Given that a * b = $\frac{a + b}{\text{ab}}$ + (a - b). Find the value of 3 * 2

1. Analyze the question

You are given a binary operation defined as $a * b = \frac{a + b}{ab} + (a - b)$. You need to substitute the values $a = 3$ and $b = 2$ into this formula to find the result.

2. Explain the concept

A binary operation is simply a rule that tells you how to combine two numbers to get a new result. In this case, the rule has two parts:

• A fraction part: $\frac{a + b}{ab}$
• A subtraction part: $(a - b)$

To solve, we calculate each part separately and then add them together.

3. Show the solution

Step 1: Identify the values $a = 3$ $b = 2$

Step 2: Substitute into the formula $3 * 2 = \frac{3 + 2}{3 \times 2} + (3 - 2)$

Step 3: Solve the fraction part $\frac{3 + 2}{3 \times 2} = \frac{5}{6}$

Step 4: Solve the subtraction part $(3 - 2) = 1$

Step 5: Combine the results $3 * 2 = \frac{5}{6} + 1$

To add these, convert $1$ to a fraction with a denominator of $6$: $1 = \frac{6}{6}$

So, $\frac{5}{6} + \frac{6}{6} = \frac{11}{6}$

4. Identify the answer

The calculated value is $\frac{11}{6}$, which corresponds to option B.

5. Tip

When dealing with binary operations in JAMB, always use brackets to separate the different parts of the equation. This prevents "sign errors" (like accidentally subtracting when you should be adding) and keeps your work organized. If you get a fraction, always check if it can be simplified or if it needs to be converted to a mixed fraction to match the options provided.