To solve the equation:

\[
\frac{4}{3}b = \frac{4}{5}
\]

we need to isolate \( b \). Here's the step-by-step process:

### Step 1: Eliminate the fraction from the left side
Multiply both sides of the equation by the reciprocal of \( \frac{4}{3} \), which is \( \frac{3}{4} \), to isolate \( b \).

\[
b = \frac{4}{5} \times \frac{3}{4}
\]

### Step 2: Simplify the right side
Now, multiply the fractions:

\[
b = \frac{4 \times 3}{5 \times 4} = \frac{12}{20}
\]

### Step 3: Simplify the fraction
Divide both the numerator and the denominator by 4:

\[
b = \frac{12 \div 4}{20 \div 4} = \frac{3}{5}
\]

Thus, the solution is:

\[
b = \frac{3}{5}
\]

Would you like more details or have any questions?

Here are 5 related questions to deepen understanding:

1. What would happen if you multiplied both sides by \( \frac{5}{4} \) instead of \( \frac{3}{4} \)?
2. How would you solve \( \frac{5}{3}b = \frac{6}{5} \)?
3. Can you explain the importance of using the reciprocal when solving equations like this?
4. What if the equation was \( \frac{4}{3}b = \frac{6}{5} \)? How would the solution change?
5. How do you simplify more complex fractions like \( \frac{16}{12} \)?

**Tip:** Always simplify fractions at the end of the calculation to get the most reduced form of the answer.

Learn how to solve the linear equation \dfrac{4}{3}b = \dfrac{4}{5} with a step-by-step guide. This solution covers important algebraic concepts like fractions and reciprocals. Suitable for students in Grades 6-8.

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