# How to Multiply Fractions

To multiply fractions is as easy as following the 3 suggested steps below.

**Steps in Multiplying Fractions**

Given two fractions with nonzero denominators :

**Step 1:** Multiply the numerators together

- This will be the numerator of the “new” fraction.

**Step 2:** Multiply the denominators together

- This will be the denominator of the “new” fraction.

**Step 3:** Simplify the resulting fraction by reducing it to the lowest term, if needed.

Before we go over some examples, there are other ways to mean multiplication.

**Dot symbol**as a multiplication operator

**Parenthesis**as a multiplication operator

**Examples of How to Multiply Fractions**

**Example 1**: Multiply the fractions .

Multiply the numerators of the fractions

Similarly, multiply the denominators together.

The resulting fraction after multiplication is already in its reduced form. That becomes our final answer!

**Example 2**: Multiply the fractions .

Step 1: Multiply the top numbers together

Step 2: Multiply the bottom numbers together

Step 3: Simplify the answer by reducing to the lowest term.

Divide the top and bottom by its greatest common divisor (GCD) which is **10**.

**Example 3**: Multiply the three fractions .

You may encounter a problem where you will be asked to multiply three fractions.

The general idea remains the same just like when you multiply two fractions, as shown in previous examples.

Step 1: Get the product of the numerators

Step 2: Get the product of the denominators

Step 3: Reduce the answer to the lowest term

Divide both the numerator and denominator by the greatest common divisor that is **12**.

**Example 4**: Multiply a whole number and a fraction .

When you multiply a whole number to a fraction, think of the whole number as a fraction with a **denominator of 1**. Since

Therefore, we can rewrite the original problem as . With that, it should allow us to multiply the fractions as usual.

Finally, reduce the answer by dividing the numerator and denominator by** 5**.

**Example 5**: Multiply .

Step 1: Multiply the numerators

**5 x 6 = 30**

Step 2: Multiply the denominators

**3 x 15 = 45**

Step 3: Reduce the answer to the lowest term by dividing the top and bottom by the greatest common divisor which is **15**.

**Example 6**: Multiply .

Solution:

**Example 7**: Multiply .

Solution:

Rewrite the whole number 9 with a denominator of 1.