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Bilamana dua bilangan dijumlahkan bersama, hasilnya disebut ''[[jumlah]]''. Kedua bilangan yang dijumlahkan itu disebut ''penambah''.
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===What does it mean to add two natural numbers? ===
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If at least one of the numbers has a hundreds-digit then if one of the numbers has a missing hundreds-digit then write a 0 digit in its place. Add the two hundreds-digits, and to their sum add the carry digit if there is one. Then write the sum of the hundreds-column under the line, also in the hundreds column. If the sum has two digits then write down the last digit of the sum in the hundreds-column and write the carry digit to its left: on the thousands-column.
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====Contoh====
Misalnya orang ingin menghitung jumlah bilangan 653 dan 274. Tuliskan bilangan kedua di bawah bilangan pertama, dengan digit-digitnya diurutkan dalam kolom-kolom, seperti:
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Selanjutnya, kolom puluhan. Digit puluhan dari bilangan pertama adalah 5, dan dari bilangan kedua adalah 7. Lima ditambah tujuh adalah dua belas: 12, yang terdiri dari dua digit, sehingga tulis digit terakhir, 2, pada kolom puluhan di bawah garis, dan tulis digit bawaan pada kolom ratusan di atas bilangan pertama:
Next, the tens-column. The tens-digit of the first number is 5, and the tens-digit of the second number is 7, and five plus seven is twelve: 12, which has two digits, so write its last digit, 2, in the tens-column under the line, and write the carry digit on the hundreds-column above the first number:
 
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Lalu, kolom ratusan. Digit ratusan dari bilangan pertama adalah 6, sedangkan dari bilangan kedua adalah 2. Jumlah 6 dan 2 adalah 8, tetapi ada satu digit bawaan, 1, yang harus ditambahkan ke jumlah 8, menjadi 9. Tulis angka 9 di bawah garis pada kolom ratusan:
Next, the hundreds-column. The hundreds-digit of the first number is 6, while the hundreds-digit of the second number is 2. The sum of six and two is eight, but there is a carry digit, which added to eight is equal to nine. Write the 9 under the line in the hundreds-column:
 
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Tidak ada digit (dan tidak ada kolom) yang belum dijumlahkan, sehingga algoritme ini selesai, dan hasilnya
No digits (and no columns) have been left unadded, so the algorithm finishes, and
:653 + 274 = 927.
 
== Kelanjutan dan ukuran ==
==Successorship and size==
TheHasil resultpenjumlah ofsatu theke additionsuatu ofbilangan onemerupakan to a number is the"kelanjutan" (''successor''; "penerus", of"penerusan") thatbilangan numberitu. ExamplesContoh:<br>
kelanjutan nol adalah satu,<br>
the successor of zero is one,<br>
kelanjutan satu adalah dua,<br>
the successor of one is two,<br>
kelanjutan dua adalah tiga,<br>
the successor of two is three,<br>
kelanjutan sepuluh adalah sebelas.<br>
the successor of ten is eleven.<br>
Setiap bilangan asli mempunyai satu kelanjutan .
Every natural number has a successor.
 
Pendahulu dari bilangan kelanjutan suatu bilangan adalah bilangan itu sendiri. Contoh: lima adalah kelanjutan dari empat, karena itu empat adalah pendahulu lima. Setiap bilangan asli, kecuali bilangan nol, mempunyai satu pendahulu.
The predecessor of the successor of a number is the number itself. For example, five is the successor of four therefore four is the predecessor of five. Every natural number except zero has a predecessor.
 
Jika suatu bilangan merupakan kelanjutan dari bilangan lain, maka bilangan kelanjutan itu dikatakan ''lebih besar dari'' bilangan pendahulunya. Jika suatu bilangan lebih besar dari bilangan lain, dan jika bilangan lain itu lebih besar dari bilangan ketiga, maka bilangan pertama itu juga lebih besar dari bilangan ketiga. Contoh: five lebih besar dari empat, dan empat lebih besar dari tiga, maka lima lebih besar dari tiga. Tetapi enam lebih besar dari lima, sehingga enam juga lebih besar dari tiga. Tetapi tujuh lebih besar dari enam, maka tujuh juga lebih besar dari tiga&nbsp;... maka delapan lebih besar dari tiga&nbsp;... maka sembilan lebih besar dari tiga, dst.
If a number is the successor of another number, then the first number is said to be ''larger than'' the other number. If a number is larger than another number, and if the other number is larger than a third number, then the first number is also larger than the third number. Example: five is larger than four, and four is larger than three, therefore five is larger than three. But six is larger than five, therefore six is also larger than three. But seven is larger than six, therefore seven is also larger than three&nbsp;... therefore eight is larger than three&nbsp;... therefore nine is larger than three, etc.
 
<!--If two non-zero natural numbers are added together, then their sum is larger than either one of them. Example: three plus five equals eight, therefore eight is larger than three ({{nowrap|8 &gt; 3}}) and eight is larger than five ({{nowrap|8 &gt; 5}}). The symbol for "larger than" is &gt;.
 
