Let's start by determining how much strawberry jam Stefan made in terms of jars. He made 4 \( \frac{7}{8} \) jars of strawberry jam.
First, we convert the mixed number \( 4 \frac{7}{8} \) into an improper fraction:
\[ 4 \frac{7}{8} = \frac{4 \times 8 + 7}{8} = \frac{32 + 7}{8} = \frac{39}{8} \]
Now we know that Stefan made \( \frac{39}{8} \) jars of strawberry jam.
Next, we calculate how much raspberry jam he made, which is \( \frac{2}{3} \) of the amount of strawberry jam:
\[ \text{Raspberry jam} = \frac{2}{3} \times \frac{39}{8} \]
To multiply these fractions, we do:
\[ \frac{2 \times 39}{3 \times 8} = \frac{78}{24} \]
Now we simplify \( \frac{78}{24} \):
The greatest common divisor (GCD) of 78 and 24 is 6. Therefore, we divide both numerator and denominator by 6:
\[ \frac{78 \div 6}{24 \div 6} = \frac{13}{4} \]
Now we convert \( \frac{13}{4} \) into a mixed number:
\[ \frac{13}{4} = 3 \frac{1}{4} \]
Thus, the number of jars the raspberry jam will fill is
\[ \boxed{3 \frac{1}{4}} \] jars.
1 answer