To find out how much more the green grapes weigh than the red grapes, we need to subtract the weight of the red grapes from the weight of the green grapes.
Ruth bought:
- Green grapes: \( 2 \frac{1}{2} \) pounds
- Red grapes: \( \frac{1}{3} \) pounds
First, let's convert \( 2 \frac{1}{2} \) pounds into an improper fraction.
\[ 2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2} \]
Now we can subtract the weight of the red grapes from the weight of the green grapes:
\[ \frac{5}{2} - \frac{1}{3} \]
To perform this subtraction, we need a common denominator. The least common multiple of 2 and 3 is 6. So we convert both fractions to have a denominator of 6.
For \( \frac{5}{2} \):
\[ \frac{5}{2} = \frac{5 \times 3}{2 \times 3} = \frac{15}{6} \]
For \( \frac{1}{3} \):
\[ \frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6} \]
Now we can subtract:
\[ \frac{15}{6} - \frac{2}{6} = \frac{15 - 2}{6} = \frac{13}{6} \]
Thus, the green grapes weigh \( \frac{13}{6} \) pounds more than the red grapes.
To express \( \frac{13}{6} \) as a mixed number, we can divide 13 by 6:
\[ 13 \div 6 = 2 \quad \text{(remainder 1)} \]
So, we have:
\[ \frac{13}{6} = 2 \frac{1}{6} \]
Therefore, the answer is:
\[ \boxed{\frac{13}{6}} \quad \text{or} \quad \boxed{2 \frac{1}{6}} \]
8 answers