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Sample set e

Perform this subtraction.

503 -   37 ̲

The number 503 contains a single zero

  1. The number to the immediate left of 0 is 5. Decrease 5 by 1.

    5 1 = 4 size 12{5 - 1=4} {}

    503 - 37. The 5 is crossed out, with a 4 above it. The 0 is crossed out, with a 10 above it.

  2. Draw a line through the zero and make it a 10.
  3. Borrow from the 10 and proceed.

    503 - 37. The 5 is crossed out, with a 4 above it. The 0 is crossed out, with a 10 above it. The 10 is crossed out, with a 9 above it. The 3 is crossed out, with a 13 above it. The difference is 466.

    1 ten + 10 ones

    10 ones + 3 ones = 13 ones

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Practice set e

Perform each subtraction.

Borrowing from a group of zeros

Consider the problem 5000 -     37 ̲

In this case, we have a group of zeros.

Vertical subtraction. 5000 - 37 is equal to 5 thousands + 0 hundred + 0 tens + 0 ones, minus 3 tens + 7 ones.

Since we cannot borrow any tens or hundreds, we must borrow 1 thousand. One thousand = 10 hundreds.

Vertical subtraction. 4 thousands + 10 hundreds + 0 tens + 0 ones, minus 3 tens + 7 ones.

We can now borrow 1 hundred from 10 hundreds. One hundred = 10 tens.

Vertical subtraction. 4 thousands + 9 hundreds + 10 tens + 0 ones, minus 3 tens + 7 ones.

We can now borrow 1 ten from 10 tens. One ten = 10 ones.

Vertical subtraction. 4 thousands + 9 hundreds + 9 tens + 10 ones, minus 3 tens + 7 ones = 4 thousands + 9 hundreds + 6 tens + 3 ones, equal to 4,963

From observations made in this procedure we can suggest the following method for borrowing from a group of zeros.

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Borrowing from a group of zeros

To borrow from a group of zeros,
  1. Decrease the digit to the immediate left of the group of zeros by one.
  2. Draw a line through each zero in the group and make it a 9, except the rightmost zero, make it 10.
  3. Proceed to subtract as usual.

Sample set f

Perform each subtraction.

40,000 -     125 ̲

The number 40,000 contains a group of zeros.

  1. The number to the immediate left of the group is 4. Decrease 4 by 1.

    4 1 = 3 size 12{4 - 1=3} {}

  2. Make each 0, except the rightmost one, 9. Make the rightmost 0 a 10.

    40,000 - 125. Each digit of 40,000 is crossed out, and above it from left to right are the numbers, 3, 9, 9, 9, and 10.

  3. Subtract as usual.

    40,000 - 125. Each digit of 40,000 is crossed out, and above it from left to right are the numbers, 3, 9, 9, 9, and 10. The difference is 39,875.

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8,000,006 -       41,107 ̲

The number 8,000,006 contains a group of zeros.

  1. The number to the immediate left of the group is 8. Decrease 8 by 1.

    8 1 = 7 size 12{8 - 1=7} {}

  2. Make each zero, except the rightmost one, 9. Make the rightmost 0 a 10.

    8,000,006 - 41,107. All but the ones digit are crossed out, and above them from left to right are 7, 9, 9, 9, 9, and 10.

  3. To perform the subtraction, we’ll need to borrow from the ten.

    8,000,006 - 41,107. All but the ones digit are crossed out, and above them from left to right are 7, 9, 9, 9, 9, and 10. The 10 is crossed out, with a 9 above it. Above the 6 is a 16. The difference is 7,958,899.


    1 ten = 10 ones 10 ones + 6 ones = 16 ones

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Practice set f

Perform each subtraction.

21,007 -   4,873 ̲

16,134

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10,004 -   5,165 ̲

4,839

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16,000,000 -      201,060 ̲

15,789,940

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Calculators

In practice, calculators are used to find the difference between two whole numbers.

Sample set g

Find the difference between 1006 and 284.

Display Reads
Type 1006 1006
Press size 12{` - `} {} 1006
Type 284 284
Press = 722

The difference between 1006 and 284 is 722.

(What happens if you type 284 first and then 1006? We'll study such numbers in [link] Chapter 10.)

Practice set g

Use a calculator to find the difference between 7338 and 2809.

4,529

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Use a calculator to find the difference between 31,060,001 and 8,591,774.

22,468,227

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Exercises

For the following problems, perform the subtractions. You may check each difference with a calculator.

35,002 - 14,001 ̲

21,001

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5,000,566 - 2,441,326 ̲

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400,605 - 121,352 ̲

279,253

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77,893 -      421 ̲

77,472

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42,041 - 15,355 ̲

26,686

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64,000,002 -     856,743 ̲

63,143,259

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10,113 -   2,079 ̲

8,034

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92,526,441,820 - 59,914,805,253 ̲

32,611,636,567

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30,000 - 26,062 ̲

3,938

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9,000,003 -    726,048 ̲

8,273,955

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For the following problems, perform each subtraction.

Subtract 63 from 92.

The word "from" means "beginning at." Thus, 63 from 92 means beginning at 92, or 92 63 size 12{"92" - "63"} {} .
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Questions & Answers

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
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
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
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
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?
Damian Reply
absolutely yes
Daniel
how did you get the value of 2000N.What calculations are needed to arrive at it
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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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