1. Home
  2. Contemporary math applications
  3. Exam 1
  4. Fractions
  5. Fractions: divisibility rules

1.1 Fractions: divisibility rules

<< Chapter < Page
  Contemporary math applications   Page 1 / 1
Chapter >> Page >
This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses interesting facts about diving whole numbers. By the end of the module students should be able to recognize a whole number that is divisible by 2, 3, 4, 5, 6, 8, 9, or 10.

Section overview

  • Division by 2, 3, 4, and 5
  • Division by 6, 8, 9, and 10

Quite often, we are able to determine if a whole number is divisible by another whole number just by observing some simple facts about the number. Some of these facts are listed in this section.

Division by 2, 3, 4, and 5

Division by 2

A whole number is divisible by 2 if its last digit is 0, 2, 4, 6, or 8.

The numbers 80, 112, 64, 326, and 1,008 are all divisible by 2 since the last digit of each is 0, 2, 4, 6, or 8, respectively.

The numbers 85 and 731 are not divisible by 2.

Division by 3

A whole number is divisible by 3 if the sum of its digits is divisible by 3.

The number 432 is divisible by 3 since 4 + 3 + 2 = 9 size 12{4+5+2=9} {} and 9 is divisible by 3.

432 ÷ 3 = 144 size 12{"432" div 3="144"} {}

The number 25 is not divisible by 3 since 2 + 5 = 7 size 12{2+5=7} {} , and 7 is not divisible by 3.

Division by 4

A whole number is divisible by 4 if its last two digits form a number that is divisible by 4.
The number 31,048 is divisible by 4 since the last two digits, 4 and 8, form a number, 48, that is divisible by 4.
31048 ÷ 4 = 7262 size 12{"31048" div 4="7262"} {}
The number 137 is not divisible by 4 since 37 is not divisible by 4.

Division by 5

A whole number is divisible by 5 if its last digit is 0 or 5.

Sample set a

The numbers 65, 110, 8,030, and 16,955 are each divisible by 5 since the last digit of each is 0 or 5.

Practice set a

State which of the following whole numbers are divisible by 2, 3, 4, or 5. A number may be divisible by more than one number.

26

2

81

3

51

3

385

5

6,112

2, 4

470

2, 5

113,154

2, 3

Division by 6, 8, 9, 10

Division by 6

A number is divisible by 6 if it is divisible by both 2 and 3.
The number 234 is divisible by 2 since its last digit is 4. It is also divisible by 3 since 2 + 3 + 4 = 9 size 12{2+3+4=9} {} and 9 is divisible by 3. Therefore, 234 is divisible by 6.
The number 6,532 is not divisible by 6. Although its last digit is 2, making it divisible by 2, the sum of its digits, 6 + 5 + 3 + 2 = 16 size 12{6+5+3+2="16"} {} , and 16 is not divisible by 3.

Division by 8

A whole number is divisible by 8 if its last three digits form a number that is divisible by 8.
The number 4,000 is divisible by 8 since 000 is divisible by 8.
The number 13,128 is divisible by 8 since 128 is divisible by 8.
The number 1,170 is not divisible by 8 since 170 is not divisible by 8.

Division by 9

A whole number is divisible by 9 if the sum of its digits is divisible by 9.
The number 702 is divisible by 9 since 7 + 0 + 2 size 12{7+0+2} {} is divisible by 9.
The number 6588 is divisible by 9 since 6 + 5 + 8 + 8 = 27 size 12{6+5+8+8="27"} {} is divisible by 9.
The number 14,123 is not divisible by 9 since 1 + 4 + 1 + 2 + 3 = 11 size 12{1+4+1+2+3="11"} {} is not divisi­ble by 9.

Division by 10

A Whole number is divisible by 10 if its last digit is 0.

Sample set b

The numbers 30, 170, 16,240, and 865,000 are all divisible by 10.

Practice set b

State which of the following whole numbers are divisible 6, 8, 9, or 10. Some numbers may be divisible by more than one number.

