# 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 can chip be made from sand
is this allso about nanoscale material
Almas
are nano particles real
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
no can't
Lohitha
where is the latest information on a no technology how can I find it
William
currently
William
where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
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
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
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
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
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
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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
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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 ?
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
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.
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.
What is the expressiin for seven less than four times the number of nickels
How do i figure this problem out.
how do you translate this in Algebraic Expressions
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?