What’s 2/3 x 2/3 x 2/3 in fraction form?
(How did u get your answer?)
The Correct Answer and Explanation is:
To solve ( \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} ), we multiply the fractions step by step.
Step 1: Multiply the numerators
The numerators are all ( 2 ), so we multiply them:
[ 2 \times 2 \times 2 = 8 ]
Step 2: Multiply the denominators
The denominators are all ( 3 ), so we multiply them:
[ 3 \times 3 \times 3 = 27 ]
Step 3: Combine the results
Put the product of the numerators over the product of the denominators:
[ \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} = \frac{8}{27} ]
Thus, the answer is ( \frac{8}{27} ).
Explanation:
Fraction multiplication follows a straightforward rule: multiply the numerators (the top numbers) to get the new numerator and the denominators (the bottom numbers) to get the new denominator. This avoids finding a common denominator, unlike fraction addition or subtraction.
In this problem:
- The fraction ( \frac{2}{3} ) is multiplied by itself three times, representing ( \left(\frac{2}{3}\right)^3 ), or ( \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} ).
- When repeated multiplication of a fraction occurs, it’s an example of raising the fraction to a power. For ( \left(\frac{2}{3}\right)^3 ), the numerator ( 2^3 = 8 ), and the denominator ( 3^3 = 27 ).
The result, ( \frac{8}{27} ), is already in its simplest form because ( 8 ) and ( 27 ) have no common factors besides ( 1 ).
This process illustrates how exponents simplify repeated multiplication. In practical applications, such calculations might represent scaling down proportions, probabilities, or areas in geometry. Understanding this method ensures accurate results when working with fractions repeatedly multiplied.