Calculate The Product of 8/15 6/5 and 1/3

Multiplying fractions is a fundamental math operation that involves finding the product of two or more fractions. This guide explains how to calculate the product of 8/15, 6/5, and 1/3, including the step-by-step process and practical applications.

How to Calculate the Product of Fractions

To multiply fractions, follow these steps:

Multiply the numerators (top numbers) together.
Multiply the denominators (bottom numbers) together.
Simplify the resulting fraction if possible.

Formula: (a/b) × (c/d) × (e/f) = (a × c × e) / (b × d × f)

For the given fractions 8/15, 6/5, and 1/3, we'll apply this formula to find the product.

Step-by-Step Calculation

Step 1: Multiply the Numerators

Multiply the top numbers of each fraction:

8 (from 8/15) × 6 (from 6/5) × 1 (from 1/3) = 48

Step 2: Multiply the Denominators

Multiply the bottom numbers of each fraction:

15 (from 8/15) × 5 (from 6/5) × 3 (from 1/3) = 225

Step 3: Combine the Results

Now combine the multiplied numerators and denominators:

48/225

Step 4: Simplify the Fraction

Check if 48/225 can be simplified by finding the greatest common divisor (GCD) of 48 and 225. The GCD is 3.

Divide both numerator and denominator by 3:

48 ÷ 3 = 16

225 ÷ 3 = 75

Simplified fraction: 16/75

Worked Example

Let's calculate the product of 8/15, 6/5, and 1/3 using the step-by-step method:

Multiply numerators: 8 × 6 × 1 = 48
Multiply denominators: 15 × 5 × 3 = 225
Combine results: 48/225
Simplify: 48 ÷ 3 = 16, 225 ÷ 3 = 75 → 16/75

The final product is 16/75.

FAQ

How do I multiply more than two fractions?

Multiply all the numerators together and all the denominators together, then simplify the resulting fraction if possible.

What if the fractions have different denominators?

You can multiply them directly without finding a common denominator, as shown in this example.

How do I simplify a fraction?

Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by the GCD.