Final answer:
When multiplying 5 1/6 by (-2/5), you first convert 5 1/6 into an improper fraction (31/6), then multiply it by -2/5, resulting in -62/30. This can be simplified to -31/15.
Step-by-step explanation:
The question asks to multiply 5 1/6 by (-2/5) and to express it as a fraction. First, we convert 5 1/6 into an improper fraction by multiplying the whole number 5 by the denominator 6 and adding the numerator 1. The result is:
5 * 6 + 1 = 30 + 1 = 31
So, 5 1/6 becomes 31/6. Now we multiply this by -2/5. Step by step, this is:
(31/6) * (-2/5)
To multiply fractions, we multiply the numerators together and the denominators together:
Numerator: 31 * (-2) = -62
Denominator: 6 * 5 = 30
Therefore, the answer is:
-62/30, which can be simplified to -31/15 by dividing both the numerator and the denominator by 2.