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

A. [tex]$\frac{48}{30}$[/tex]
B. [tex]$\frac{48}{15}$[/tex]
C. [tex][tex]$\frac{16}{75}$[/tex][/tex]
D. [tex]$\frac{16}{15}$[/tex]

Sagot :

GinnyAnswer
To solve the problem of calculating the product of the fractions [tex]\( \frac{8}{15}, \frac{6}{5}, \)[/tex] and [tex]\( \frac{1}{3} \)[/tex], we can follow these steps:

1. Multiply the Numerators:
- Multiply the numerators of the fractions together: [tex]\( 8 \times 6 \times 1 = 48 \)[/tex].

2. Multiply the Denominators:
- Multiply the denominators of the fractions together: [tex]\( 15 \times 5 \times 3 = 225 \)[/tex].

3. Form the Product of the Fractions:
- Combine the results from steps 1 and 2 into a single fraction:
[tex]\[ \frac{48}{225} \][/tex]

4. Simplify the Fraction:
- Determine the greatest common divisor (GCD) of the numerator (48) and the denominator (225). By simplifying the fraction:
- The GCD of 48 and 225 is 3.
- Divide both the numerator and the denominator by their GCD:
[tex]\[ \frac{48 \div 3}{225 \div 3} = \frac{16}{75} \][/tex]

After simplifying, the final answer is [tex]\(\frac{16}{75}\)[/tex].

Thus, the correct choice is:
C. [tex]\(\frac{16}{75}\)[/tex]
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