Answer :
To determine which expression equals [tex]\(\frac{14}{15}\)[/tex], let's evaluate each expression step-by-step:
1. Expression [tex]\(\frac{3}{5} + \frac{1}{3}\)[/tex]:
- First, find a common denominator for the fractions. The denominators are 5 and 3, so the least common denominator is 15.
- Convert [tex]\(\frac{3}{5}\)[/tex] to have a denominator of 15:
[tex]\[
\frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15}
\][/tex]
- Convert [tex]\(\frac{1}{3}\)[/tex] to have a denominator of 15:
[tex]\[
\frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}
\][/tex]
- Add the fractions:
[tex]\[
\frac{9}{15} + \frac{5}{15} = \frac{9 + 5}{15} = \frac{14}{15}
\][/tex]
Therefore, the expression [tex]\(\frac{3}{5} + \frac{1}{3}\)[/tex] equals [tex]\(\frac{14}{15}\)[/tex].
2. Expression [tex]\(\frac{11}{10} + \frac{3}{5}\)[/tex]:
- Find a common denominator for the fractions. The denominators are 10 and 5, so the least common denominator is 10.
- [tex]\(\frac{11}{10}\)[/tex] already has a denominator of 10.
- Convert [tex]\(\frac{3}{5}\)[/tex] to have a denominator of 10:
[tex]\[
\frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10}
\][/tex]
- Add the fractions:
[tex]\[
\frac{11}{10} + \frac{6}{10} = \frac{11 + 6}{10} = \frac{17}{10} = 1.7
\][/tex]
Therefore, the expression [tex]\(\frac{11}{10} + \frac{3}{5}\)[/tex] does not equal [tex]\(\frac{14}{15}\)[/tex].
Based on these calculations, the expression [tex]\(\frac{3}{5} + \frac{1}{3}\)[/tex] is equal to [tex]\(\frac{14}{15}\)[/tex].
1. Expression [tex]\(\frac{3}{5} + \frac{1}{3}\)[/tex]:
- First, find a common denominator for the fractions. The denominators are 5 and 3, so the least common denominator is 15.
- Convert [tex]\(\frac{3}{5}\)[/tex] to have a denominator of 15:
[tex]\[
\frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15}
\][/tex]
- Convert [tex]\(\frac{1}{3}\)[/tex] to have a denominator of 15:
[tex]\[
\frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}
\][/tex]
- Add the fractions:
[tex]\[
\frac{9}{15} + \frac{5}{15} = \frac{9 + 5}{15} = \frac{14}{15}
\][/tex]
Therefore, the expression [tex]\(\frac{3}{5} + \frac{1}{3}\)[/tex] equals [tex]\(\frac{14}{15}\)[/tex].
2. Expression [tex]\(\frac{11}{10} + \frac{3}{5}\)[/tex]:
- Find a common denominator for the fractions. The denominators are 10 and 5, so the least common denominator is 10.
- [tex]\(\frac{11}{10}\)[/tex] already has a denominator of 10.
- Convert [tex]\(\frac{3}{5}\)[/tex] to have a denominator of 10:
[tex]\[
\frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10}
\][/tex]
- Add the fractions:
[tex]\[
\frac{11}{10} + \frac{6}{10} = \frac{11 + 6}{10} = \frac{17}{10} = 1.7
\][/tex]
Therefore, the expression [tex]\(\frac{11}{10} + \frac{3}{5}\)[/tex] does not equal [tex]\(\frac{14}{15}\)[/tex].
Based on these calculations, the expression [tex]\(\frac{3}{5} + \frac{1}{3}\)[/tex] is equal to [tex]\(\frac{14}{15}\)[/tex].
