Chapter 24, Problem 14A

To determine

(a)

Find the addition or subtraction of the given expression.

Answer to Problem 14A

The addition of the given expression is $\text{7}\text{ft}10\text{in}\text{.}$.

Explanation of Solution

Given information:

The given expression is $5\text{ft 4}\text{in}\text{.+2}\text{ft 6}\text{in}\text{.}$.

Calculation:

Given: $5\text{ft 4}\text{in}\text{.+2}\text{ft 6}\text{in}\text{.}$

The relation between feet and inch is,

  $1\text{ft}=12\text{in}\text{.}$

Apply principle of subtraction rule

  $\begin{array}{l}5\text{ft 4}\text{in}\text{.+2}\text{ft 6}\text{in}\text{.}\\ =\left(5+2\right)\text{ft}\left(4+6\right)\text{in}\text{.}\\ \text{=7}\text{ft}10\text{in}\text{.}\end{array}$

Hence the addition of the given expression is $\text{7}\text{ft}10\text{in}\text{.}$.

To determine

(b)

Find the addition or subtraction of the given expression.

Answer to Problem 14A

The addition of the given expression is $\text{7}\text{ft}11\text{in}\text{.}$.

Explanation of Solution

Given information:

The given expression is $3\text{ft 8}\text{in}\text{.+}4\text{ft 3}\text{in}\text{.}$.

Calculation:

Given: $3\text{ft 8}\text{in}\text{.+}4\text{ft 3}\text{in}\text{.}$

The relation between feet and inch is,

  $1\text{ft}=12\text{in}\text{.}$

Apply principle of subtraction rule

  $\begin{array}{l}3\text{ft 8}\text{in}\text{.+}4\text{ft 3}\text{in}\text{.}\\ =\left(3+4\right)\text{ft}\left(8+3\right)\text{in}\text{.}\\ \text{=7}\text{ft}11\text{in}\text{.}\end{array}$

Hence the addition of the given expression is $\text{7}\text{ft}11\text{in}\text{.}$.

To determine

(c)

Find the addition or subtraction of the given expression.

Answer to Problem 14A

The subtraction of the given expression is $\text{1}\text{ft}1\text{in}\text{.}$.

Explanation of Solution

To solve the give expression.

Given information:

The given expression is $3\text{ft 7}\text{in}\text{.}-2\text{ft 6}\text{in}\text{.}$.

Calculation:

Given: $3\text{ft 7}\text{in}\text{.}-2\text{ft 6}\text{in}\text{.}$

The relation between feet and inch is,

  $1\text{ft}=12\text{in}\text{.}$

Apply principle of subtraction rule

  $\begin{array}{l}3\text{ft 7}\text{in}\text{.}-2\text{ft 6}\text{in}\text{.}\\ =\left(3-2\right)\text{ft}\left(7-6\right)\text{in}\text{.}\\ \text{=1}\text{ft}1\text{in}\text{.}\end{array}$

Hence the subtraction of the given expression is $\text{1}\text{ft}1\text{in}\text{.}$

To determine

(d)

Find the addition or subtraction of the given expression.

Answer to Problem 14A

The subtraction of the given expression is $\text{3}\text{ft}2\text{in}\text{.}$.

Explanation of Solution

Given information:

The given expression is $5\text{ft }9\text{in}\text{.}-2\text{ft 7}\text{in}\text{.}$.

Calculation:

Given: $5\text{ft }9\text{in}\text{.}-2\text{ft 7}\text{in}\text{.}$

The relation between feet and inch is,

  $1\text{ft}=12\text{in}\text{.}$

Apply principle of subtraction rule

  $\begin{array}{l}5\text{ft }9\text{in}\text{.}-2\text{ft 7}\text{in}\text{.}\\ =\left(5-2\right)\text{ft}\left(9-\text{7}\right)\text{in}\text{.}\\ \text{=3}\text{ft}2\text{in}\text{.}\end{array}$

Hence the subtraction of the given expression is $\text{3}\text{ft}2\text{in}\text{.}$

To determine

(e)

Find the addition or subtraction of the given expression.

Answer to Problem 14A

The addition of the given expression is $\text{12}\text{ft}5\frac{7}{8}\text{in}\text{.}$.

Explanation of Solution

Given information:

The given expression is $7\text{ft 3}\frac{1}{2}\text{in}\text{.+5}\text{ft 2}\frac{3}{8}\text{in}\text{.}$.

Calculation:

Given: $7\text{ft 3}\frac{1}{2}\text{in}\text{.+5}\text{ft 2}\frac{3}{8}\text{in}\text{.}$

The relation between feet and inch is,

  $1\text{ft}=12\text{in}\text{.}$

Apply principle of subtraction rule

  $\begin{array}{l}7\text{ft 3}\frac{1}{2}\text{in}\text{.+5}\text{ft 2}\frac{3}{8}\text{in}\text{.}\\ =\left(7+5\right)\text{ft}\left(\text{3}\frac{1}{2}\text{+2}\frac{3}{8}\right)\text{in}\text{.}\\ =12\text{ft}\left(\frac{7}{2}+\frac{19}{8}\right)\text{in}\text{.}\\ \text{=12}\text{ft}\left(\frac{28+19}{8}\right)\text{in}\text{.}\\ \text{=12}\text{ft}\left(\frac{47}{8}\right)\text{in}\text{.}\\ \text{=12}\text{ft}5\frac{7}{8}\text{in}\text{.}\end{array}$

Hence the addition of the given expression is $\text{12}\text{ft}5\frac{7}{8}\text{in}\text{.}$.

