To convert the division of fractions into a multiplication expression, we can use the property that dividing by a fraction is the same as multiplying by its reciprocal.
The expression you want to rewrite is:
\[
5 \frac{1}{3} \div 4 \frac{1}{3}
\]
First, let's convert the mixed numbers into improper fractions:
-
For \(5 \frac{1}{3}\):
- Multiply the whole number by the denominator: \(5 \times 3 = 15\)
- Add the numerator: \(15 + 1 = 16\)
- So, \(5 \frac{1}{3} = \frac{16}{3}\)
-
For \(4 \frac{1}{3}\):
- Multiply the whole number by the denominator: \(4 \times 3 = 12\)
- Add the numerator: \(12 + 1 = 13\)
- So, \(4 \frac{1}{3} = \frac{13}{3}\)
Now we can rewrite the division as:
\[ \frac{16}{3} \div \frac{13}{3} \]
To change this to a multiplication expression, we multiply by the reciprocal of the second fraction:
\[ \frac{16}{3} \times \frac{3}{13} \]
Now you can proceed to simplify this expression:
The \(3\) in the numerator of the second fraction and the \(3\) in the denominator of the first fraction cancel each other out:
\[ \frac{16 \cancel{3}}{\cancel{3} \cdot 13} = \frac{16}{13} \]
Therefore, the expression \(5 \frac{1}{3} \div 4 \frac{1}{3}\) can be written as:
\[ 5 \frac{1}{3} \div 4 \frac{1}{3} = \frac{16}{3} \times \frac{3}{13} = \frac{16}{13} \]
So the answer is:
\[ \frac{16}{13} \]
This concludes the calculations, and you can maintain the proportions of almonds and raisins accordingly.