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The denominate number 55 min is simplified since it is smaller than the next higher type of unit, 1 hr. The denominate number 65 min is not simplified since it is not smaller than the next higher type of unit, 1 hr. The denominate number 65 min can be simplified to 1 hr 5 min. The denominate number 1 hr 5 min is simplified since the next higher type of unit is day, and 1 hr does not exceed 1 day.
Simplify 19 in.
Since $\text{12}\text{in}\text{.}=\text{1 ft}$ , and $\text{19}=\text{12}+7$ ,
$\begin{array}{ccc}\hfill \text{19 in.}& =& \text{12 in.}+\text{7 in.}\hfill \\ & =& \text{1 ft}+\text{7 in.}\hfill \\ & =& \text{1 ft 7 in.}\hfill \end{array}$
Simplify 4 gal 5 qt.
Since $4\text{qt}=\text{1 gal}$ , and $5=4+1$ ,
$\begin{array}{ccc}\hfill \text{4 gal 5 qt}& =& \text{4 gal}+\text{4 qt}+\text{1qt}\hfill \\ & =& \text{4 gal}+\text{1 gal}+\text{1 qt}\hfill \\ & =& \text{5 gal}+\text{1 qt}\hfill \\ & =& \text{5 gal 1 qt}\hfill \end{array}$
Simplify 2 hr 75 min.
Since $\text{60 min}=\text{1 hr}$ , and $\text{75}=\text{60}+\text{15}$ ,
$\begin{array}{ccc}\hfill \text{2 hr 75 min}& =& \text{2 hr}+\text{60 min}+\text{15 min}\hfill \\ & =& \text{2 hr}+\text{1 hr}+\text{15 min}\hfill \\ & =& \text{3 hr}+\text{15 min}\hfill \\ & =& \text{3 hr 15 min}\hfill \end{array}$
Simplify 43 fl oz.
Since $\text{8 fl oz}=\text{1 c}$ (1 cup), and $\text{43}\xf78=5\text{R3}$ ,
$\begin{array}{ccc}\hfill \text{43 fl oz}& =& \text{40 fl oz}+\text{3 fl oz}\hfill \\ & =& 5\cdot \text{8 fl oz}+\text{3 fl oz}\hfill \\ & =& 5\cdot \text{1 c}+\text{3 fl oz}\hfill \\ & =& \text{5 c}+\text{3 fl oz}\hfill \end{array}$
But, $\text{2 c}=\text{1 pt}$ and $5\xf72=2\text{R1}$ . So,
$\begin{array}{ccc}\hfill \text{5 c}+\text{3 fl oz}& =& \text{2}\cdot \text{2 c}+\text{1 c}+\text{3 fl oz}\hfill \\ & =& 2\cdot \text{1 pt}+\text{1 c}+\text{3 fl oz}\hfill \\ & =& \text{2 pt}+\text{1 c}+\text{3 fl oz}\hfill \end{array}$
But, $\text{2 pt}=\text{1 qt}$ , so
$\text{2 pt}+\text{1 c}+\text{3 fl oz}=\text{1 qt 1 c 3 fl oz}$
Simplify each denominate number. Refer to the conversion tables given in [link] , if necessary.
Add 6 ft 8 in. to 2 ft 9 in.
$\begin{array}{cc}\hfill \text{6 ft8 in}\text{.}& \\ \hfill \underline{+\text{2 ft9 in}\text{.}}& \\ \hfill \text{8 ft 17 in}\text{.}& \text{Simplify this denominate number.}\hfill \end{array}$
Since $\text{12 in}\text{.}=\text{1 ft}$ ,
$\begin{array}{ccc}\hfill \text{8 ft}+\text{12 in.}+\text{5 in.}& =& \text{8 ft}+\text{1 ft}+\text{5 in.}\hfill \\ & =& \text{9 ft}+\text{5 in.}\hfill \\ & =& \text{9 ft 5 in.}\hfill \end{array}$
Subtract 5 da 3 hr from 8 da 11 hr.
$\begin{array}{c}\hfill \text{8 da11 hr}\\ \hfill \underline{-\text{5 da3 hr}}\\ \hfill \text{3 da8 hr}\end{array}$
Subtract 3 lb 14 oz from 5 lb 3 oz.
$\begin{array}{c}\hfill \text{5 lb3 oz}\\ \hfill \underline{-\text{3 lb 14 oz}}\end{array}$
We cannot directly subtract 14 oz from 3 oz, so we must borrow 16 oz from the pounds.
$\begin{array}{cccc}\hfill \text{5 lb 3 oz}& =& \text{5 lb}+\text{3 oz}\hfill & \\ & =& \text{4 lb}+\text{1 lb}+\text{3 oz}\hfill & \\ & =& \text{4 lb}+\text{16 oz}+\text{3 oz}\hfill & (\text{Since 1 lb}=\text{16 oz.})\hfill \\ & =& \text{4 lb}+\text{19 oz}\hfill & \\ & =& \text{4 lb 19 oz}\hfill & \end{array}$
$\begin{array}{c}\hfill \text{4 lb 19 oz}\\ \hfill \underline{-\text{3 lb 14 oz}}\\ \hfill \text{1 lb5 oz}\end{array}$
Subtract 4 da 9 hr 21 min from 7 da 10 min.
$\begin{array}{c}\hfill \text{7 da 0 hr 10 min}\\ \hfill \underline{-\text{4 da 9 hr 21 min}}\end{array}$ Borrow 1 da from the 7 da.
$\begin{array}{c}\hfill \text{6 da 24 hr 10 min}\\ \hfill \underline{-\text{4 da9 hr 21 min}}\end{array}$ Borrow 1 hr from the 24 hr.
$\begin{array}{c}\hfill \text{6 da 23 hr 70 min}\\ \hfill \underline{-\text{4 da9 hr 21 min}}\\ \hfill \text{2 da 14 hr 49 min}\end{array}$
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