To find out how much space Connie has left in the jar, we first need to add together the amounts of oats and raisins she's already added, and then subtract that from the total capacity of the jar.
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Capacity of the jar: \( 2 \frac{1}{2} \) cups = \( \frac{5}{2} \) cups
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Oats added: \( 1 \frac{2}{3} \) cups = \( \frac{5}{3} \) cups
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Raisins added: \( \frac{1}{4} \) cup
Now, let's add the oats and raisins together. First, we need to convert both \( \frac{5}{3} \) cups and \( \frac{1}{4} \) cup to a common denominator. The least common denominator of 3 and 4 is 12.
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Convert \( \frac{5}{3} \) to twelfths: \[ \frac{5}{3} = \frac{5 \times 4}{3 \times 4} = \frac{20}{12} \]
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Convert \( \frac{1}{4} \) to twelfths: \[ \frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12} \]
Now we can add the two fractions: \[ \frac{20}{12} + \frac{3}{12} = \frac{23}{12} \]
Next, we'll subtract this total from the jar's capacity: \[ 2 \frac{1}{2} = \frac{5}{2} = \frac{30}{12} \]
The calculation is: \[ \frac{30}{12} - \frac{23}{12} = \frac{7}{12} \]
Thus, the amount of space Connie has left in the jar is \( \frac{7}{12} \) cups.