Recipe A calls for 2 tablespoons of chocolate powder for every

Question

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?
Now, write 2·
3
4
​
as a single fraction.
÷
4
3
​

÷
4
3
​

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

= 2·
3
4
​

=
•
•

Answer 1

To compare the chocolatey-ness of both recipes, we will calculate the ratio of chocolate powder to milk for both Recipe A and Recipe B.

Recipe A

• Chocolate Powder: 2 tablespoons
• Milk: \( \frac{4}{3} \) cups

The ratio for Recipe A can be calculated as follows:

\[ \text{Ratio A} = \frac{\text{Chocolate Powder}}{\text{Milk}} = \frac{2 \text{ tablespoons}}{\frac{4}{3} \text{ cups}} \]

To divide by a fraction, we multiply by its reciprocal:

\[ \text{Ratio A} = 2 \times \frac{3}{4} = \frac{6}{4} = \frac{3}{2} \]

Recipe B

• Chocolate Powder: 3 tablespoons
• Milk: \( \frac{6}{5} \) cups

The ratio for Recipe B is:

\[ \text{Ratio B} = \frac{3 \text{ tablespoons}}{\frac{6}{5} \text{ cups}} = 3 \times \frac{5}{6} = \frac{15}{6} = \frac{5}{2} \]

Comparison

• Recipe A: \( \frac{3}{2} \) tablespoons of chocolate powder per cup of milk.
• Recipe B: \( \frac{5}{2} \) tablespoons of chocolate powder per cup of milk.

Since \( \frac{5}{2} > \frac{3}{2} \), Recipe B tastes more chocolatey.

Simplifying \( 2 \cdot \frac{3}{4} \div \frac{4}{3} \)

Now, to simplify \( 2 \cdot \frac{3}{4} \div \frac{4}{3} \):

1. First, convert the division into multiplication by the reciprocal:

\[ 2 \cdot \frac{3}{4} \cdot \frac{3}{4} \]

2. Multiply:

\[ = 2 \cdot \frac{9}{16} = \frac{18}{16} = \frac{9}{8} \]

Final Result

So, \( 2 \cdot \frac{3}{4} \div \frac{4}{3} = \frac{9}{8} \).