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Answer :
To solve the problem of adding the fractions [tex]\(\frac{13}{15}\)[/tex] and [tex]\(\frac{14}{15}\)[/tex], follow these steps:
1. Check the Denominators: Since both fractions have the same denominator, we can directly add the numerators. The common denominator for both fractions is 15.
2. Add the Numerators: Add the numerators of the two fractions:
[tex]\[
13 + 14 = 27
\][/tex]
3. Write the Resulting Fraction: The result of adding the fractions [tex]\(\frac{13}{15}\)[/tex] and [tex]\(\frac{14}{15}\)[/tex] is:
[tex]\[
\frac{27}{15}
\][/tex]
4. Simplify the Fraction: To simplify [tex]\(\frac{27}{15}\)[/tex], find the greatest common divisor (GCD) of 27 and 15. The GCD is 3. Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{27 \div 3}{15 \div 3} = \frac{9}{5}
\][/tex]
5. Convert to a Mixed Number: If needed, you can express [tex]\(\frac{9}{5}\)[/tex] as a mixed number. Divide 9 by 5:
[tex]\[
9 \div 5 = 1 \text{ with a remainder of } 4
\][/tex]
Thus, [tex]\(\frac{9}{5}\)[/tex] can be written as the mixed number:
[tex]\[
1 \frac{4}{5}
\][/tex]
6. Decimal Form: If needed, convert [tex]\(\frac{9}{5}\)[/tex] into a decimal by performing the division:
[tex]\[
9 \div 5 = 1.8
\][/tex]
So, the result of [tex]\(\frac{13}{15} + \frac{14}{15}\)[/tex] is [tex]\(\frac{9}{5}\)[/tex], or written as a mixed number, [tex]\(1 \frac{4}{5}\)[/tex], or in decimal form, 1.8.
1. Check the Denominators: Since both fractions have the same denominator, we can directly add the numerators. The common denominator for both fractions is 15.
2. Add the Numerators: Add the numerators of the two fractions:
[tex]\[
13 + 14 = 27
\][/tex]
3. Write the Resulting Fraction: The result of adding the fractions [tex]\(\frac{13}{15}\)[/tex] and [tex]\(\frac{14}{15}\)[/tex] is:
[tex]\[
\frac{27}{15}
\][/tex]
4. Simplify the Fraction: To simplify [tex]\(\frac{27}{15}\)[/tex], find the greatest common divisor (GCD) of 27 and 15. The GCD is 3. Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{27 \div 3}{15 \div 3} = \frac{9}{5}
\][/tex]
5. Convert to a Mixed Number: If needed, you can express [tex]\(\frac{9}{5}\)[/tex] as a mixed number. Divide 9 by 5:
[tex]\[
9 \div 5 = 1 \text{ with a remainder of } 4
\][/tex]
Thus, [tex]\(\frac{9}{5}\)[/tex] can be written as the mixed number:
[tex]\[
1 \frac{4}{5}
\][/tex]
6. Decimal Form: If needed, convert [tex]\(\frac{9}{5}\)[/tex] into a decimal by performing the division:
[tex]\[
9 \div 5 = 1.8
\][/tex]
So, the result of [tex]\(\frac{13}{15} + \frac{14}{15}\)[/tex] is [tex]\(\frac{9}{5}\)[/tex], or written as a mixed number, [tex]\(1 \frac{4}{5}\)[/tex], or in decimal form, 1.8.
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