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Find the product:

[tex]\left(\frac{2}{7}\right)\left(\frac{14}{15}\right)\left(-\frac{1}{2}\right)[/tex]

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Answer :

To find the product of the fractions [tex]\(\left(\frac{2}{7}\right)\left(\frac{14}{15}\right)\left(-\frac{1}{2}\right)\)[/tex], follow these steps:

1. Multiply the numerators:
- The numerators are [tex]\(2\)[/tex], [tex]\(14\)[/tex], and [tex]\(-1\)[/tex].
- Multiply them together: [tex]\(2 \times 14 \times (-1) = -28\)[/tex].

2. Multiply the denominators:
- The denominators are [tex]\(7\)[/tex], [tex]\(15\)[/tex], and [tex]\(2\)[/tex].
- Multiply them together: [tex]\(7 \times 15 \times 2 = 210\)[/tex].

3. Form the fraction:
- The product of the fractions is [tex]\(-\frac{28}{210}\)[/tex].

4. Simplify the fraction:
- Both [tex]\(28\)[/tex] and [tex]\(210\)[/tex] can be divided by their greatest common divisor, which is [tex]\(14\)[/tex].
- Divide the numerator and denominator by [tex]\(14\)[/tex]:
[tex]\(-\frac{28}{210} = -\frac{28 \div 14}{210 \div 14} = -\frac{2}{15}\)[/tex].

Therefore, the product of the fractions is [tex]\(-\frac{2}{15}\)[/tex], which is approximately [tex]\(-0.1333\)[/tex] when expressed as a decimal.

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