Chapter 0.5, Problem 46E

To determine

To find: The number of boards, each 2 feet 8 inches long, can be cut from a board 16 feet long.

Answer to Problem 46E

6 boards, each 2 feet 8 inches long, can be cut from a board 16 feet long.

Explanation of Solution

Given information:

A board which is 16 feet long from which smaller boards each 2 feet 8 inches long can be cut.

Formula used:

Conversion rule of converting feet into inches which can be mathematically expressed as,

  $\text{1 feet = 12 inches}$

Division in real numbers is multiplication by reciprocal. If $b\ne 0$ , then,

  $\begin{array}{c}a÷b=a\left(\frac{1}{b}\right)\\ =\frac{a}{b}\end{array}$

Here, $\frac{1}{b}$ is the multiplicative inverse.

Calculation:

Consider the given statement “A board which is 16 feet long from which smaller boards each 2 feet 8 inches long can be cut.”

Recall conversion rule of converting feet into inches which can be mathematically expressed as,

  $\text{1 feet = 12 inches}$

So, 2 feet 8 inches will be evaluated as when 2 is multiplied to 12 and 8 is added to it.

So, 2 feet 8 inches is calculated as,

  $\begin{array}{c}\text{2 feet 8 inches =}\left[\left(\text{2}\cdot \text{12}\right)\text{+8}\right]\text{ inches}\\ \text{=32 inches}\end{array}$

And 16 feet will be calculated as,

  $\begin{array}{c}\text{1 feet = 12 inches}\\ \text{16 feet = 16}\cdot \text{12 inches}\\ \text{=192 inches}\end{array}$

Now, the number of boards, each 2 feet 8 inches long, can be cut from a board 16 feet long,

will be evaluated when $192$ is divided by $32$ .

Recall that the division in real numbers is multiplication by reciprocal. If $b\ne 0$ , then,

  $\begin{array}{c}a÷b=a\left(\frac{1}{b}\right)\\ =\frac{a}{b}\end{array}$

Here, $\frac{1}{b}$ is the multiplicative inverse.

So, number of boards, each 2 feet 8 inches long, can be cut from a board 16 feet long,

is calculated as,

  $\begin{array}{c}192÷32=192\cdot \frac{1}{32}\\ =\frac{32\cdot 6}{32}\\ =6\end{array}$

Thus, 6 number of boards, each 2 feet 8 inches long, can be cut from a board 16 feet long,