Question

You need to divide
4
3
​
cup of almonds by
4
3
​
to find 1 cup of almonds. To keep the ratio the same, you also need to divide
5
1
​
cup of raisins by
4
3
​
. Start by writing
5
1
​
÷
4
3
​
as a multiplication expression.
÷
4
3
​

÷
4
3
​

Almonds (cups) Raisins (cups)
4
3
​

5
1
​

1 ?
5
1
​
÷
4
3
​


=
•

Answer 1

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:

1. For **\(5 \frac{1}{3}\)**:
- Multiply the whole number by the denominator: \(5 \times 3 = 15\)
- Add the numerator: \(15 + 1 = 16\)
- So, \(5 \frac{1}{3} = \frac{16}{3}\)

2. 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.