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Calculate the product of [tex]\frac{8}{15}[/tex], [tex]\frac{6}{5}[/tex], and [tex]\frac{1}{3}[/tex].

A) [tex]\frac{48}{15}[/tex]

B) [tex]\frac{16}{15}[/tex]

C) [tex]\frac{48}{30}[/tex]

D) [tex]\frac{16}{75}[/tex]


Sagot :

Let's calculate the product of the fractions [tex]\( \frac{8}{15} \)[/tex], [tex]\( \frac{6}{5} \)[/tex], and [tex]\( \frac{1}{3} \)[/tex].

1. Multiply the numerators:
[tex]\[ \text{Numerator} = 8 \times 6 \times 1 = 48 \][/tex]

2. Multiply the denominators:
[tex]\[ \text{Denominator} = 15 \times 5 \times 3 = 225 \][/tex]

3. Form the resulting fraction:
[tex]\[ \frac{48}{225} \][/tex]

4. Simplify the resulting fraction:

To simplify the fraction [tex]\(\frac{48}{225}\)[/tex], we'll find the greatest common divisor (GCD) of 48 and 225.

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

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

The common factors are evaluated:
- The GCD of 48 and 225 is [tex]\(3\)[/tex] (since only 3 is common to both factorizations).

Now, divide both the numerator and the denominator by their GCD [tex]\( \)[/tex]:

[tex]\[ \frac{48 \div 3}{225 \div 3} = \frac{16}{75} \][/tex]

Therefore, the product of [tex]\(\frac{8}{15}\)[/tex], [tex]\(\frac{6}{5}\)[/tex], and [tex]\(\frac{1}{3}\)[/tex] simplifies to [tex]\(\frac{16}{75}\)[/tex].

Hence, the correct answer is:
D) [tex]\(\frac{16}{75}\)[/tex].