# 9.3 Simplification of denominate numbers  (Page 2/2)

 Page 2 / 2

## Practice set b

Perform each operation. Simplify when possible.

Add 4 gal 3 qt to 1 gal 2 qt.

6 gal 1 qt

Add 9 hr 48 min to 4 hr 26 min.

14 hr 14 min

Subtract 2 ft 5 in. from 8 ft 7 in.

6 ft 2in.

Subtract 15 km 460 m from 27 km 800 m.

12 km 340 m

Subtract 8 min 35 sec from 12 min 10 sec.

3 min 35 sec

Add 4 yd 2 ft 7 in. to 9 yd 2 ft 8 in.

14 yd 2 ft 3 in

Subtract 11 min 55 sec from 25 min 8 sec.

13 min 13 sec

## Multiplying a denominate number by a whole number

Let's examine the repeated sum

$\underset{\text{3 times}}{\underbrace{\text{4 ft 9 in.}+\text{4 ft 9 in.}+\text{4 ft 9 in.}}}=\text{12 ft 27 in.}$

Recalling that multiplication is a description of repeated addition, by the distribu­tive property we have

$\begin{array}{cccc}\hfill 3\left(\text{4 ft 9 in}\text{.}\right)& =& 3\left(\text{4 ft}+\text{9 in.}\right)\hfill & \\ & =& 3\cdot \text{4 ft}+3\cdot \text{9 in.}\hfill & \\ & =& \text{12 ft}+\text{27 in.}\hfill & \text{Now, 27 in.}=\text{2 ft 3 in.}\hfill \\ & =& \text{12 ft}+\text{2 ft}+\text{3 in.}\hfill & \\ & =& \text{14 ft}+\text{3 in.}\hfill & \\ & =& \text{14 ft 3 in.}\hfill & \end{array}$

From these observations, we can suggest the following rule.

## Multiplying a denominate number by a whole number

To multiply a denominate number by a whole number, multiply the number part of each unit by the whole number and affix the unit to this product.

## Sample set c

Perform the following multiplications. Simplify if necessary.

$\begin{array}{ccc}\hfill 6\cdot \left(\text{2 ft 4 in.}\right)& =& 6\cdot \text{2 ft}+6\cdot \text{4 in.}\hfill \\ & =& \text{12 ft}+\text{24 in.}\hfill \end{array}$

Since $\text{3 ft}=\text{1 yd}$ and ,

$\begin{array}{ccc}\hfill \text{12 ft}+\text{24 in.}& =& \text{4 yd}+\text{2 ft}\hfill \\ & =& \text{4 yd 2 ft}\hfill \end{array}$

$\begin{array}{ccc}\hfill 8\cdot \left(\text{5 hr 21 min 55 sec}\right)& =& 8\cdot 5\text{hr}+8\cdot \text{21 min}+8\cdot \text{55 sec}\hfill \\ & =& \text{40 hr}+\text{168 min}+\text{440sec}\hfill \\ & =& \text{40 hr}+\text{168 min}+\text{7 min}+\text{20 sec}\hfill \\ & =& \text{40 hr}+\text{175 min}+\text{20 sec}\hfill \\ & =& \text{40 hr}+\text{2 hr}+\text{55 min}+\text{20 sec}\hfill \\ & =& \text{42 hr}+\text{55 min}+\text{20 sec}\hfill \\ & =& \text{24hr}+\text{18hr}+\text{55 min}+\text{20 sec}\hfill \\ & =& \text{1 da}+\text{18 hr}+\text{55 min}+\text{20 sec}\hfill \\ & =& \text{1 da 18 hr 55 min 20 sec}\hfill \end{array}$

## Practice set c

Perform the following multiplications. Simplify.

$2\cdot \left(\text{10 min}\right)$

20 min

$5\cdot \left(\text{3 qt}\right)$

$\text{15 qt}=\text{3 gal 3 qt}$

$4\cdot \left(5\text{ft 8 in}\text{.}\right)$

$\text{20 ft 32 in}\text{.}=\text{7 yd 1 ft 8 in}\text{.}$

$\text{10}\cdot \left(2\text{hr 15 min 40 sec}\right)$

$\text{20 hr 150 min 400 sec}=\text{22 hr 36 min 40 sec}$

## Dividing a denominate number by a whole number

To divide a denominate number by a whole number, divide the number part of each unit by the whole number beginning with the largest unit. Affix the unit to this quotient. Carry any remainder to the next unit.

