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Answer as a fraction. Do not include spaces in your answer.

[tex]\[ 5 \frac{1}{6} \cdot\left(-\frac{2}{5}\right) = \][/tex]
[tex]\[\boxed{\square} \][/tex]


Sagot :

To find the product of [tex]\(5 \frac{1}{6} \cdot \left(-\frac{2}{5}\right)\)[/tex], follow these steps:

1. Convert the mixed number [tex]\(5 \frac{1}{6}\)[/tex] to an improper fraction.

[tex]\[5 \frac{1}{6} = 5 + \frac{1}{6}\][/tex]

To express [tex]\(5\)[/tex] as a fraction with a denominator of 6:

[tex]\[5 = \frac{30}{6}\][/tex]

Therefore,

[tex]\[5 \frac{1}{6} = \frac{30}{6} + \frac{1}{6} = \frac{31}{6}\][/tex]

2. Multiply the improper fraction [tex]\(\frac{31}{6}\)[/tex] by the negative fraction [tex]\(-\frac{2}{5}\)[/tex]:

[tex]\[\frac{31}{6} \cdot \left(-\frac{2}{5}\right) = \frac{31 \cdot (-2)}{6 \cdot 5} = \frac{-62}{30}\][/tex]

3. Simplify the resulting fraction. The greatest common divisor of 62 and 30 is 2, so divide both the numerator and the denominator by 2:

[tex]\[\frac{-62}{30} = \frac{-62 \div 2}{30 \div 2} = \frac{-31}{15}\][/tex]

Therefore, the answer is:

[tex]\[ \boxed{\frac{-31}{15}} \][/tex]
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