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By the end of this section, you will be able to:
  • Add and subtract decimals
  • Multiply decimals
  • Divide decimals
  • Use decimals in money applications

Before you get started, take this readiness quiz.

Add and subtract decimals

Let’s take one more look at the lunch order from the start of Decimals , this time noticing how the numbers were added together.

A vertical addition problem is shown. The top line shows $3.45 for a sandwich, the next line shows $1.25 for water, and the last line shows $0.33 for tax. The total is shown to be $5.03.

All three items (sandwich, water, tax) were priced in dollars and cents, so we lined up the dollars under the dollars and the cents under the cents, with the decimal point s lined up between them. Then we just added each column, as if we were adding whole numbers. By lining up decimal s this way, we can add or subtract the corresponding place values just as we did with whole numbers.

Add or subtract decimals.

  1. Write the numbers vertically so the decimal points line up.
  2. Use zeros as place holders, as needed.
  3. Add or subtract the numbers as if they were whole numbers. Then place the decimal in the answer under the decimal points in the given numbers.

Add: 3.7 + 12.4 .

Solution

3.7 + 12.4
Write the numbers vertically so the decimal points line up. 3.7 + 12.4 _____
Place holders are not needed since both numbers have the same number of decimal places.
Add the numbers as if they were whole numbers. Then place the decimal in the answer under the decimal points in the given numbers. 3 1 . 7 + 12.4 _____ 16.1
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Add: 18.32 + 14.79 .

33.11

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Add: 23.5 + 41.38 .

Solution

23.5 + 41.38
Write the numbers vertically so the decimal points line up. .
Place 0 as a place holder after the 5 in 23.5, so that both numbers have two decimal places. .
Add the numbers as if they were whole numbers. Then place the decimal in the answer under the decimal points in the given numbers. .
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Add: 4.8 + 11.69 .

16.49

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Add: 5.123 + 18.47 .

23.593

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How much change would you get if you handed the cashier a $20 bill for a $14.65 purchase? We will show the steps to calculate this in the next example.

Subtract: 20 14.65 .

Solution

20 14.65
Write the numbers vertically so the decimal points line up. Remember 20 is a whole number, so place the decimal point after the 0. .
Place two zeros after the decimal point in 20, as place holders so that both numbers have two decimal places. .
Subtract the numbers as if they were whole numbers. Then place the decimal in the answer under the decimal points in the given numbers. .
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Subtract:

10 9.58 .

0.42

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Subtract:

50 37.42 .

12.58

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Subtract: 2.51 7.4 .

Solution

If we subtract 7.4 from 2.51 , the answer will be negative since 7.4 > 2.51 . To subtract easily, we can subtract 2.51 from 7.4 . Then we will place the negative sign in the result.

2.51 7.4
Write the numbers vertically so the decimal points line up. .
Place zero after the 4 in 7.4 as a place holder, so that both numbers have two decimal places. .
Subtract and place the decimal in the answer. .
Remember that we are really subtracting 2.51 7.4 as a place holder, so that both numbers have two decimal places. 2.51 7.4 = 4.89

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Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
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
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
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
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Kimberly Reply
Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
August Reply
What is the expressiin for seven less than four times the number of nickels
Leonardo Reply
How do i figure this problem out.
how do you translate this in Algebraic Expressions
linda Reply
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply

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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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