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This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses how to simplify denominate numbers. By the end of the module students should be able to convert an unsimplified unit of measure to a simplified unit of measure, be able to add and subtract denominate numbers and be able to multiply and divide a denominate number by a whole number.

Section overview

  • Converting to Multiple Units
  • Adding and Subtracting Denominate Numbers
  • Multiplying a Denominate Number by a Whole Number
  • Dividing a Denominate Number by a Whole Number

Converting to multiple units

Denominate numbers

Numbers that have units of measure associated with them are called denominate numbers . It is often convenient, or even necessary, to simplify a denominate number.

Simplified denominate number

A denominate number is simplified when the number of standard units of measure associated With it does not exceed the next higher type of unit.

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.

Sample set a

Simplify 19 in.

Since 12   in . = 1 ft size 12{"12"" in" "." ="1 ft"} {} , and 19 = 12 + 7 size 12{"19"="12"+7} {} ,

19 in. = 12 in. + 7 in. = 1 ft + 7 in. = 1 ft 7 in.

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Simplify 4 gal 5 qt.

Since 4   qt = 1 gal size 12{4" qt"="1 gal"} {} , and 5 = 4 + 1 size 12{5=4+1} {} ,

4 gal 5 qt = 4 gal + 4 qt + 1qt = 4 gal + 1 gal + 1 qt = 5 gal + 1 qt = 5 gal 1 qt

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Simplify 2 hr 75 min.

Since 60 min = 1 hr size 12{"60 min "="1 hr"} {} , and 75 = 60 + 15 size 12{"75"="60"+"15"} {} ,

2 hr 75 min = 2 hr + 60 min + 15 min = 2 hr + 1 hr + 15 min = 3 hr + 15 min = 3 hr 15 min

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Simplify 43 fl oz.

Since 8 fl oz = 1 c size 12{"8 fl oz"="1 c"} {} (1 cup), and 43 ÷ 8 = 5 R3 size 12{"43" div 8=5" R3"} {} ,

43 fl oz = 40 fl oz + 3 fl oz = 5 8 fl oz + 3 fl oz = 5 1 c + 3 fl oz = 5 c + 3 fl oz

But, 2 c = 1 pt size 12{"2 c"="1 pt"} {} and 5 ÷ 2 = 2 R1 size 12{5 div 2=2" R1"} {} . So,

5 c + 3 fl oz = 2 2 c + 1 c + 3 fl oz = 2 1 pt + 1 c + 3 fl oz = 2 pt + 1 c + 3 fl oz

But, 2 pt = 1 qt size 12{"2 pt"="1 qt"} {} , so

2 pt + 1 c + 3 fl oz = 1 qt 1 c 3 fl oz size 12{"1 pt "+" 1 c "+" 3 fl oz"=" 1 qt 1 c 3 fl oz"} {}

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Practice set a

Simplify each denominate number. Refer to the conversion tables given in [link] , if necessary.

Adding and subtracting denominate numbers

Adding and subtracting denominate numbers

Denominate numbers can be added or subtracted by:
  1. writing the numbers vertically so that the like units appear in the same column.
  2. adding or subtracting the number parts, carrying along the unit.
  3. simplifying the sum or difference.

Sample set b

Add 6 ft 8 in. to 2 ft 9 in.

6 ft  8 in . + 2 ft  9 in . ̲ 8 ft 17 in . Simplify this denominate number. alignr { stack { size 12{"6 ft 8 in" "." } {} #size 12{ {underline {+"2 ft 9 in" "." }} } {} # size 12{"8 ft 17 in" "." } {}} } {}

Since 12 in . = 1 ft size 12{"12 in" "." =" 1 ft"} {} ,

8 ft + 12 in. + 5 in. = 8 ft + 1 ft + 5 in. = 9 ft + 5 in. = 9 ft 5 in.

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Subtract 5 da 3 hr from 8 da 11 hr.

8 da 11 hr - 5 da   3 hr ̲ 3 da   8 hr alignr { stack { size 12{"8 da 11 hr"} {} #size 12{ {underline {"-5 da 3 hr"}} } {} # size 12{"3 da 8 hr"} {}} } {}

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Subtract 3 lb 14 oz from 5 lb 3 oz.

5 lb   3 oz - 3 lb 14 oz ̲ alignr { stack { size 12{"5 lb 3 oz"} {} #size 12{ {underline {"-3 lb 14 oz"}} } {} } } {}

We cannot directly subtract 14 oz from 3 oz, so we must borrow 16 oz from the pounds.

5 lb 3 oz = 5 lb + 3 oz = 4 lb + 1 lb + 3 oz = 4 lb + 16 oz + 3 oz ( Since 1 lb = 16 oz. ) = 4 lb + 19 oz = 4 lb 19 oz

4 lb 19 oz - 3 lb 14 oz ̲ 1 lb   5 oz alignr { stack { size 12{"4 lb 19 oz"} {} #size 12{ {underline {"-3 lb 14 oz"}} } {} # size 12{"1 lb 5 oz"} {}} } {}

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Subtract 4 da 9 hr 21 min from 7 da 10 min.

7 da 0 hr 10 min - 4 da 9 hr 21 min ̲ alignr { stack { size 12{"7 da 0 hr 10 min"} {} #size 12{ {underline {"-4 da 9 hr 21 min"}} } {} } } {} Borrow 1 da from the 7 da.

6 da 24 hr 10 min - 4 da   9 hr 21 min ̲ alignr { stack { size 12{"6 da 24 hr 10 min"} {} #size 12{ {underline {"-4 da 9 hr 21 min"}} } {} } } {} Borrow 1 hr from the 24 hr.

6 da 23 hr 70 min - 4 da   9 hr 21 min ̲ 2 da 14 hr 49 min alignr { stack { size 12{"6 da 23 hr 70 min"} {} #size 12{ {underline {"-4 da 9 hr 21 min"}} } {} # size 12{"2 da 14 hr 49 min"} {}} } {}

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Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
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
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
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?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
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
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
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?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
In the number 779,844,205 how many ten millions are there?
TELLY Reply
From 1973 to 1979, in the United States, there was an increase of 166.6% of Ph.D. social scien­tists to 52,000. How many were there in 1973?
Khizar Reply
7hours 36 min - 4hours 50 min
Tanis Reply

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Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
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