Stefan made strawberry jam and raspberry jam. He made enough strawberry jam to fill 4 7/8 jars. If he made 2/3 as much raspberry jam as strawberry jam, how many jars will the raspberry jam fill?

Write your answer as a fraction or as a whole or mixed number.

jars

1 answer

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.