Final answer:
The statement 9/(4/9)=(4/4)/9 is false because the left side simplifies to 20.25, while the right side simplifies to 1/9, which are not equal values.
Step-by-step explanation:
The question is asking whether the expression 9/(4/9)=(4/4)/9 is true or false. To solve this, we can simplify both sides of the equation and compare the results.
On the left side, dividing by a fraction is the same as multiplying by its reciprocal. Therefore, 9/(4/9) is equal to 9 × (9/4), which simplifies to 81/4 or 20.25.
On the right side, we have (4/4)/9. Any fraction that has the same quantity in the numerator and the denominator has a value of 1. Hence, (4/4) simplifies to 1, making the whole expression 1/9.
Comparing both sides, we can clearly see that 20.25 is not equal to 1/9. Therefore, the statement 9/(4/9)=(4/4)/9 is false.