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This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses how to multiply whole numbers. By the end of the module students should be able to understand the process of multiplication, multiply whole numbers, simplify multiplications with numbers ending in zero, and use a calculator to multiply one whole number by another.

Section overview

  • Multiplication
  • The Multiplication Process With a Single Digit Multiplier
  • The Multiplication Process With a Multiple Digit Multiplier
  • Multiplication With Numbers Ending in Zero
  • Calculators

Multiplication

Multiplication is a description of repeated addition.

In the addition of

5 + 5 + 5 size 12{5+5+5} {}

the number 5 is repeated 3 times. Therefore, we say we have three times five and describe it by writing

3 × 5 size 12{3 times 5} {}

Thus,

3 × 5 = 5 + 5 + 5 size 12{3 times 5=5+5+5} {}

Multiplicand

In a multiplication, the repeated addend (number being added) is called the multi­plicand . In 3 × 5 size 12{3 times 5} {} , the 5 is the multiplicand.

Multiplier

Also, in a multiplication, the number that records the number of times the multiplicand is used is called the multiplier . In 3 × 5 size 12{3 times 5} {} , the 3 is the multiplier.

Sample set a

Express each repeated addition as a multiplication. In each case, specify the multiplier and the multiplicand.

7 + 7 + 7 + 7 + 7 + 7 size 12{7+7+7+7+7+7} {}

6 × 7 size 12{6 times 7} {} . Multiplier is 6. Multiplicand is 7.

18 + 18 + 18 size 12{"18"+"18"+"18"} {}

3 × 18 size 12{3 times "18"} {} . Multiplier is 3. Multiplicand is 18.

Practice set a

Express each repeated addition as a multiplication. In each case, specify the multiplier and the multiplicand.

12 + 12 + 12 + 12 size 12{"12"+"12"+"12"+"12"} {}

. Multiplier is . Multiplicand is .

4 × 12 size 12{4 times "12"} {} . Multiplier is 4. Multiplicand is 12.

36 + 36 + 36 + 36 + 36 + 36 + 36 + 36 size 12{"36"+"36"+"36"+"36"+"36"+"36"+"36"+"36"} {}

. Multiplier is . Multiplicand is .

8 × 36 size 12{8 times "36"} {} . Multiplier is 8. Multiplicand is 36.

0 + 0 + 0 + 0 + 0 size 12{0+0+0+0+0} {}

. Multiplier is . Multiplicand is .

5 × 0 size 12{5 times 0} {} . Multiplier is 5. Multiplicand is 0.

1847 + 1847 + ... + 1847 12,000 times

. Multiplier is . Multiplicand is .

12 , 000 × 1, 847 size 12{"12","000" times 1,"847"} {} . Multiplier is 12,000. Multiplicand is 1,847.

Factors

In a multiplication, the numbers being multiplied are also called factors .

Products

The result of a multiplication is called the product . In 3 × 5 = 15 size 12{3 times 5="15"} {} , the 3 and 5 are not only called the multiplier and multiplicand, but they are also called factors. The product is 15.

Indicators of multiplication × ,⋅,( )

The multiplication symbol ( × ) is not the only symbol used to indicate multiplication. Other symbols include the dot ( ⋅ ) and pairs of parentheses ( ). The expressions

3 × 5 size 12{3 times 5} {} , 3 5 size 12{3 cdot 5} {} , 3 ( 5 ) size 12{3 \( 5 \) } {} , ( 3 ) 5 size 12{ \( 3 \) 5} {} , ( 3 ) ( 5 ) size 12{ \( 3 \) \( 5 \) } {}

all represent the same product.

The multiplication process with a single digit multiplier

Since multiplication is repeated addition, we should not be surprised to notice that carrying can occur. Carrying occurs when we find the product of 38 and 7:

Vertical multiplication. 38 times 7 is 266. The 5 is carried on top of the 3.

First, we compute 7 × 8 = 56 size 12{7 times 8="56"} {} . Write the 6 in the ones column. Carry the 5. Then take 7 × 3 = 21 size 12{7 times 3="21"} {} . Add to 21 the 5 that was carried: 21 + 5 = 26 size 12{"21"+5="26"} {} . The product is 266.

Sample set b

Find the following products.

Vertical multiplication. 64 times 3 is 192. The 1 is carried on top of the 6.

3 × 4 = 12 Write the 2, carry the 1. 3 × 6 = 18 Add to 18 the 1 that was carried: 18 + 1 = 19 .

The product is 192.

Vertical multiplication. 526 times 5 is 2,630. The 2 is carried on top of the 2, and the 1 is carried on top of the 5.

5 × 6 = 30 Write the 0, carry the 3. 5 × 2 = 10 Add to 10 the 3 that was carried: 10 + 3 = 13 . Write the 3, carry the 1. 5 × 5 = 25 Add to 25 the 1 that was carried: 25 + 1 = 6 .

The product is 2,630.

Questions & Answers

find the 15th term of the geometric sequince whose first is 18 and last term of 387
Jerwin Reply
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
virgelyn Reply
hmm well what is the answer
Abhi
how do they get the third part x = (32)5/4
kinnecy Reply
can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
Commplementary angles
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hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
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hii
Uday
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
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Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
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No. 7x -4y is simplified from 4x + (3y + 3x) -7y
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how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
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. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
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I start with an easy one. carbon nanotubes woven into a long filament like a string
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many many of nanotubes
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I'm interested in nanotube
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what is nano technology
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what is system testing?
AMJAD
preparation of nanomaterial
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Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
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AMJAD
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AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Contemporary math applications. OpenStax CNX. Dec 15, 2014 Download for free at http://legacy.cnx.org/content/col11559/1.6
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