Chapter 0.5, Problem 44E

To determine

To find: The number of hours that Samantha practices flute in a month.

Answer to Problem 44E

Samantha practices flute for $18$ hours in a month.

Explanation of Solution

Given information:

Samantha practices flute for $4\frac{1}{2}$ hours each week.

Formula used:

Mixed fractions of the form $m\frac{p}{q}$ can be converted into proper fractions as,

  $m\frac{p}{q}=\frac{\left(m\times q\right)+p}{q}$

A month normally contains 4 weeks. Weeks and month are related to each other, which can be expressed by a mathematical equation as,

  $\text{1 month}=\text{4 weeks}$

Calculation:

Consider the given statement “Samantha practices flute for $4\frac{1}{2}$ hours each week.”

Recall that the mixed fractions of the form $m\frac{p}{q}$ can be converted into proper fractions as,

  $m\frac{p}{q}=\frac{\left(m\times q\right)+p}{q}$

So, $4\frac{1}{2}$ will be converted as,

  $\begin{array}{c}4\frac{1}{2}=\frac{\left(2\times 4\right)+1}{2}\\ =\frac{9}{2}\end{array}$

Recall that a month normally contains 4 weeks. Weeks and month are related to each other, which can be expressed by a mathematical equation as,

  $\text{1 month}=\text{4 weeks}$

So, number of hours that Samantha practices flute in a month will be evaluated as when $4\frac{1}{2}$ is multiplied by 4.

  $4\frac{1}{2}=\frac{9}{2}\cdot 4$

4 can be expressed as a product of 2 and 2.

  $\begin{array}{c}4\frac{1}{2}=\frac{9}{2}\cdot 4\\ =\frac{9\cdot 2\cdot 2}{2}\\ =18\end{array}$

Thus, Samantha practices flute for $18$ hours in a month.