Question

Recipe A calls for 2 tablespoons of chocolate powder for every
4
3
​
of a cup of milk. Recipe B calls for 3 tablespoons of chocolate powder for every
6
5
​
of a cup of milk. Which chocolate milk recipe tastes more chocolatey?
Let’s break this down. You’re trying to determine the unit rate of tablespoons of chocolate powder to cups of milk by finding 2÷
4
3
​
. Start by writing 2÷
4
3
​
as a multiplication expression.
÷
4
3
​

÷
4
3
​

Recipe A
Milk (cups) Chocolate Powder (tablespoons)
4
3
​
2
1 ?
2 ÷
4
3
​

= 2 ·

Answer 1

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!