Answer: 8 sections
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Step-by-step explanation:
Let's convert the mixed number 5 & 1/3 to an improper fraction.
The formula to use is
a & b/c = (a*c + b)/c
So,
a & b/c = (a*c + b)/c
5 & 1/3 = (5*3 + 1)/3
5 & 1/3 = 16/3
Imagine you had 16 pieces of candy, and imagine you wanted to divide that up amongst 3 friends. Each friend would get 15/3 = 5 whole pieces. There would be 1 candy left over. The 5 and 1 help then form the 5 & 1/3. So this is one way to visualize how 5 & 1/3 is the same as 16/3.
Another way to see why this works is to note how 16/3 = 5.333 approximately. The '5' before the decimal point is the whole part of the mixed number 5 & 1/3; the decimal portion 0.333 is the approximate value of the fractional part 1/3.
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The total length of fencing needed is 16/3 yards. Each section is 2/3 of a yard long. Since both denominators are "thirds", we can ignore them. An equivalent problem is this: "He needs 16 yards of fencing and each section is 2 yards long"
Based on the new problem without fractions involved, we can see that he'll need 16/2 = 8 sections in total.
You should find that dividing (16/3) over (2/3) will lead to 8 as well. You could say this:
(16/3) divide (2/3) = (16/3)*(3/2) = (16*3)/(3*2) = 48/6 = 8
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An alternative method:
Let's start with 2/3 of a yard. That doubles to 4/3 which is the same as 1 & 1/3. Think of it as 4/3 = (3+1)/3 = 3/3+1/3 = 1+1/3 = 1 & 1/3.
Next, we'll double 1 & 1/3 to land on 2 & 2/3. You simply multiply each '1' by 2 to end up with those '2's shown.
Now we'll double 2 & 2/3 like so:
2*(2 & 2/3) = 2*(2 + 2/3) = 4 + 4/3 = 4 + (1+1/3) = 5 + 1/3 = 5 & 1/3
The act of doubling exactly three times leads to us ultimately multiplying by 2*2*2 = 8, so he needs 8 sections that are each 2/3 of a yard long.
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Whichever method you prefer, the final answer is 8 sections.