A farmer has 2 3/4 hectares of an orchard. 1 1/4 hectares of land is occupied by apples. One-fourth of the remainder is occupied by lemon trees and the rest of it is occupied by tree tomatoes. Find the fraction of the land occupied by the tree tomatoes? A. 1 7/8 ha B. 3/8 ha C. 7/8 ha D. 1 1/2 ha
Answer (1)
Let's solve the problem step-by-step to find the fraction of the land occupied by the tree tomatoes.
Determine the Total Remaining Land After Apples:
The farmer has a total of 2 4 3 hectares of orchard. First, convert this mixed number to an improper fraction.
2 4 3 = 4 11
The apples occupy 1 4 1 hectares. Convert this mixed number to an improper fraction as well.
1 4 1 = 4 5
The remaining land after accounting for apples is:
4 11 − 4 5 = 4 6 = 2 3
Calculate the Land Occupied by Lemon Trees:
One-fourth of the remaining land is occupied by lemon trees. Calculate this fraction of the remaining land:
4 1 × 2 3 = 8 3
Find Out the Land Occupied by Tree Tomatoes:
The land occupied by tree tomatoes is the remainder of the land after accounting for the lemon trees. The remaining part is:
2 3 − 8 3
To subtract these fractions, we need a common denominator. The least common denominator of 2 and 8 is 8.
Convert 2 3 to a fraction with a denominator of 8:
2 3 = 8 12
Now, subtract:
8 12 − 8 3 = 8 9
In mixed number form, 8 9 = 1 8 1 .
Therefore, the fraction of the land occupied by the tree tomatoes is 8 9 or 1 8 1 hectares. The corresponding multiple-choice answer is not listed among options A, B, C, or D, which means there might be a misunderstanding of the options provided.
