Calculate the Product of 8/15, 6/5, and 1/3

Understanding how to multiply fractions is a fundamental skill in mathematics, crucial for everything from baking to advanced engineering. In this article, we'll break down the process of finding the product of three specific fractions: 8/15, 6/5, and 1/3, step by step. We'll also explore the importance of simplifying your results and how to use the interactive calculator above to verify your work.

What is a Fraction?

At its core, a fraction represents a part of a whole. It consists of two numbers: a numerator (the top number), which tells you how many parts you have, and a denominator (the bottom number), which tells you how many equal parts the whole is divided into. For example, in 8/15, you have 8 parts out of a total of 15 equal parts.

Multiplying Fractions: The Basics

Multiplying fractions is surprisingly straightforward, especially compared to adding or subtracting them, which require a common denominator. When you multiply fractions, you simply:

• Multiply all the numerators together to get the new numerator.
• Multiply all the denominators together to get the new denominator.

There's no need to find a common denominator!

Step-by-Step Calculation: 8/15 × 6/5 × 1/3

Step 1: Multiply the Numerators

Let's take the numerators from our three fractions: 8, 6, and 1. We multiply them together:

8 × 6 × 1 = 48

So, our new numerator is 48.

Step 2: Multiply the Denominators

Next, we take the denominators: 15, 5, and 3. We multiply them:

15 × 5 × 3 = 75 × 3 = 225

Thus, our new denominator is 225.

Step 3: Form the New Fraction

Now we combine our new numerator and denominator to form the product fraction:

Product = 48/225

This is the correct product, but it's often not in its simplest form.

Step 4: Simplify the Fraction

Simplifying a fraction means reducing it to its lowest terms. This is done by dividing both the numerator and the denominator by their greatest common divisor (GCD). For 48/225:

• Find common factors: Both 48 and 225 are divisible by 3.
• Divide numerator by 3: 48 ÷ 3 = 16
• Divide denominator by 3: 225 ÷ 3 = 75

Our simplified fraction is 16/75.

Can we simplify further? Let's check the factors of 16 (1, 2, 4, 8, 16) and 75 (1, 3, 5, 15, 25, 75). They share no common factors other than 1, so 16/75 is in its simplest form.

The Final Result

The product of 8/15, 6/5, and 1/3 is 16/75. As a decimal, this is approximately 0.2133.

Why is this skill important?

Multiplying fractions is a foundational concept that supports more complex mathematical operations. It's used in:

• Cooking and Baking: Adjusting recipes that call for fractional ingredients.
• Finance: Calculating portions of investments or interest rates.
• Engineering and Science: Working with ratios, proportions, and scaling quantities.
• Everyday Problem Solving: Understanding how parts of parts combine.

Using the Calculator

The interactive calculator at the top of this page is pre-filled with our example fractions. You can change the numerators and denominators to experiment with other fractions. Just enter your values and click "Calculate Product" to instantly see the simplified fractional and decimal results. This tool can be incredibly helpful for checking your work or exploring different scenarios.

Mastering fraction multiplication is a stepping stone to greater mathematical confidence and capability. Keep practicing, and don't hesitate to use tools like our calculator to help you along the way!