900

6, 9, 10

6,402

6

6,660

6, 9, 10

55,116

6, 9

Exercises

For the following 30 problems, specify if the whole number is divisible by 2, 3, 4, 5, 6, 8, 9, or 10. Write "none" if the number is not divisible by any digit other than 1. Some numbers may be divisible by more than one number.

48

2, 3, 4, 6, 8

85

30

2, 3, 5, 6, 10

83

98

2

972

892

2, 4

676

903

3

800

223

none

836

665

5

4,381

2,195

5

2,544

5,172

2, 3, 4, 6

1,307

1,050

2, 3, 5, 6, 10

3,898

1,621

none

27,808

45,764

2, 4

49,198

296,122

2

178,656

5,102,417

none

16,990,792

620,157,659

none

457,687,705

Exercises for review

( [link] ) In the number 412, how many tens are there?

1

( [link] ) Subtract 613 from 810.

( [link] ) Add 35, 16, and 7 in two different ways.

( 35 + 16 ) + 7 = 51 + 7 = 58 size 12{ \( "35"+"16" \) +7="51"+7="58"} {}
35 + ( 16 + 7 ) = 35 + 23 = 58 size 12{"35"+ \( "16"+7 \) ="35"+"23"="58"} {}

( [link] ) Find the quotient 35 ÷ 0 size 12{"35" div 0} {} , if it exists.

( [link] ) Find the quotient. 3654 ÷ 42 size 12{"3654" div "42"} {} .

87

Questions & Answers

what does preconceived mean
sammie Reply
physiological Psychology
Nwosu Reply
How can I develope my cognitive domain
Amanyire Reply
why is communication effective
Dakolo Reply
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
it starts up serve and return practice/assessments.it helps find voice talking therapy also assessments through relaxed conversation.
miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
Wekolamo Reply
please i need answer
Wekolamo
because it helps many people around the world to understand how to interact with other people and understand them well, for example at work (job).
Manix Reply
Agreed 👍 There are many parts of our brains and behaviors, we really need to get to know. Blessings for everyone and happy Sunday!
ARC
A child is a member of community not society elucidate ?
JESSY Reply
Isn't practices worldwide, be it psychology, be it science. isn't much just a false belief of control over something the mind cannot truly comprehend?
Simon Reply
compare and contrast skinner's perspective on personality development on freud
namakula Reply
Skinner skipped the whole unconscious phenomenon and rather emphasized on classical conditioning
war
explain how nature and nurture affect the development and later the productivity of an individual.
Amesalu Reply
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills
Zyryn Reply
good👍
Jonathan
and having a good philosophy of the world is like a sandwich and a peanut butter 👍
Jonathan
generally amnesi how long yrs memory loss
Kelu Reply
interpersonal relationships
Abdulfatai Reply
What would be the best educational aid(s) for gifted kids/savants?
Heidi Reply
treat them normal, if they want help then give them. that will make everyone happy
Saurabh
What are the treatment for autism?
Magret Reply
hello. autism is a umbrella term. autistic kids have different disorder overlapping. for example. a kid may show symptoms of ADHD and also learning disabilities. before treatment please make sure the kid doesn't have physical disabilities like hearing..vision..speech problem. sometimes these
Jharna
continue.. sometimes due to these physical problems..the diagnosis may be misdiagnosed. treatment for autism. well it depends on the severity. since autistic kids have problems in communicating and adopting to the environment.. it's best to expose the child in situations where the child
Jharna
child interact with other kids under doc supervision. play therapy. speech therapy. Engaging in different activities that activate most parts of the brain.. like drawing..painting. matching color board game. string and beads game. the more you interact with the child the more effective
Jharna
results you'll get.. please consult a therapist to know what suits best on your child. and last as a parent. I know sometimes it's overwhelming to guide a special kid. but trust the process and be strong and patient as a parent.
Jharna
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
<< Chapter < Page Page > Chapter >>

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Contemporary math applications. OpenStax CNX. Dec 15, 2014 Download for free at http://legacy.cnx.org/content/col11559/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Contemporary math applications' conversation and receive update notifications?

Ask