# 1.4 Multiply whole numbers

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Jane is tiling her living room floor. She will need 16 rows of tile, with 2 tiles in each row. How many tiles does she need for the living room floor?

Jane needs 320 tiles.

Yousef is putting shingles on his garage roof. He will need 24 rows of shingles, with 45>shingles in each row. How many shingles does he need for the garage roof?

Yousef needs 1,080 tiles.

If we want to know the size of a wall that needs to be painted or a floor that needs to be carpeted, we will need to find its area . The area is a measure of the amount of surface that is covered by the shape. Area is measured in square units. We often use square inches, square feet, square centimeters, or square miles to measure area. A square centimeter is a square that is one centimeter (cm.) on a side. A square inch is a square that is one inch on each side, and so on.

For a rectangular figure, the area is the product of the length and the width. [link] shows a rectangular rug with a length of $2$ feet and a width of $3$ feet. Each square is $1$ foot wide by $1$ foot long, or $1$ square foot. The rug is made of $6$ squares. The area of the rug is $6$ square feet.

Jen’s kitchen ceiling is a rectangle that measures 9 feet long by 12 feet wide. What is the area of Jen’s kitchen ceiling?

## Solution

We are asked to find the area of the kitchen ceiling.

 Write a phrase for the area. the product of 9 and 12 Translate to math notation. $9\cdot 12$ Multiply. $\begin{array}{c}\phantom{\rule{2em}{0ex}}\\ \phantom{\rule{0.5em}{0ex}}\stackrel{1}{1}2\hfill \\ \phantom{\rule{0.1em}{0ex}}\underset{\text{___}}{×9}\hfill \\ 108\hfill \end{array}$ Answer with a sentence. The area of Jen's kitchen ceiling is 108 square feet.

Zoila bought a rectangular rug. The rug is 8 feet long by 5 feet wide. What is the area of the rug?

The area of the rug is 40 square feet.

Rene’s driveway is a rectangle 45 feet long by 20 feet wide. What is the area of the driveway?

The area of the driveway is 900 square feet

## Key concepts

Operation Notation Expression Read as Result
$\text{Multiplication}$ $×$
$·$
$\left(\phantom{\rule{0.2em}{0ex}}\right)$
$3\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}8$
$3·8$
$3\left(8\right)$
$\text{three times eight}$ $\text{the product of 3 and 8}$
• Multiplication Property of Zero
• The product of any number and 0 is 0.
$a\cdot 0=0$
$0\cdot a=0$
• Identity Property of Multiplication
• The product of any number and 1 is the number.
$1\cdot a=a$
$a\cdot 1=a$
• Commutative Property of Multiplication
• Changing the order of the factors does not change their product.
$a\cdot b=b\cdot a$
• Multiply two whole numbers to find the product.
1. Write the numbers so each place value lines up vertically.
2. Multiply the digits in each place value.
3. Work from right to left, starting with the ones place in the bottom number.
4. Multiply the bottom number by the ones digit in the top number, then by the tens digit, and so on.
5. If a product in a place value is more than 9, carry to the next place value.
6. Write the partial products, lining up the digits in the place values with the numbers above. Repeat for the tens place in the bottom number, the hundreds place, and so on.
7. Insert a zero as a placeholder with each additional partial product.

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
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
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
While the American heart association suggests that meditation might be used in conjunction with more traditional treatments as a way to manage hypertension
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What is the expressiin for seven less than four times the number of nickels
How do i figure this problem out.
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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)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?