To convert the division of 2 by \( \frac{4}{3} \) into a multiplication expression, you can multiply by the reciprocal of \( \frac{4}{3} \). The reciprocal of \( \frac{4}{3} \) is \( \frac{3}{4} \).
So, we rewrite the expression \( 2 \div \frac{4}{3} \) as:
\[ 2 \cdot \frac{3}{4} \]
Now let's calculate that:
\[ 2 \cdot \frac{3}{4} = \frac{2 \cdot 3}{4} = \frac{6}{4} = \frac{3}{2} \]
This means for Recipe A, the unit rate of tablespoons of chocolate powder to cups of milk is \( \frac{3}{2} \) (1.5 tablespoons of chocolate powder per cup of milk).
Now let’s calculate the unit rate for Recipe B. Recipe B calls for 3 tablespoons of chocolate powder for every \( \frac{6}{5} \) of a cup of milk. Following the same method, we can express this as:
\[ 3 \div \frac{6}{5} = 3 \cdot \frac{5}{6} \]
Calculating that:
\[ 3 \cdot \frac{5}{6} = \frac{3 \cdot 5}{6} = \frac{15}{6} = \frac{5}{2} \]
This means for Recipe B, the unit rate of tablespoons of chocolate powder to cups of milk is \( \frac{5}{2} \) (2.5 tablespoons of chocolate powder per cup of milk).
Comparison of Recipes:
- Recipe A: 1.5 tablespoons of chocolate powder per cup of milk
- Recipe B: 2.5 tablespoons of chocolate powder per cup of milk
Since Recipe B contains more chocolate powder per cup of milk, it is the more chocolatey recipe!