Chapter 7, Problem 3PTTS

To determine

To calculate: The amount of each ingredient needed if recipe is reduced to half.

Answer to Problem 3PTTS

To reduce the recipe to half, $\frac{1}{3}$ cups of milk, $\frac{1}{4}$ cups of sugar and $1\frac{1}{8}$ cups of flour is needed.

Explanation of Solution

Given information:

Amount of milk required = $\frac{2}{3}$ cups.

Amount of sugar required = $\frac{1}{2}$ cups.

Amount of flour required = $2\frac{1}{4}$ cups.

Calculation:

To reduce the recipe by half, reduce each ingredient by half. To reduce each ingredient by half, divide by $2$ .

Amount of milk required:

  $\begin{array}{l}\frac{2}{3}÷2\text{ [Divide by 2]}\\ \Rightarrow \frac{2}{3}\cdot \frac{1}{2}\text{ [Multiply by reciprocal]}\\ \Rightarrow \frac{2\cdot 1}{3\cdot 2}\text{ [Use rules for multiplying fractions]}\\ \Rightarrow \frac{2}{6}\text{ [Multiply]}\\ \Rightarrow \frac{1}{3}\text{ [Sinmplify]}\end{array}$

Amount of sugar required:

  $\begin{array}{l}\frac{1}{2}÷2\text{ [Divide by 2]}\\ \Rightarrow \frac{1}{2}\cdot \frac{1}{2}\text{ [Multiply by reciprocal]}\\ \Rightarrow \frac{1\cdot 1}{2\cdot 2}\text{ [Use rules for multiplying fractions]}\\ \Rightarrow \frac{1}{4}\text{ [Multiply]}\end{array}$

Amount of flour required:

  $\begin{array}{l}2\frac{1}{4}÷2\text{ [Divide by 2]}\\ \Rightarrow \frac{9}{4}÷2\text{ [Write number as improper fraction]}\\ \Rightarrow \frac{9}{4}\cdot \frac{1}{2}\text{ [Multiply by reciprocal]}\\ \Rightarrow \frac{9\cdot 1}{4\cdot 2}\text{ [Use rules for multiplying fractions]}\\ \Rightarrow \frac{9}{8}\text{ [Multiply]}\\ \Rightarrow 1\frac{1}{8}\text{ [Write fraction as mixed number]}\end{array}$

Therefore, to reduce the recipe to half, $\frac{1}{3}$ cups of milk, $\frac{1}{4}$ cups of sugar and $1\frac{1}{8}$ cups of flour is needed.