Answer :
Sure! Let's find the value of the expression [tex]\(-\frac{5}{21} - \left(-\frac{13}{15}\right)\)[/tex] step-by-step.
1. Rewrite the expression:
[tex]\[
-\frac{5}{21} - \left(-\frac{13}{15}\right)
\][/tex]
Notice the double negative, which can be simplified:
[tex]\[
-\frac{5}{21} + \frac{13}{15}
\][/tex]
2. Find a common denominator:
The denominators are 21 and 15. The least common multiple (LCM) of 21 and 15 is 105.
3. Convert each fraction to have the common denominator:
For [tex]\(-\frac{5}{21}\)[/tex]:
[tex]\[
-\frac{5}{21} = -\frac{5 \times 5}{21 \times 5} = -\frac{25}{105}
\][/tex]
For [tex]\(\frac{13}{15}\)[/tex]:
[tex]\[
\frac{13}{15} = \frac{13 \times 7}{15 \times 7} = \frac{91}{105}
\][/tex]
4. Add the fractions:
Now that they have a common denominator, we can combine them:
[tex]\[
-\frac{25}{105} + \frac{91}{105} = \frac{-25 + 91}{105} = \frac{66}{105}
\][/tex]
5. Simplify the fraction:
To reduce [tex]\(\frac{66}{105}\)[/tex], find the greatest common divisor (GCD) of 66 and 105, which is 3.
[tex]\[
\frac{66}{105} = \frac{66 \div 3}{105 \div 3} = \frac{22}{35}
\][/tex]
So, the simplified answer is:
[tex]\[
\boxed{\frac{22}{35}}
\][/tex]
1. Rewrite the expression:
[tex]\[
-\frac{5}{21} - \left(-\frac{13}{15}\right)
\][/tex]
Notice the double negative, which can be simplified:
[tex]\[
-\frac{5}{21} + \frac{13}{15}
\][/tex]
2. Find a common denominator:
The denominators are 21 and 15. The least common multiple (LCM) of 21 and 15 is 105.
3. Convert each fraction to have the common denominator:
For [tex]\(-\frac{5}{21}\)[/tex]:
[tex]\[
-\frac{5}{21} = -\frac{5 \times 5}{21 \times 5} = -\frac{25}{105}
\][/tex]
For [tex]\(\frac{13}{15}\)[/tex]:
[tex]\[
\frac{13}{15} = \frac{13 \times 7}{15 \times 7} = \frac{91}{105}
\][/tex]
4. Add the fractions:
Now that they have a common denominator, we can combine them:
[tex]\[
-\frac{25}{105} + \frac{91}{105} = \frac{-25 + 91}{105} = \frac{66}{105}
\][/tex]
5. Simplify the fraction:
To reduce [tex]\(\frac{66}{105}\)[/tex], find the greatest common divisor (GCD) of 66 and 105, which is 3.
[tex]\[
\frac{66}{105} = \frac{66 \div 3}{105 \div 3} = \frac{22}{35}
\][/tex]
So, the simplified answer is:
[tex]\[
\boxed{\frac{22}{35}}
\][/tex]
