Question

A farmer has a field that is 7 1/4 acres in size. He wants to divide the field into equal sections, with each section being 2/3 of an acre. How many equal sections can the farmer create from the field?

Answer 1

To solve this problem, we need to find the number of times the size of each section, 2/3 of an acre, is contained within the size of the field, 7 1/4 acres.

To find the answer, we divide the size of the field by the size of each section:

7 1/4 ÷ 2/3

First, we need to convert the mixed number, 7 1/4, to an improper fraction. To do this, we multiply the whole number, 7, by the denominator, 4, and add the numerator, 1:

7 × 4 = 28

28 + 1 = 29

So 7 1/4 can be rewritten as the improper fraction 29/4.

Now we can divide 29/4 by 2/3:

(29/4) ÷ (2/3)

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:

(29/4) × (3/2)

Multiplying the numerators gives us:

(29 × 3) = 87

And multiplying the denominators gives us:

(4 × 2) = 8

So now we have 87/8.

To simplify this fraction, we find the greatest common divisor (GCD) of the numerator, 87, and denominator, 8. The GCD of 87 and 8 is 1.

Dividing both the numerator and denominator by 1 gives us:

87 ÷ 1 = 87
8 ÷ 1 = 8

So the simplified fraction is 87/8.

Therefore, the farmer can create 87/8 equal sections from the field. This can also be written as a mixed number:

87 ÷ 8 = 10 remainder 7

So the answer is 10 7/8 equal sections.