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Victoria is going to put a fence around her rectangular yard which measures 15 1/9 yards by 11 5/9 yards. If she buys 120 yards of fencing, how many yards of fencing will be left?

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Video Transcript

Victoria is going to put a fence around her rectangular yard which measures 15 and one-ninth yards by 11 and five-ninths yards. If she buys 120 yards of fencing, how many yards of fencing will be left?

Let’s firstly consider the rectangular yard, which has a length of 15 and one-ninth yards and a width of 11 and five-ninths yards. The opposite sides of a rectangle are equal in length. As Victoria is putting a fence around the outside of the yard, we need to firstly work out the perimeter.

We do this by adding two 15 and one-ninth to two 11 and five-ninths. If we consider the whole numbers first, we need to add 15, 15, 11, and 11. 15 plus 15 is equal to 30. 11 plus 11 is equal to 22. This means that the four whole numbers add up to 52. We also need to add the four fractions, one-ninth, one- ninth, five-ninths, and five-ninths. As the denominators of all four fractions are the same, we just need to add the numerators. One plus one plus five plus five is equal to 12. Therefore, one-ninth plus one-ninth plus five-ninths plus five-ninths is equal to twelve-ninths. This means that the total length of fencing required is 52 plus twelve-ninths.

We can simplify this fraction by dividing the numerator and denominator by three. Remember, whatever you do to the top, you must do to the bottom. 12 divided by three is equal to four. And, nine divided by three is equal to three. Therefore, twelve-ninths is equivalent to four-thirds. The line in a fraction means divide, and four divided by three is equal to one remainder one. Therefore, four-thirds is the same as one and one-third. The total length of fencing is therefore 52 plus one and a third. This gives us 53 and one-third yards of fencing.

We were told that Victoria bought 120 yards of fencing. And, we need to calculate how much she has left. In order to do this, we need to subtract 53 and one-third from 120. We can work this out in three steps. Firstly, we can subtract 50 from 120. This gives us 70. We can then subtract three. 70 minus three is equal to 67. At this stage, we have subtracted 53. We also need to subtract one-third. As there are three-thirds in one whole one, 67 minus one-third is equal to 66 and two-thirds. This means that 120 minus 53 and one-third is equal to 66 and two-thirds. If Victoria buys 120 yards of fencing, she will have 66 and two-thirds yards left over.

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