Solve for v: v - 1/5 = -5/6. Simplify your answer as much as possible.
Understand the Problem
The question is asking us to solve the equation for the variable v, specifically starting from the equation given and simplifying the result as much as possible.
Answer
$$ v = -\frac{19}{30} $$
Answer for screen readers
The simplified solution for $v$ is:
$$ v = -\frac{19}{30} $$
Steps to Solve
- Add $\frac{1}{5}$ to both sides
To isolate $v$, we need to get rid of $-\frac{1}{5}$ on the left side. We do this by adding $\frac{1}{5}$ to both sides of the equation.
$$ v - \frac{1}{5} + \frac{1}{5} = -\frac{5}{6} + \frac{1}{5} $$
This simplifies to:
$$ v = -\frac{5}{6} + \frac{1}{5} $$
- Find a common denominator
To combine the fractions on the right side, we need a common denominator. The denominators are 6 and 5. The least common multiple (LCM) of 6 and 5 is 30.
- Rewrite the fractions with the common denominator
Convert each fraction to have a denominator of 30:
$$ -\frac{5}{6} = -\frac{5 \times 5}{6 \times 5} = -\frac{25}{30} $$
$$ \frac{1}{5} = \frac{1 \times 6}{5 \times 6} = \frac{6}{30} $$
- Combine the fractions
Now substitute back into the equation:
$$ v = -\frac{25}{30} + \frac{6}{30} $$
Combine the numerators:
$$ v = \frac{-25 + 6}{30} = \frac{-19}{30} $$
The simplified solution for $v$ is:
$$ v = -\frac{19}{30} $$
More Information
This result shows that $v$ is in the fraction form of negative nineteen-thirtieths, indicating that its value is less than zero. This might be significant in contexts where physical quantities must be positive.
Tips
- Forgetting to find a common denominator when adding fractions.
- Not properly combining the numerators of the fractions after finding a common denominator.
- Miscalculating the addition of the numerators, leading to incorrect answers.
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