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Answer :
To determine the next fraction in the sequence, let's look at the given fractions:
1. [tex]\(\frac{2}{3}\)[/tex]
2. [tex]\(\frac{11}{15}\)[/tex]
3. [tex]\(\frac{4}{5}\)[/tex]
4. [tex]\(\frac{13}{15}\)[/tex]
We want to express each fraction with a common denominator to find a pattern in the sequence. The least common denominator for all these fractions is 15. Let's convert each fraction to have this common denominator:
1. [tex]\(\frac{2}{3}\)[/tex] becomes [tex]\(\frac{10}{15}\)[/tex] [tex]\((2 \times 5 = 10)\)[/tex].
2. [tex]\(\frac{11}{15}\)[/tex] stays [tex]\(\frac{11}{15}\)[/tex].
3. [tex]\(\frac{4}{5}\)[/tex] becomes [tex]\(\frac{12}{15}\)[/tex] [tex]\((4 \times 3 = 12)\)[/tex].
4. [tex]\(\frac{13}{15}\)[/tex] stays [tex]\(\frac{13}{15}\)[/tex].
Now, we see the pattern in the numerators: [tex]\(10, 11, 12, 13\)[/tex].
This shows that the numerators are increasing by 1 each time. Therefore, the next numerator in the sequence is [tex]\(14\)[/tex].
Hence, the next fraction in the sequence is [tex]\(\frac{14}{15}\)[/tex].
Since [tex]\(14\)[/tex] and [tex]\(15\)[/tex] have no common factors other than 1, the fraction [tex]\(\frac{14}{15}\)[/tex] is already in its simplest form.
So, the next fraction in the sequence is [tex]\(\frac{14}{15}\)[/tex].
1. [tex]\(\frac{2}{3}\)[/tex]
2. [tex]\(\frac{11}{15}\)[/tex]
3. [tex]\(\frac{4}{5}\)[/tex]
4. [tex]\(\frac{13}{15}\)[/tex]
We want to express each fraction with a common denominator to find a pattern in the sequence. The least common denominator for all these fractions is 15. Let's convert each fraction to have this common denominator:
1. [tex]\(\frac{2}{3}\)[/tex] becomes [tex]\(\frac{10}{15}\)[/tex] [tex]\((2 \times 5 = 10)\)[/tex].
2. [tex]\(\frac{11}{15}\)[/tex] stays [tex]\(\frac{11}{15}\)[/tex].
3. [tex]\(\frac{4}{5}\)[/tex] becomes [tex]\(\frac{12}{15}\)[/tex] [tex]\((4 \times 3 = 12)\)[/tex].
4. [tex]\(\frac{13}{15}\)[/tex] stays [tex]\(\frac{13}{15}\)[/tex].
Now, we see the pattern in the numerators: [tex]\(10, 11, 12, 13\)[/tex].
This shows that the numerators are increasing by 1 each time. Therefore, the next numerator in the sequence is [tex]\(14\)[/tex].
Hence, the next fraction in the sequence is [tex]\(\frac{14}{15}\)[/tex].
Since [tex]\(14\)[/tex] and [tex]\(15\)[/tex] have no common factors other than 1, the fraction [tex]\(\frac{14}{15}\)[/tex] is already in its simplest form.
So, the next fraction in the sequence is [tex]\(\frac{14}{15}\)[/tex].
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