Solve for yy. Express your answer as a proper or improper fraction in simplest terms.
one eigth, minus, start fraction, 3, divided by, 5, end fraction, y, equals, minus, start fraction, 3, divided by, 8, end fraction
8
1
​
 − 
5
3
​
 y=
− 
8
3
​


The equation is given as:

\[
\frac{1}{8} - \frac{3}{5} y = - \frac{3}{8}
\]

### Step 1: Isolate the term with \( y \)
First, subtract \(\frac{1}{8}\) from both sides:

\[
- \frac{3}{5} y = - \frac{3}{8} - \frac{1}{8}
\]

### Step 2: Simplify the right-hand side
The right-hand side has like denominators, so we can combine the fractions:

\[
- \frac{3}{8} - \frac{1}{8} = - \frac{4}{8} = - \frac{1}{2}
\]

Now, the equation is:

\[
- \frac{3}{5} y = - \frac{1}{2}
\]

### Step 3: Solve for \( y \)
To solve for \( y \), divide both sides of the equation by \(- \frac{3}{5}\). This is equivalent to multiplying by the reciprocal:

\[
y = \left( - \frac{1}{2} \right) \div \left( - \frac{3}{5} \right) = \left( - \frac{1}{2} \right) \times \left( - \frac{5}{3} \right)
\]

Multiplying the fractions:

\[
y = \frac{1 \times 5}{2 \times 3} = \frac{5}{6}
\]

Thus, the solution is:

\[
y = \frac{5}{6}
\]

Let me know if you'd like more details or have questions!

Here are 5 related questions:
1. How do you solve a linear equation with fractions?
2. What is the reciprocal of a fraction, and when do you use it?
3. How can you combine fractions with different denominators?
4. How do you know when a fraction is in its simplest form?
5. Can you explain how to multiply and divide fractions?

**Tip:** Always remember to check your solution by plugging it back into the original equation to verify its correctness!

Solve for y. Express your answer as a proper or improper fraction in simplest terms.

\[ \frac{1}{8} - \frac{3}{5} y = - \frac{3}{8} \]

Learn how to solve the linear equation with fractions: 1/8 - 3/5y = -3/8. This step-by-step guide covers important algebraic concepts, including isolating variables, combining fractions, and dividing by fractions. Suitable for students in Grades 6-8.

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