## Multiplying Fractions: A Step-by-Step Guide

Let's break down these fraction multiplication problems step by step:

### (9)/(16) x (4)/(12)

**1. Simplifying Fractions:**

Before multiplying, check if we can simplify any fractions. In this case, both (4/12) and (9/16) can be simplified:

- (4/12) simplifies to (1/3) by dividing both numerator and denominator by 4.
- (9/16) remains as it is.

**2. Multiplication:**

Now we have: (9/16) x (1/3)

To multiply fractions, we simply multiply the numerators and the denominators:

- Numerator: 9 x 1 = 9
- Denominator: 16 x 3 = 48

**3. Final Result:**

The product of (9/16) and (4/12) is **(9/48)**. This fraction can be further simplified by dividing both numerator and denominator by 3, giving us **(3/16)**.

### (9)/(16 x (-3)/(9))

**1. Order of Operations:**

We need to follow the order of operations (PEMDAS/BODMAS). This means we perform the multiplication inside the parentheses first.

**2. Multiplying Fractions Inside Parentheses:**

- Numerator: 16 x -3 = -48
- Denominator: 9 x 1 = 9

**3. Result of Parentheses:**

The result inside the parentheses is (-48/9).

**4. Division of Fractions:**

Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of (-48/9) is (9/-48).

Now we have: (9/16) x (9/-48).

**5. Simplifying:**

Both fractions can be simplified:

- (9/16) remains as it is.
- (9/-48) simplifies to (3/-16) by dividing both numerator and denominator by 3.

**6. Multiplication:**

Now we have: (9/16) x (3/-16)

Multiplying the numerators and denominators:

- Numerator: 9 x 3 = 27
- Denominator: 16 x -16 = -256

**7. Final Result:**

The result of (9)/(16 x (-3)/(9)) is **(27/-256)** or **(-27/256)**.