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Sarah uses a roll of border fencing that is 25 and one-fourth feet long to surround a rectangular flower bed in her garden.

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If the width of the flower bed is one and five-eighths feet, what is its length?

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Let’s think about what we know.

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Sarah has a flower bed with a rectangular fence around it.

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The border fencing is 25 and one-fourth feet long.

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Mathematically, we would call this the perimeter, the distance around a 2D shape.

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And because a rectangle has two sets of equal sides, we add the length twice and then the width twice to find the perimeter.

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If the distance around Sarah’s flower bed, the perimeter of her flower bed, was 25 and one-fourth feet, we want to know what the length of the flower bed is.

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And we already know that the width was one and five-eighths feet.

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Our first step will be to add up how much of the fence is used on the two pieces representing the width of the flower bed.

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This means we need to add one and five-eighths plus one and five-eighths.

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If we add the two fractions, they need a common denominator.

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Both of these fractions are out of eight.

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And that means we can add their numerators together.

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Five-eighths plus five-eighths equals ten-eighths.

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And one plus one equals two.

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But we noticed that ten-eighths is an improper fraction.

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We could write two and ten-eighths as two plus eight-eighths plus two-eighths.

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And we know that eight-eighths equals one.

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So we would add two plus one to get three, three and two-eighths.

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We can simplify one final time.

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Two-eighths is the same as one-fourth.

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We can divide our numerator by two and our denominator by two.

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And that reduces two-eighths to one-fourth.

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This means that the width takes up three and one-fourth feet of the total fencing.

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If three and one-fourth of the total fencing is used on the width, we can subtract that from the amount of total fencing used.

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One-fourth minus one-fourth equals zero.

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And 25 minus three equals 22.

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This means there are 22 feet left to be divided evenly between the two length sides.

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22 divided by two equals 11.

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This means that the length of Sarah’s flower bed was 11 feet.

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11 plus 11 equals 22.

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And one and five-eighths plus one and five-eighths equals three and one-fourth.

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When we add all four of these sides together, we get 25 and one-fourth feet.

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And so, we can say that the length of Sarah’s flower bed is 11 feet.