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Answer :
To find the fraction that is halfway between [tex]\(\frac{4}{5}\)[/tex] and [tex]\(\frac{14}{15}\)[/tex], follow these steps:
1. Convert the fractions to common denominators:
- The denominators are 5 and 15. The least common denominator for these two is 15.
- Convert [tex]\(\frac{4}{5}\)[/tex] to a fraction with the denominator of 15:
[tex]\[
\frac{4}{5} = \frac{4 \times 3}{5 \times 3} = \frac{12}{15}
\][/tex]
2. Identify the fractions with a common denominator:
- Now, we have [tex]\(\frac{12}{15}\)[/tex] and [tex]\(\frac{14}{15}\)[/tex].
3. Calculate the halfway point:
- To find a fraction that is halfway between [tex]\(\frac{12}{15}\)[/tex] and [tex]\(\frac{14}{15}\)[/tex], average the numerators:
[tex]\[
\frac{12 + 14}{2} = \frac{26}{2} = 13
\][/tex]
- So the fraction halfway between is [tex]\(\frac{13}{15}\)[/tex].
4. Simplify the fraction if possible:
- Check if [tex]\(\frac{13}{15}\)[/tex] can be simplified. Since 13 is a prime number and does not divide evenly into 15, [tex]\(\frac{13}{15}\)[/tex] is already in its simplest form.
Therefore, the fraction halfway between [tex]\(\frac{4}{5}\)[/tex] and [tex]\(\frac{14}{15}\)[/tex] is [tex]\(\frac{13}{15}\)[/tex].
1. Convert the fractions to common denominators:
- The denominators are 5 and 15. The least common denominator for these two is 15.
- Convert [tex]\(\frac{4}{5}\)[/tex] to a fraction with the denominator of 15:
[tex]\[
\frac{4}{5} = \frac{4 \times 3}{5 \times 3} = \frac{12}{15}
\][/tex]
2. Identify the fractions with a common denominator:
- Now, we have [tex]\(\frac{12}{15}\)[/tex] and [tex]\(\frac{14}{15}\)[/tex].
3. Calculate the halfway point:
- To find a fraction that is halfway between [tex]\(\frac{12}{15}\)[/tex] and [tex]\(\frac{14}{15}\)[/tex], average the numerators:
[tex]\[
\frac{12 + 14}{2} = \frac{26}{2} = 13
\][/tex]
- So the fraction halfway between is [tex]\(\frac{13}{15}\)[/tex].
4. Simplify the fraction if possible:
- Check if [tex]\(\frac{13}{15}\)[/tex] can be simplified. Since 13 is a prime number and does not divide evenly into 15, [tex]\(\frac{13}{15}\)[/tex] is already in its simplest form.
Therefore, the fraction halfway between [tex]\(\frac{4}{5}\)[/tex] and [tex]\(\frac{14}{15}\)[/tex] is [tex]\(\frac{13}{15}\)[/tex].
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