the fractions [tex]\(\frac{14}{15}\)[/tex], [tex]\(\frac{11}{15}\)[/tex], and [tex]\(\frac{1}{15}\)[/tex] is [tex]\(\frac{26}{15}\)[/tex].
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