Connie is putting the ingredients for her favorite oatmeal into a jar. The jar holds 2 ½ cups of ingredients. So far she has added 1 ⅔ cups of oats to the jar and ¼ cup of raisins. How much does Connie have left in the jar?(4 points)

Answer 1

To find out how much space Connie has left in the jar, we need to subtract the total amount of ingredients she has added from the total capacity of the jar.

1. Total capacity of the jar:
   \( 2 \frac{1}{2} \) cups can be converted to an improper fraction:
   \( 2 \frac{1}{2} = \frac{5}{2} \) cups

2. Total amount added so far:
   Connie has added \( 1 \frac{2}{3} \) cups of oats and \( \frac{1}{4} \) cup of raisins.
   First, convert \( 1 \frac{2}{3} \) to an improper fraction:
   \( 1 \frac{2}{3} = \frac{5}{3} \) cups.

Now, we need to find a common denominator to add \( \frac{5}{3} \) and \( \frac{1}{4} \). The least common multiple of 3 and 4 is 12.

3. Convert the fractions to have a common denominator of 12:

   • For \( \frac{5}{3} \):
     \( \frac{5}{3} = \frac{5 \times 4}{3 \times 4} = \frac{20}{12} \)

   • For \( \frac{1}{4} \):
     \( \frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12} \)

4. Add the two fractions together:
   \[ \frac{20}{12} + \frac{3}{12} = \frac{23}{12} \text{ cups} \]

5. Now subtract the total added from the total capacity of the jar:
   Convert \( \frac{5}{2} \) to a fraction over 12:
   \( \frac{5}{2} = \frac{5 \times 6}{2 \times 6} = \frac{30}{12} \)

   Now perform the subtraction:
   \[ \frac{30}{12} - \frac{23}{12} = \frac{7}{12} \text{ cups} \]

So, Connie has \( \frac{7}{12} \) cups left in the jar.