https://file.aiquickdraw.com/mathbot/file/1726971734086m14o4dku.jpg

Let's solve the equation provided in the image step-by-step:

The equation is:

\[
2 \frac{1}{3} \div y = 1 \frac{2}{5} \div (-1.1)
\]

### Step 1: Convert mixed numbers to improper fractions
- \( 2 \frac{1}{3} \) becomes \( \frac{7}{3} \).
- \( 1 \frac{2}{5} \) becomes \( \frac{7}{5} \).

Now the equation becomes:

\[
\frac{7}{3} \div y = \frac{7}{5} \div (-1.1)
\]

### Step 2: Simplify the right-hand side
- Dividing by \(-1.1\) is equivalent to multiplying by its reciprocal:

\[
\frac{7}{5} \div (-1.1) = \frac{7}{5} \times \frac{1}{-1.1}
\]

We know \( -1.1 = -\frac{11}{10} \), so:

\[
\frac{7}{5} \times \frac{1}{-\frac{11}{10}} = \frac{7}{5} \times \frac{10}{-11} = \frac{70}{-55} = -\frac{14}{11}
\]

Now the equation becomes:

\[
\frac{7}{3} \div y = -\frac{14}{11}
\]

### Step 3: Solve for \(y\)
Dividing by \(y\) is the same as multiplying by \( \frac{1}{y} \), so:

\[
\frac{7}{3} \times \frac{1}{y} = -\frac{14}{11}
\]

Now, solve for \(y\) by multiplying both sides by \(y\) and then by \(-\frac{14}{11}\):

\[
y = \frac{7}{3} \times \frac{11}{-14}
\]

Simplify:

\[
y = \frac{7 \times 11}{3 \times -14} = \frac{77}{-42} = -\frac{11}{6}
\]

### Final Answer:
\[
y = -\frac{11}{6}
\]

Would you like more details or have any questions? Here are some related questions you could explore:

1. What are the steps for converting mixed numbers into improper fractions?
2. How do you simplify complex fractions with division?
3. Can you explain why dividing by a fraction is the same as multiplying by its reciprocal?
4. How can you check the solution of an equation after solving it?
5. What strategies are helpful when solving equations involving decimals?

**Tip:** Always double-check your work by substituting your solution back into the original equation to verify it works!

Learn how to solve the equation 2 1/3 ÷ y = 1 2/5 ÷ (-1.1) with a detailed step-by-step guide. This problem involves converting mixed numbers to improper fractions, working with reciprocals, and solving for the variable y. Perfect for students in Grade 8-10.

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