If a number is larger than another one, then the other is ''smaller than'' the first one. Examples: three is smaller than eight ({{nowrap|3 &lt; 8}}) and five is smaller than eight ({{nowrap|5 &lt; 8}}). The symbol for smaller than is &lt;. A number cannot be at the same time larger and smaller than another number. Neither can a number be at the same time larger than and equal to another number. Given a pair of natural numbers, one and only one of the following cases must be true:
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*the first number is equal to the second one,
*the first number is smaller than the second one.
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==Pencacahan==
Menghitung (atau mencacah) suatu kelompok benda berarti menggunakan suatu bilangan asli sebagai label bagi setiap benda, sedemikian sehingga suatu bilangan asli hanya akan dijadikan lambang suatu benda setelah pendahulunya telah diberikan. kepada suTo count a group of objects means to assign a natural number to each one of thebenda objectslain, askecuali ifbilangan itnol weretidak adijadikan labellambang forbenda thatapapun: object,bilangan suchasli thatterkecil ayang naturaldapat numberdijadikan islambang neveradalah assignedbilangan to an object unless its predecessor was already assigned to another objectsatu, withdan thebilangan exceptionasli thatterbesar zeroyang isdapat notdijadikan assignedlambang totergantung anydari object:ukuran thekelompok smallest natural number to be assigned is one, and the largest natural number assigned depends on the size of the groupitu. ItIni isdikatakan called''hasil pencacahan'' (''the count'') anddan it is equal to thesama numberdengan ofjumlah objectsbenda indalam thatkelompok groupitu.
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The process of [[counting]] a group is the following:
# Let "the count" be equal to zero. "The count" is a variable quantity, which though beginning with a value of zero, will soon have its value changed several times.
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Often, when counting objects, one does not keep track of what numerical label corresponds to which object: one only keeps track of the subgroup of objects which have already been labeled, so as to be able to identify unlabeled objects necessary for Step 2. However, if one is counting persons, then one can ask the persons who are being counted to each keep track of the number which the person's self has been assigned. After the count has finished it is possible to ask the group of persons to file up in a line, in order of increasing numerical label. What the persons would do during the process of lining up would be something like this: each pair of persons who are unsure of their positions in the line ask each other what their numbers are: the person whose number is smaller should stand on the left side and the one with the larger number on the right side of the other person. Thus, pairs of persons compare their numbers and their positions, and commute their positions as necessary, and through repetition of such conditional commutations they become ordered.
 
==SubtractionPengurangan==
{{Main|SubtractionPengurangan}}
SubtractionPengurangan isadalah theoperasi mathematicalmatematika operationyang whichmenyatakan describespenurunan a reduced quantitykuantitas. TheHasil resultoperasi ofini thisadalah operation is the"perbedaan" (''difference'') betweenantara twodua numbersbilangan, theyaitu bilangan "yang dikurangi" (''minuend'') anddan thebilangan "yang mengurangi" (''subtrahend''). AsSebagaimana withdengan additionpenjumlahan, subtractionpengurangan candapat havemempunyai asejumlah number of interpretationspenafsiran, such asseperti:
*"memisahkan" (''separating''): ("TomToto hasmempunyai 8 applesbuah apel. HeIa gives awaymemberikan 3 applesapel ke orang lain. HowBerapa manybanyak doessisa heyang haveia leftmiliki?")
*"membandingkan" (''comparing''): ("TomToto hasmempunyai 8 applesbuah apel. JaneYati hasmempunyai 3 fewerapel lebih applessedikit thandaripada TomToto. HowBerapa manyapel doesyang Janedimiliki haveYati?")
*"menggabungkan" (''combining''): ("TomToto hasmempunyai 8 apples.buah Three of theapel. applesTiga areapel greenberwarna andhijau thedan restsisanya areberwarna redmerah. HowBerapa manyapel areyang redmerah?")
*anddan sometimeskadang kala "menyatukan" (''joining''): ("TomToto hadmempunyai somesejumlah applesapel. JaneYati gave himmemberinya 3 moreapel appleslagi, sosehingga nowsekarang heToto hasmempunyai 8 applesbuah apel. HowBerapa apel manyyang diddimiliki heToto startpada withmulanya?").
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As with addition, there are other possible interpretations, such as ''motion''.
 
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The answer is
:<math>789 \times 345 = 272205</math>.
-->
 
==Pembagian==
{{Main|Pembagian}}
Dalam [[matematika]], khususnya aritmetika dasar, pembagian adalah operasi aritmetika yang merupakan [[fungsi invers]] dari [[perkalian]].
In [[mathematics]], especially in elementary [[arithmetic]], '''division''' is an arithmetic operation which is the inverse of [[multiplication]].
 
SpecificallySecara khusus, ifjika ''c'' timesdikalikan ''b'' equalssama dengan ''a'', writtenditulis:
:<math>c \times b = a\,</math>
wheredi mana ''b'' is notbukan [[0 (numberangka)|zeronol]], thenmaka ''a'' divideddibagi bydengan ''b'' equalssama dengan ''c'', writtenditulis:
:<math>\frac ab = c</math>
 
Misalnya,
For instance,
:<math>\frac 63 = 2</math>
karena
since
:<math>2 \times 3 = 6\,</math>.
 
InDalam theekspresi abovedi atas expression, ''a'' isdisebut calledbilangan the"yang 'dibagi" (''dividend'''), ''b'' thedisebut 'bilangan "pembagi" (''divisor''') anddan ''c'' theadalah '"hasil bagi" (''quotient''').
 
[[Division by zero]] (i.e. where the divisor is zero) is not defined.
 
[[:en:Division by zero|Pembagian dengan nol]] (yaitu di mana bilangan pembagi adalah nol) tidak dapat didefinisikan.
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===Division notation===
Division is most often shown by placing the ''dividend'' over the ''divisor'' with a horizontal line, also called a [[Vinculum (symbol)|vinculum]], between them. For example, ''a'' divided by ''b'' is written
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