1/8 x 1/8 x 1/8 answer in fraction form

1/8 x 1/8 x 1/8 answer in fraction form

The Correct Answer and Explanation is :

The multiplication of fractions follows a simple rule: multiply the numerators (top numbers) together and the denominators (bottom numbers) together. Let’s go step-by-step with the given fractions:

Problem:

[
\frac{1}{8} \times \frac{1}{8} \times \frac{1}{8}
]

Step 1: Multiply the Numerators

We multiply the numerators of each fraction. Since each fraction has a numerator of 1:
[
1 \times 1 \times 1 = 1
]

Step 2: Multiply the Denominators

Next, multiply the denominators of each fraction. Each denominator is 8:
[
8 \times 8 \times 8 = 512
]

Step 3: Write the Result

Now, we combine the results of the numerators and denominators:
[
\frac{1}{512}
]

Final Answer:

[
\frac{1}{512}
]

Explanation:

When multiplying fractions, we are essentially scaling the value of one fraction by the other. In this case, we are multiplying three fractions, each with the same value of ( \frac{1}{8} ). Each multiplication reduces the overall value further, as each new fraction is one-eighth of the previous result.

Why This Happens:

Each fraction represents a division of a whole into equal parts. For example, ( \frac{1}{8} ) means the whole is divided into 8 equal parts, and you are taking 1 part of those 8. When you multiply fractions, the result becomes smaller because you’re continuously dividing the value into smaller parts. Multiplying by ( \frac{1}{8} ) three times is like breaking a single piece into smaller and smaller pieces.

Thus, the multiplication of these three ( \frac{1}{8} ) fractions results in ( \frac{1}{512} ), indicating a further subdivision of the original whole. This process is consistent with the general rule for multiplying fractions: multiply numerators together and denominators together.