To find the sum of the fractions [tex]\(-\frac{17}{30} + \frac{27}{30}\)[/tex], we can proceed with the following steps:
1. Identify Common Denominator:
Both fractions already have the same denominator, which is 30.
2. Add the Numerators:
We add the numerators of the fractions while keeping the common denominator:
[tex]\[
-\frac{17}{30} + \frac{27}{30} = \frac{-17 + 27}{30}
\][/tex]
3. Calculate the Numerator:
Perform the arithmetic operation in the numerator:
[tex]\[
-17 + 27 = 10
\][/tex]
So, the numerator is 10.
4. Form the Fraction:
The resulting fraction from the addition is:
[tex]\[
\frac{10}{30}
\][/tex]
5. Simplify the Fraction:
The fraction [tex]\(\frac{10}{30}\)[/tex] can be simplified by finding the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 10 and 30 is 10.
Divide the numerator and the denominator by their GCD:
[tex]\[
\frac{10 \div 10}{30 \div 10} = \frac{1}{3}
\][/tex]
Therefore, the sum [tex]\(-\frac{17}{30} + \frac{27}{30}\)[/tex] simplifies to [tex]\(\frac{1}{3}\)[/tex].
To conclude:
### Sum:
The value of [tex]\(\frac{1}{3}\)[/tex].
In numerical form, the intermediate step gives a decimal equivalent of [tex]\(0.3333\ldots\)[/tex], which supports our final simplified fraction.
