<< Chapter < Page Chapter >> Page >
Not all divisions end in zero. We will examine such divisions in a subsequent subsection.

Practice set a

Perform the following divisions.

126 ÷ 7 size 12{"126" div 7} {}

18

Got questions? Get instant answers now!

324 ÷ 4 size 12{"324" div 4} {}

81

Got questions? Get instant answers now!

2, 559 ÷ 3 size 12{2,"559" div 3} {}

853

Got questions? Get instant answers now!

5, 645 ÷ 5 size 12{5,"645" div 5} {}

1,129

Got questions? Get instant answers now!

757 , 125 ÷ 9 size 12{"757","125" div 9} {}

84,125

Got questions? Get instant answers now!

Division with a multiple digit divisor

The process of division also works when the divisor consists of two or more digits. We now make educated guesses using the first digit of the divisor and one or two digits of the dividend.

Sample set b

Find 2, 232 ÷ 36 size 12{2,"232" div "36"} {} .

36 2232

Use the first digit of the divisor and the first two digits of the dividend to make the educated guess.

3 goes into 22 at most 7 times.

Try 7: 7 × 36 = 252 size 12{7 times "36"="252"} {} which is greater than 223. Reduce the estimate.

Try 6: 6 × 36 = 216 size 12{6 times "36"="216"} {} which is less than 223.

The first step of a long division problem. 2232 divided by 36. 36 goes into 223 approximately 6 times, with a remainder of 7. The ones digit of 2232 is then brought down to adjoin the 7. Multiply: 6 × 36 = 216. Write 216 below 223. Subtract: 223 - 216 = 7. Bring down the 2.

Divide 3 into 7 to estimate the number of times 36 goes into 72. The 3 goes into 7 at most 2 times.

Try 2: 2 × 36 = 72 size 12{2 times "36"="72"} {} .

Long division. 2232 divided by 36. 36 goes into 223 approximately 6 times, with a remainder of 7. The ones digit of 2232 is then brought down to adjoin the 7. 36 goes into 72 exactly twice, leaving a remainder of 0.

Check : Is 2232 equal to 36 time 62? Yes.

Thus, 2, 232 ÷ 36 = 62 size 12{2,"232" div "36"="62"} {} .

Got questions? Get instant answers now!

Find 2, 417 , 228 ÷ 802 size 12{2,"417","228" div "802"} {} .

802 2417228

First, the educated guess: 24 ÷ 8 = 3 size 12{"24" div 8=3} {} . Then 3 × 802 = 2406 size 12{3 times "802"="2406"} {} , which is less than 2417. Use 3 as the guess. Since 3 × 802 = 2406 size 12{3 times "802"="2406"} {} , and 2406 has four digits, place the 3 above the fourth digit of the dividend.

The first step of a long division problem. 2417228 divided by 802. 802 goes into 2417 approximately 3 times, with a remainder of 11. The hundreds digit of 2417228 is then brought down to adjoin the 11.
Subtract: 2417 - 2406 = 11.
Bring down the 2.

The divisor 802 goes into 112 at most 0 times. Use 0.

The second step of a long division problem. 802 goes into 112 0 times, so a zero is placed above, and the next digit is brought down.
Multiply: 0 × 802 = 0. Subtract: 112 - 0 = 112. Bring down the 2.

The 8 goes into 11 at most 1 time, and 1 × 802 = 802 size 12{1 times "802"="802"} {} , which is less than 1122. Try 1.

The third step of a long division problem. 802 goes into 1122 once, so a 1 is placed above and the ones digit is brought down.
Subtract 1122 - 802 = 320
Bring down the 8.

8 goes into 32 at most 4 times.

4 × 802 = 3208 size 12{4 times "802"="3208"} {} .

Use 4.

The third step of a long division problem. 2417228 divided by 802. 802 goes into 2417 approximately 3 times, with a remainder of 11. The hundreds digit of 2417228 is then brought down to adjoin the 11. 802 goes into 112 0 times, so a zero is placed above, and the next digit is brought down. 802 goes into 1122 once, so a 1 is placed above and the ones digit is brought down. 802 goes into 3208 4 times, leaving a remainder of 0.

Check: Is 2417228 equal to 3014 times 802? Yes.

Thus, 2, 417 , 228 ÷ 802 = 3, 014 size 12{2,"417","228" div "802"=3,"014"} {} .

Got questions? Get instant answers now!

Practice set b

Perform the following divisions.

1, 376 ÷ 32 size 12{1,"376" div "32"} {}

43

Got questions? Get instant answers now!

6, 160 ÷ 55 size 12{6,"160" div "55"} {}

112

Got questions? Get instant answers now!

18 , 605 ÷ 61 size 12{"18","605" div "61"} {}

305

Got questions? Get instant answers now!

144 , 768 ÷ 48 size 12{"144","764" div "48"} {}

3,016

Got questions? Get instant answers now!

Division with a remainder

We might wonder how many times 4 is contained in 10. Repeated subtraction yields

10 -   4 ̲ 6 - 4 ̲ 2

Since the remainder is less than 4, we stop the subtraction. Thus, 4 goes into 10 two times with 2 remaining. We can write this as a division as follows.

2 4 10 -   8 ̲ 2
Divide: 4 goes into 10 at most 2 times. Multiply: 2 × 4 = 8. Write 8 below 0. Subtract: 10 - 8 = 2.

