Maya has a rectangular corn field. The area of the field is 1 1/6 square miles with a length of 1/2 mile. If area=length×width, what is the width of the field? Simplify the answer if possible.
1. 2 1/3
2. 7/ 12
3. 14/16
4. 6/14
2 1/3
To find the width of the field, we can use the formula for the area of a rectangle: Area = Length × Width.
Given that the area of the field is 1 1/6 (or 7/6) square miles and the length is 1/2 mile, we can substitute these values into the formula: 7/6 = 1/2 × Width.
To solve for the width, we need to isolate it by dividing both sides of the equation by 1/2: (7/6) ÷ (1/2) = Width.
Dividing fractions involves multiplying the first fraction by the reciprocal of the second fraction: (7/6) × (2/1) = Width.
Multiplying the numerators and denominators gives us: (7 × 2) / (6 × 1) = Width.
Simplifying the expression gives: 14/6 = Width.
Since 14 and 6 are both divisible by 2, we can simplify further: 7/3 = Width.
Therefore, the width of the field is 7/3.
Out of the given options, the simplified answer is 2 1/3, which matches option 1.
To find the width of the corn field, we need to divide the area of the field by its length.
Given:
Area = 1 1/6 square miles
Length = 1/2 mile
To divide a mixed number by a fraction, we need to convert the mixed number to a fraction.
Converting the area to a fraction:
1 1/6 = 6/6 + 1/6 = 7/6
Now, divide the area by the length:
Width = Area/Length
Width = (7/6 square miles) / (1/2 mile)
To divide fractions, we multiply the numerator of the first fraction by the reciprocal of the second fraction.
Width = (7/6 square miles) * (2/1 mile)
Width = (7*2) / (6*1) square miles/mile
Width = 14/6 square miles/mile
Simplifying the fraction:
14/6 = 2 2/6 = 2 1/3
Therefore, the width of the field is 2 1/3. So, the correct answer is option 1, 2 1/3.