Calculate the product of 8/15 6/5 and 1/3

Calculate the product of 8/15 6/5 and 1/3

The Correct Answer and Explanation is :

To calculate the product of the fractions ( \frac{8}{15} \times \frac{6}{5} \times \frac{1}{3} ), follow these steps:

Step 1: Multiply the numerators

The numerators are the top numbers in each fraction. Multiply them together:
[
8 \times 6 \times 1 = 48
]
So, the product of the numerators is 48.

Step 2: Multiply the denominators

Next, multiply the denominators (the bottom numbers in each fraction):
[
15 \times 5 \times 3 = 225
]
So, the product of the denominators is 225.

Step 3: Form the new fraction

Now that we have the product of the numerators and denominators, the resulting fraction is:
[
\frac{48}{225}
]

Step 4: Simplify the fraction

To simplify the fraction, we need to find the greatest common divisor (GCD) of 48 and 225. We can use the prime factorization method or the Euclidean algorithm.

Prime factorization of 48:
[
48 = 2^4 \times 3
]

Prime factorization of 225:
[
225 = 3^2 \times 5^2
]

The common factor between 48 and 225 is (3), so we divide both the numerator and the denominator by 3:
[
\frac{48}{225} = \frac{48 \div 3}{225 \div 3} = \frac{16}{75}
]

Thus, the simplified product of the fractions is ( \frac{16}{75} ).

Final Answer:

The product of ( \frac{8}{15} \times \frac{6}{5} \times \frac{1}{3} ) is ( \frac{16}{75} ).

Explanation:

In this calculation, we performed the multiplication of fractions step by step. First, we multiplied the numerators and denominators separately. Then, we simplified the result by finding the greatest common divisor (GCD) of the numerator and denominator. Simplifying fractions is important because it ensures the answer is in the most reduced form, making it easier to understand and work with.