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Answer :
Let's solve the problem step by step:
We have two fractions that need to be subtracted:
[tex]\[
\frac{14}{15} - \left(-\frac{3}{5}\right)
\][/tex]
First, recognize that subtracting a negative fraction is the same as adding the positive of that fraction. So, we rewrite the expression:
[tex]\[
\frac{14}{15} + \frac{3}{5}
\][/tex]
Next, to add these fractions, we need to find a common denominator. The denominators given are 15 and 5. The least common denominator (LCD) between 15 and 5 is 15.
We convert [tex]\(\frac{3}{5}\)[/tex] to an equivalent fraction with a denominator of 15. To do this, multiply both the numerator and the denominator by 3:
[tex]\[
\frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15}
\][/tex]
Now, our problem looks like this:
[tex]\[
\frac{14}{15} + \frac{9}{15}
\][/tex]
Since the denominators are now the same, we can simply add the numerators:
[tex]\[
\frac{14 + 9}{15} = \frac{23}{15}
\][/tex]
Thus, the result of the subtraction [tex]\(\frac{14}{15} - \left(-\frac{3}{5}\right)\)[/tex] is [tex]\(\frac{23}{15}\)[/tex].
This fraction is already in its simplest form, as the numerator and the denominator have no common factors other than 1.
Therefore, the final answer is:
[tex]\[
\frac{23}{15}
\][/tex]
We have two fractions that need to be subtracted:
[tex]\[
\frac{14}{15} - \left(-\frac{3}{5}\right)
\][/tex]
First, recognize that subtracting a negative fraction is the same as adding the positive of that fraction. So, we rewrite the expression:
[tex]\[
\frac{14}{15} + \frac{3}{5}
\][/tex]
Next, to add these fractions, we need to find a common denominator. The denominators given are 15 and 5. The least common denominator (LCD) between 15 and 5 is 15.
We convert [tex]\(\frac{3}{5}\)[/tex] to an equivalent fraction with a denominator of 15. To do this, multiply both the numerator and the denominator by 3:
[tex]\[
\frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15}
\][/tex]
Now, our problem looks like this:
[tex]\[
\frac{14}{15} + \frac{9}{15}
\][/tex]
Since the denominators are now the same, we can simply add the numerators:
[tex]\[
\frac{14 + 9}{15} = \frac{23}{15}
\][/tex]
Thus, the result of the subtraction [tex]\(\frac{14}{15} - \left(-\frac{3}{5}\right)\)[/tex] is [tex]\(\frac{23}{15}\)[/tex].
This fraction is already in its simplest form, as the numerator and the denominator have no common factors other than 1.
Therefore, the final answer is:
[tex]\[
\frac{23}{15}
\][/tex]
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