Solve the Fraction Equation: Finding the Missing Term with 2/5a and 3/4ab

To solve this problem, we'll follow these steps:

• Step 1: Compare the given equation with the incomplete side.

• Step 2: Isolate terms involving the same variables for comparison.

• Step 3: Calculate the required terms to balance the equation.

Now, let's work through each step:

Step 1: The equation is given:
$\frac{2}{5}a + \frac{3}{4}ab + \frac{2}{3}b = \_ - a + \frac{1}{3}b + \frac{1}{3}b$

Step 2: Combine like terms on the right side. Notice $\frac{1}{3}b + \frac{1}{3}b = \frac{2}{3}b$.

The equation becomes:
$\frac{2}{5}a + \frac{3}{4}ab + \frac{2}{3}b = \_ - a + \frac{2}{3}b$

Step 3: Compare the terms involving $a$, $b$, and constants:

• Terms with $a$: $\frac{2}{5}a$ should remain, meaning we need to offset the $-a$.

• To balance: $a(\frac{2}{5}) = \frac{2}{5}a$

• Terms with $ab$: $\frac{3}{4}ab$ needs to be transferred directly.

Since $-$ on right side requires its cancellation, a plus $\frac{3}{4}b$ on missing term substitutes division. Hence,$\frac{2}{5} + \frac{3}{4}b$ is needed to balance and supplement.

Therefore, the solution to the problem is $\frac{2}{5} + \frac{3}{4}b$, which matches choice 4.