Final answer:
After converting mixed numbers to improper fractions and performing the addition, Mr. Joseph used 35/9 pounds of fertilizer in total. Converting this to a mixed number and subtracting from the initial 9 pounds, there are 5 1/9 pounds of fertilizer left.
Step-by-step explanation:
Mr. Joseph bought 9 pounds of fertilizer for his lawn and used 2 2/3 pounds for his backyard, and 1 2/9 pounds for his front yard. To find out how much fertilizer is left, we need to subtract the total amount used from the initial amount.
To perform the subtraction, we convert the mixed numbers to improper fractions. 2 2/3 becomes 8/3 (because 2 × 3 + 2 = 8), and 1 2/9 becomes 11/9 (because 1 × 9 + 2 = 11).
Now we sum the two fractions: 8/3 + 11/9, the common denominator is 9, so we convert 8/3 to 24/9, and then we add them to get 35/9.
So, Mr. Joseph used 35/9 pounds in total. We convert 35/9 back to a mixed number, which is 3 8/9.
Subtracting from the initial 9 pounds: 9 - 3 8/9 = 5 1/9 pounds of fertilizer left.