Final answer:
The correct way to use the rule 'multiply by the reciprocal' for the expression 5 - 5/9 is demonstrated in option D: 5 - (5/9) x 9, which properly applies the multiplication of 5/9 by its reciprocal before subtracting from 5.
Step-by-step explanation:
The question asks which option demonstrates the correct way to apply the rule 'multiply by the reciprocal' for the expression 5 - 5/9. The reciprocal of a number is what you multiply that number by to get 1. In this case, the reciprocal of 5/9 is 9/5. Therefore, to subtract 5/9 from 5 using multiplication by the reciprocal, you would multiply 5/9 by its reciprocal, which is 9/5, and then subtract this result from 5. Let's look at the options presented.
- A. 5 - (5/9) simply restates the original expression.
- B. (5 - 5)/9 suggests dividing the result of 5 - 5 by 9, which is not using the reciprocal correctly.
- C. 5 - (9/5) incorrectly uses the reciprocal of the whole number 5, rather than of 5/9.
- D. 5 - (5/9) x 9 correctly applies the rule by multiplying 5/9 by 9, which is its reciprocal, and then subtracting the result from 5.
The correct answer is D. 5 - (5/9) x 9, as it correctly uses the 'multiply by the reciprocal' rule by multiplying 5/9 by 9 before subtracting from 5.