Since 4 does not divide into 2 (the remainder is less than the divisor) and there are no digits to bring down to continue the process, we are done. We write

2 R 2 4    10 - 8 ̲ 2 or 10 ÷ 4 = 2 R 2 2 with remainder 2

Sample set c

Find 85 ÷ 3 size 12{"85" div 3} {} .

Long division. 85 divided by 3. 3 goes into 8 twice, with a remainder of 2. The ones digit is then brought down. 3 goes into 25 8 times, with a remainder of 1.
Divide: 3 goes into 8 at most 2 times. Multiply: 2 × 3 = 6. Write 6 below 8. Subtract: 8 - 6 = 2. Bring down the 5. Divide: 3 goes into 25 at most 8 times. Multiply: 3 × 8 = 24. Write 24 below 25. Subtract: 25 - 24 = 1.

There are no more digits to bring down to continue the process. We are done. One is the remainder.

Check: Multiply 28 and 3, then add 1.

28 ×   3 ̲ 84 +   1 ̲ 85

Thus, 85 ÷ 3 = 28 R1 size 12{"85" div 3="28"`R1} {} .

Got questions? Get instant answers now!

Find 726 ÷ 23 size 12{"726" div "23"} {} .

Long division. 726 divided by 23. 23 goes into 72 three times, with a remainder of 3. The ones digit is then brought down. 23 goes into 36 once, with a remainder of 13.

Check: Multiply 31 by 23, then add 13.

31 times 23 equals 713. 713 plus 13 equals 726.

Thus, 726 ÷ 23 = 31 R 13 size 12{"726" div "23"="31"````R"13"} {} .

Got questions? Get instant answers now!

Practice set c

Perform the following divisions.

75 ÷ 4 size 12{"75" div 4} {}

18 R3

Got questions? Get instant answers now!

346 ÷ 8 size 12{"346" div 8} {}

43 R2

Got questions? Get instant answers now!

489 ÷ 21 size 12{"489" div "21"} {}

23 R6

Got questions? Get instant answers now!

5, 016 ÷ 82 size 12{5,"016" div "82"} {}

61 R14

Got questions? Get instant answers now!

41 , 196 ÷ 67 size 12{"41","196" div "67"} {}

614 R58

Got questions? Get instant answers now!

Calculators

The calculator can be useful for finding quotients with single and multiple digit divisors. If, however, the division should result in a remainder, the calculator is unable to provide us with the particular value of the remainder. Also, some calculators (most nonscientific) are unable to perform divisions in which one of the numbers has more than eight digits.

Questions & Answers

the art of managing the production, distribution and consumption.
Satangthem Reply
what is economics
Khawar Reply
okk
damfash
marginal utility is the additional satisfaction one derives from consuming additional unit of a good or service.
Fred
It's the allocation of scarce resources.
Fred
marginal utility please?
Dishan
marginal utility is the additional satisfaction one derives from consuming additional unit of a good or service.
Fred
I know the definition, but I don't understand its meaning.
Dishan
what is the must definition of economic please?
Nurudeen
demand lfs
Alpha
Economics is derived from the word Oikonomia which means management of household things. Thus, Economics is a study of household things with the constrains of allocating scare resources.
Dishan
what is Open Market Operation
Adu Reply
dominating middlemen men activities circumstances
Christy Reply
what Equilibrium price
Adji Reply
what is gap
mirwais
who is good with the indifference curve
Dexter
What is diseconomic
Alixe Reply
what are the types of goods
WARIDI
how can price determination be the central problem of micro economics
simon Reply
marginal cost formula
Nandu Reply
you should differentiate the total cost function in order to get marginal cost function then you can get marginal cost from it
boniphace
What about total cost
Foday
ok
Foday
how can price determination be the central problem if micro economics
simon
formula of cross elasticity of demand
Theresia Reply
what is ceteris paribus
Priyanka Reply
what is ceteris parabus
Priyanka
Ceteris paribus - Literally, "other things being equal"; usually used in economics to indicate that all variables except the ones specified are assumed not to change.
Abdullah
What is broker
scor
land is natural resources that is made by nature
scor
What is broker
scor
what is land
kafui
What is broker
scor
land is natural resources that is made by nature
scor
whats poppina nigga turn it up for a minute get it
amarsyaheed Reply
what is this?
Philo
am from nigeria@ pilo
Frank
am from nigeria@ pilo
Frank
so
owusu
what is production possibility frontier
owusu
it's a summary of opportunity cost depicted on a curve.
okhiria
please help me solve this question with the aid of appropriate diagrams explain how each of the following changes will affect the market price and quantity of bread 1. A
Manuela Reply
please l need past question about economics
Prosper Reply
ok let me know some of the questions please.
Effah
ok am not wit some if den nw buh by tommorow I shall get Dem
adepojurafiu
Hi guys can I get Adam Smith's WEALTH OF NATIONS fo sale?
Ukpen
hello I'm Babaisa alhaji Mustapha. I'm studying Economics in the university of Maiduguri
Babaisa
okay
Humaira
my name is faisal Yahaya. i studied economics at Kaduna state university before proceeding to West African union university benin republic for masters
Faisal
Hi guys..I am from Bangladesh..
Mannan
Wat d meaning of management
igwe Reply
disaster management cycle
Gogul Reply
cooperate social responsibility
igwe
Fedric Wilson Taylor also define management as the act of knowing what to do and seeing that it is done in the best and cheapest way
OLANIYI
Difference between extinct and extici spicies
Amanpreet Reply
7hours 36 min - 4hours 50 min
Tanis Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Fundamentals of mathematics' conversation and receive update notifications?

Ask