Chapter 4.6, Problem 58CCR

a

To determine

To find : the fraction of the rectangle is not shaded area.

Answer to Problem 58CCR

The fraction of the rectangle is not shaded areais $\frac{3}{5}$

Explanation of Solution

Given information :

Suppose that four-tenths of the rectangle at the right is shaded.

  

Calculation :

The fractionfour-tenths of the rectanglein number is $\frac{4}{10}$

Let 1 be the whole rectangle area

Therefore, thenon-shaded area of the rectangle is

  $\begin{array}{l}=1-\frac{2}{5}\\ =\frac{5-2}{5}\\ =\frac{3}{5}\end{array}$

Hence, $\frac{3}{5}$ of the rectangle is not shaded.

b

To determine

To find : fraction of the rectangle would still need to be shaded for half of the rectangle to be shaded

Answer to Problem 58CCR

  $\frac{1}{10}$ Of the rectangle would still need to be shaded.

Explanation of Solution

Given information :

Suppose that four-tenths of the rectangle at the right is shaded.

  

Calculation :

For $\frac{1}{2}$ of the rectangleto be shaded, subtract to another less them half shaded area of the rectangle.

  $\begin{array}{l}=\frac{1}{2}-\frac{2}{5}\\ =\frac{5-4}{10}\\ =\frac{1}{10}\end{array}$

Hence, $\frac{1}{10}$ of the rectangle would still need to be shaded.

c

To determine

To find : fraction of the rectangle would be shaded

Answer to Problem 58CCR

  $\frac{13}{15}$ Fraction of the rectangle would be shaded

Explanation of Solution

Given information :

Suppose that four-tenths of the rectangle at the right is shaded.The fraction of the rectangle were to be shaded to be add from $\frac{7}{5}$ .

  

Calculation :

  $\begin{array}{l}=\frac{2}{5}+\frac{7}{15}\\ =\frac{2\cdot 3+7\cdot 1}{15}\\ =\frac{13}{15}\end{array}$

Hence, $\frac{13}{15}$ fraction of the rectangle would be shaded.