Final answer:
The value of 8/9 divided by 5/12 is found by multiplying 8/9 by the reciprocal of 5/12, which yields 32/15, or as a decimal, approximately 2.13. The closest given option is 2.2.
Step-by-step explanation:
The question asks what the value of 8/9 divided by 5/12 is. To find this, we apply the rule for dividing fractions, which is to multiply by the reciprocal of the divisor. We will multiply 8/9 by the reciprocal of 5/12, which is 12/5.
The calculation is as follows:
- Write down the problem: 8/9 ÷ 5/12.
- Find the reciprocal of 5/12, which is 12/5.
- Multiply 8/9 by the reciprocal: 8/9 × 12/5.
- Perform the multiplication: (8 × 12) / (9 × 5) = 96/45.
- Simplify 96/45 by dividing both numerator and denominator by the greatest common divisor, which is 3, to get 32/15.
- Convert 32/15 to a mixed number which is 2 2/15.
- Convert 2 2/15 to a decimal if needed, which results in approximately 2.13.
Therefore, the value of 8/9 divided by 5/12 is 2 2/15, or approximately 2.13, which is not one of the choices given, so there might be an error in the provided options. The closest answer to our calculation is option D, 2.2.