To determine

(f)

Find the addition or subtraction of the given expression.

Answer to Problem 14A

The addition of the given expression is $\text{5}\text{ft}10\frac{3}{16}\text{in}\text{.}$

Explanation of Solution

Given information:

The given expression is $2\text{ft 5}\frac{3}{4}\text{in}\text{.+3}\text{ft 4}\frac{7}{16}\text{in}\text{.}$.

Calculation:

Given: $2\text{ft 5}\frac{3}{4}\text{in}\text{.+3}\text{ft 4}\frac{7}{16}\text{in}\text{.}$

The relation between feet and inch is,

  $1\text{ft}=12\text{in}\text{.}$

Apply principle of subtraction rule

  $\begin{array}{l}2\text{ft 5}\frac{3}{4}\text{in}\text{.+3}\text{ft 4}\frac{7}{16}\text{in}\text{.}\\ =\left(2+3\right)\text{ft}\left(\text{5}\frac{3}{4}\text{+4}\frac{7}{16}\right)\text{in}\text{.}\\ =5\text{ft}\left(\frac{23}{4}-\frac{71}{16}\right)\text{in}\text{.}\\ \text{=5}\text{ft}\left(\frac{92+71}{16}\right)\text{in}\text{.}\\ \text{=5}\text{ft}\left(\frac{163}{16}\right)\text{in}\text{.}\\ \text{=5}\text{ft}10\frac{3}{16}\text{in}\text{.}\end{array}$

Hence the addition of the given expression is $\text{5}\text{ft}10\frac{3}{16}\text{in}\text{.}$

To determine

(g)

Find the addition or subtraction of the given expression.

Answer to Problem 14A

The subtraction of the given expression is $\text{1}\text{ft}\frac{3}{4}\text{in}\text{.}$.

Explanation of Solution

Given information:

The given expression is $7\text{ft 6}\frac{1}{2}\text{in}\text{.}-6\text{ft 5}\frac{3}{4}\text{in}\text{.}$.

Calculation:

Given: $7\text{ft 6}\frac{1}{2}\text{in}\text{.}-6\text{ft 5}\frac{3}{4}\text{in}\text{.}$

The relation between feet and inch is,

  $1\text{ft}=12\text{in}\text{.}$

Apply principle of subtraction rule

  $\begin{array}{l}7\text{ft 6}\frac{1}{2}\text{in}\text{.}-6\text{ft 5}\frac{3}{4}\text{in}\text{.}\\ =\left(7-6\right)\text{ft}\left(\text{6}\frac{1}{2}-\text{5}\frac{3}{4}\right)\text{in}\text{.}\\ =1\text{ft}\left(\frac{13}{2}-\frac{23}{4}\right)\text{in}\text{.}\\ \text{=1}\text{ft}\left(\frac{26-23}{4}\right)\text{in}\text{.}\\ \text{=1}\text{ft}\left(\frac{3}{4}\right)\text{in}\text{.}\\ \text{=1}\text{ft}\frac{3}{4}\text{in}\text{.}\end{array}$

Hence the subtraction of the given expression is $\text{1}\text{ft}\frac{3}{4}\text{in}\text{.}$

To determine

(h)

Find the addition or subtraction of the given expression.

Answer to Problem 14A

The subtraction of the given expression is $2\text{ft}2\frac{9}{16}\text{in}\text{.}$

Explanation of Solution

Given information:

The given expression is $3\text{ft }9\frac{7}{8}\text{in}\text{.}-1\text{ft 7}\frac{5}{16}\text{in}\text{.}$.

Calculation:

Given: $3\text{ft }9\frac{7}{8}\text{in}\text{.}-1\text{ft 7}\frac{5}{16}\text{in}\text{.}$

The relation between feet and inch is,

  $1\text{ft}=12\text{in}\text{.}$

Apply principle of subtraction rule

  $\begin{array}{l}3\text{ft }9\frac{7}{8}\text{in}\text{.}-1\text{ft 7}\frac{5}{16}\text{in}\text{.}\\ =\left(3-1\right)\text{ft}\left(9\frac{7}{8}-\text{7}\frac{5}{16}\right)\text{in}\text{.}\\ =2\text{ft}\left(\frac{79}{8}-\frac{117}{16}\right)\text{in}\text{.}\\ \text{=}2\text{ft}\left(\frac{158-117}{16}\right)\text{in}\text{.}\\ \text{=}2\text{ft}\left(\frac{41}{16}\right)\text{in}\text{.}\\ \text{=}2\text{ft}2\frac{9}{16}\text{in}\text{.}\end{array}$

Hence the subtraction of the given expression is $2\text{ft}2\frac{9}{16}\text{in}\text{.}$