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Answer :
To solve the question of finding which fraction is equivalent to [tex]\(\frac{7}{10} + \frac{8}{15}\)[/tex], we need to add these two fractions by finding a common denominator.
### Steps to Solve:
1. Find the Least Common Denominator (LCD):
- The denominators of the fractions [tex]\(\frac{7}{10}\)[/tex] and [tex]\(\frac{8}{15}\)[/tex] are 10 and 15.
- To find the least common denominator, we find the least common multiple (LCM) of these numbers. The LCM of 10 and 15 is 30.
2. Convert Each Fraction to the Common Denominator:
- Convert [tex]\(\frac{7}{10}\)[/tex] to have a denominator of 30:
[tex]\[
\frac{7}{10} = \frac{7 \times 3}{10 \times 3} = \frac{21}{30}
\][/tex]
- Convert [tex]\(\frac{8}{15}\)[/tex] to have a denominator of 30:
[tex]\[
\frac{8}{15} = \frac{8 \times 2}{15 \times 2} = \frac{16}{30}
\][/tex]
3. Add the Fractions:
- Now that both fractions have the same denominator, add the numerators:
[tex]\[
\frac{21}{30} + \frac{16}{30} = \frac{21 + 16}{30} = \frac{37}{30}
\][/tex]
After adding the fractions, the sum [tex]\(\frac{7}{10} + \frac{8}{15}\)[/tex] is equal to [tex]\(\frac{37}{30}\)[/tex].
Thus, the fraction equivalent to [tex]\(\frac{7}{10} + \frac{8}{15}\)[/tex] is [tex]\(\frac{37}{30}\)[/tex].
### Steps to Solve:
1. Find the Least Common Denominator (LCD):
- The denominators of the fractions [tex]\(\frac{7}{10}\)[/tex] and [tex]\(\frac{8}{15}\)[/tex] are 10 and 15.
- To find the least common denominator, we find the least common multiple (LCM) of these numbers. The LCM of 10 and 15 is 30.
2. Convert Each Fraction to the Common Denominator:
- Convert [tex]\(\frac{7}{10}\)[/tex] to have a denominator of 30:
[tex]\[
\frac{7}{10} = \frac{7 \times 3}{10 \times 3} = \frac{21}{30}
\][/tex]
- Convert [tex]\(\frac{8}{15}\)[/tex] to have a denominator of 30:
[tex]\[
\frac{8}{15} = \frac{8 \times 2}{15 \times 2} = \frac{16}{30}
\][/tex]
3. Add the Fractions:
- Now that both fractions have the same denominator, add the numerators:
[tex]\[
\frac{21}{30} + \frac{16}{30} = \frac{21 + 16}{30} = \frac{37}{30}
\][/tex]
After adding the fractions, the sum [tex]\(\frac{7}{10} + \frac{8}{15}\)[/tex] is equal to [tex]\(\frac{37}{30}\)[/tex].
Thus, the fraction equivalent to [tex]\(\frac{7}{10} + \frac{8}{15}\)[/tex] is [tex]\(\frac{37}{30}\)[/tex].
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