Final answer:
To find out how many kilometers you still have to walk to get to the library, subtract the distance you have already walked from the total distance. Convert the total distance to a mixed number, then subtract the fractions using a common denominator. Finally, convert the result back to a mixed number.
Step-by-step explanation:
To find out how many kilometers you still have to walk to get to the library, you need to subtract the distance you have already walked from the total distance between your house and the library.
The total distance between your house and the library is 2 7/9 km. You have already walked 5/6 km. To get the remaining distance, subtract 5/6 km from 2 7/9 km.
First, convert 2 7/9 km to a mixed number. 2 7/9 is equivalent to 2 + 7/9. To add the whole number part and the fraction part, multiply the whole number (2) by the denominator of the fraction (9), which equals 18. Then, add the product (18) to the numerator (7), which equals 25. So, 2 7/9 is equal to 25/9 km.
Next, subtract 5/6 km from 25/9 km. To subtract fractions, you need a common denominator. The least common denominator of 6 and 9 is 18. Convert 5/6 km to an equivalent fraction with a denominator of 18: multiply both the numerator and denominator by 3 to get 15/18 km.
To subtract fractions with the same denominator, subtract the numerators: 25/9 km - 15/18 km = (25-15)/9 km = 10/9 km.
Lastly, convert 10/9 km to a mixed number. 10/9 is equivalent to 1 + 1/9. So, the remaining distance you have to walk to get to the library is 1 1/9 km. Therefore, the correct answer is A. 1 1/9 km.