## Sample set d

Perform the following divisions. Simplify if necessary.

$\left(\text{12 min 40 sec}\right)÷4$

Thus $\left(\text{12 min 40 sec}\right)÷4=3\text{min 10 sec}$

$\left(\text{5 yd 2 ft 9 in}\text{.}\right)÷3$

$\begin{array}{}\text{Convert to feet: 2 yd 2 ft}=\text{8 ft}\text{.}\\ \text{Convert to inches: 2 ft 9 in}\text{.}=\text{33 in}\text{.}\end{array}$

Thus $\left(\text{5 yd 2 ft 9 in}\text{.}\right)÷3=1\text{yd 2 ft 11 in}\text{.}$

## Practice set d

Perform the following divisions. Simplify if necessary.

$\left(\text{18 hr 36 min}\right)÷9$

2 hr 4 min

$\left(\text{34 hr 8 min}\text{.}\right)÷8$

4 hr 16 min

$\left(\text{13 yd 7 in}\text{.}\right)÷5$

2 yd 1 ft 11 in

$\left(\text{47 gal 2 qt 1 pt}\right)÷3$

15 gal 3 qt 1 pt

## Exercises

For the following 15 problems, simplify the denominate numbers­.

16 in.

1 foot 4 inches

19 ft

85 min

1 hour 25 minutes

90 min

17 da

2 weeks 3 days

25 oz

240 oz

15 pounds

3,500 lb

26 qt

6 gallons 2 quarts

300 sec

135 oz

8 pounds 7 ounces

14 tsp

18 pt

2 gallons 1 quart

3,500 m

16,300 mL

16 liters 300 milliliters (or 1daL 6 L 3dL)

For the following 15 problems, perform the indicated opera­tions and simplify the answers if possible.

Add 6 min 12 sec to 5 min 15 sec.

Add 14 da 6 hr to 1 da 5 hr.

15 days 11 hours

Add 9 gal 3 qt to 2 gal 3 qt.

Add 16 lb 10 oz to 42 lb 15 oz.

59 pounds 9 ounces

Subtract 3 gal 1 qt from 8 gal 3 qt.

Subtract 3 ft 10 in. from 5 ft 8 in.

1 foot 10 inches

Subtract 5 lb 9 oz from 12 lb 5 oz.

Subtract 10 hr 10 min from 11 hr 28 min.

1 hour 18 minutes

Add 3 fl oz 1 tbsp 2 tsp to 5 fl oz 1 tbsp 2 tsp.

Add 4 da 7 hr 12 min to 1 da 8 hr 53 min.

5 days 16 hours 5 minutes

Subtract 5 hr 21 sec from 11 hr 2 min 14 sec.

Subtract 6 T 1,300 lb 10 oz from 8 T 400 lb 10 oz.

1 ton 1,100 pounds (or 1T 1,100 lb)

Subtract 15 mi 10 in. from 27 mi 800 ft 7 in.

Subtract 3 wk 5 da 50 min 12 sec from 5 wk 6 da 20 min 5 sec.

2 weeks 23 hours 29 minutes 53 seconds

Subtract 3 gal 3 qt 1 pt 1 oz from 10 gal 2 qt 2 oz.

## Exercises for review

( [link] ) Find the value: ${\left(\frac{5}{8}\right)}^{2}+\frac{\text{39}}{\text{64}}$ .

1

( [link] ) Find the sum: $8+6\frac{3}{5}$ .

( [link] ) Convert $2\text{.}\text{05}\frac{1}{\text{11}}$ to a fraction.

$2\frac{\text{14}}{\text{275}}$

( [link] ) An acid solution is composed of 3 parts acid to 7 parts water. How many parts of acid are there in a solution that contains 126 parts water?

( [link] ) Convert 126 kg to grams.

126,000 g

Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
hi
Loga
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
7hours 36 min - 4hours 50 min