a farmer's land and separated into sections of a size two and one seventh Acres Suppose there are 4 1/3 such sections. How many acres of land does the farmer own
A farmer owns a total of 8 acres of land. The land is separated into 3 1/3 equally sized sections. How many acres are in each section?
Write your answer as a mixed number in simplest form.
To find the total number of acres owned by the farmer, we multiply the number of sections by the size of each section.
Number of sections = 4 1/3
First, convert the mixed number 4 1/3 to an improper fraction:
4 1/3 = (4 * 3 + 1) / 3 = 13/3
Now, multiply the number of sections by the size of each section:
Total acres = (13/3) * (2 + 1/7)
To simplify, we convert the mixed number 2 1/7 to an improper fraction:
2 1/7 = (2 * 7 + 1) / 7 = 15/7
Total acres = (13/3) * (15/7)
To multiply fractions, multiply the numerators together and the denominators together:
Total acres = (13 * 15) / (3 * 7)
Total acres = 195 / 21
To simplify the fraction further, we can divide both the numerator and denominator by their greatest common divisor, which is 3 in this case:
Total acres = (195/3) / (21/3)
Total acres = 65/7
Therefore, the farmer owns 65/7 acres of land.
To find out how many acres of land the farmer owns, we need to multiply the number of sections by the size of each section.
First, let's convert the mixed number "2 and 1/7" into an improper fraction.
2 + 1/7 = (2 * 7 + 1) / 7 = 15/7
So, each section is equal to 15/7 acres.
Now, let's multiply the number of sections by the size of each section.
4 1/3 * 15/7
To multiply fractions, we multiply the numerators together and the denominators together.
(4 + 1/3) * (15/7) = (4 * 3/3 + 1/3) * 15/7 = (12/3 + 1/3) * 15/7 = (13/3) * (15/7)
To multiply whole numbers with fractions, we convert the whole number into a fraction by putting it over 1.
13/3 * 15/7 = 13/3 * 15/7 * 1/1 = (13 * 15) / (3 * 7)
Multiply the numerators and denominators together:
195 / 21
Now, we can simplify this fraction by finding the greatest common divisor (GCD) of 195 and 21, which is 3.
195 / 21 = (195 ÷ 3) / (21 ÷ 3) = 65/7
Therefore, the farmer owns 65/7 acres of land.
2 2/7 = 15/7
4 1/3 = 13/3
(15/7) * (13/3) = 195/21 = 9.29 acres