Chapter 11.4, Problem 1P

A recipe calls tor 4 ounces ot chocolate. If you make 15 batches of the recipe (for a large party), then how many pounds of chocolate will you need?

1. Use multiplication or division or both to solve the chocolate problem. Explain why your method of solution makes sense in a way that children could understand. Do not use dimensional analysis.
2. Describe a number of different correct ways to write the answer to the chocolate problem. Explain briefly why these different ways of writing the answer mean the same thing.

To determine

To discuss: The solution of the chocolate problem that makes sense to the children.

Explanation of Solution

Given information:

Chocolate problem:

A recipe calls for 4 ounces of chocolate.The number of batches of the recipe is 15, then how many pounds of chocolate is needed?

Calculation:

A recipe takes 4 ounces of chocolate.

By the use of multiplication, 15 batches of recipe take $15\cdot 4$ ounces of chocolate. That is,

  $15\cdot 4=60\text{ounces}$

It is know that 16 ounces make a pound.

Therefore, the number of pounds in 60 ounces is calculated by the use of division as,

  $\begin{array}{c}60÷16=\frac{60}{16}\\ =\frac{15}{4}\\ =3\frac{3}{4}\text{pounds}\end{array}$

Thus, the number of pounds of chocolate used in 15 batches is $3\frac{3}{4}\text{pounds}$ .

To determine

To write: The different expressions for the solution of chocolate problem.

Answer to Problem 1P

The different expressions for the solution of chocolate problem are $3\frac{3}{4}\text{pounds}$ , $3.75\text{pounds}$ , $60\text{ounces}$ and $3\text{pounds}12\text{ounces}$ .

Explanation of Solution

Given information:

Chocolate problem:

A recipe calls for 4 ounces of chocolate. The number of batches of the recipe is 15, then how many pounds of chocolate is needed?

Calculation:

From subpart (a), one of the solution for the chocolate problem is $3\frac{3}{4}\text{pounds}$ .

Simplify the expression $3\frac{3}{4}\text{pounds}$ in decimal form as follows:

  $\begin{array}{c}3\frac{3}{4}\text{pounds}=\left(3+\frac{3}{4}\right)\text{pounds}\\ \text{=}\left(3+0.75\right)\text{pounds}\\ \text{=}3.75\text{pounds}\end{array}$

Similarly, convert the expression in ounces as follows:

  $\begin{array}{c}3\frac{3}{4}\text{pounds}=\frac{15}{4}\text{pounds}\\ \text{=}\frac{15}{4}\left(16\text{ounces}\right)\\ \text{=}15\cdot 4\text{ounces}\\ \text{=}60\text{ounces}\end{array}$

Similarly, convert the expression in both pounds and ounces as follows:

  $\begin{array}{c}3\frac{3}{4}\text{pounds}=\left(3+\frac{3}{4}\right)\text{pounds}\\ =3\text{pounds}+\frac{3}{4}\text{pounds}\\ \text{=}3\text{pounds}+\frac{3}{4}\left(16\text{ounces}\right)\\ \text{=}3\text{pounds}12\text{ounces}\end{array}$

Conclusion:

Thus, the different expressions for the solution of chocolate problem are $3\frac{3}{4}\text{pounds}$ , $3.75\text{pounds}$ , $60\text{ounces}$ and $3\text{pounds}12\text{ounces}$ .