Question

y-2/5=-1/3 solve without clearing the fractions first show all of your steps

Answer 1

To solve the equation \( y - \frac{2}{5} = -\frac{1}{3} \) without clearing the fractions first, we'll isolate \( y \) while keeping the fractions in the equation. Here are the steps:

1. Start with the original equation:
\[
y - \frac{2}{5} = -\frac{1}{3}
\]

2. To isolate \( y \), we can add \(\frac{2}{5}\) to both sides of the equation:
\[
y = -\frac{1}{3} + \frac{2}{5}
\]

3. To add the fractions \(-\frac{1}{3}\) and \(\frac{2}{5}\), we need a common denominator. The least common multiple (LCM) of \(3\) and \(5\) is \(15\).

4. Convert \(-\frac{1}{3}\) to have a denominator of \(15\):
\[
-\frac{1}{3} = -\frac{1 \times 5}{3 \times 5} = -\frac{5}{15}
\]

5. Convert \(\frac{2}{5}\) to have a denominator of \(15\):
\[
\frac{2}{5} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15}
\]

6. Now, the equation looks like this:
\[
y = -\frac{5}{15} + \frac{6}{15}
\]

7. Combine the fractions:
\[
y = \frac{-5 + 6}{15} = \frac{1}{15}
\]

8. Thus, the solution to the equation is:
\[
y = \frac{1}{15}
\]

So the final answer is:
\[
y = \frac{1}{15}
\]