The value of the expression 9 2/3 x (-7.5) is -72.5. The correct answer is C.) -72.5.
To find the value of the expression, we need to multiply the mixed number 9 2/3 by the negative decimal -7.5. To do this, we can follow these steps:
- Convert the mixed number 9 2/3 to an improper fraction by multiplying the whole number 9 by the denominator 3 and adding the numerator 2. This gives us 29/3.
- Convert the decimal -7.5 to a fraction by multiplying it by 10 and putting it over 10. This gives us -75/10.
- Multiply the two fractions by cross-multiplying the numerators and denominators. This gives us (29 x -75) / (3 x 10), or -2175 / 30.
- Simplify the fraction by dividing both the numerator and denominator by the greatest common factor, which is 5. This gives us -435 / 6.
- Convert the fraction to a decimal by dividing the numerator by the denominator. This gives us -72.5.
Therefore, 9 2/3 x (-7.5) = -72.5.