Division is a math operation that tells how many equal groups you can make or how many are in each group. In English, we describe division using the ideas of sharing equally and splitting into equal parts. A division statement connects four roles: the number being divided, the number you divide by, the result, and sometimes what is left over.

English division vocabulary names each part of the operation so you can read and explain a calculation clearly. The same idea can be expressed with different words depending on whether you focus on groups, sharing, or measurement. Knowing the standard terms helps you understand textbooks, word problems, and spoken explanations.

Word/Phrase	Definition	Example
dividend	the number being divided	12 is the dividend in 12 ÷ 3
divisor	the number you divide by	3 is the divisor in 12 ÷ 3
quotient	the answer to a division	4 is the quotient in 12 ÷ 3
remainder	what is left after equal groups	14 ÷ 3 has remainder 2
factor	a number that divides another number exactly	3 is a factor of 12
multiple	a result of multiplying a number	12 is a multiple of 3

Division can be written with different symbols in English materials. You should be able to say each symbol aloud and recognize that they all represent the same operation. Some symbols are more common in school, while others appear more in higher math or on calculators.

Word/Phrase	Definition	Example
÷	division sign, said as divided by	12 ÷ 3 is twelve divided by three
/	slash used for division, often in typing	12/3 is twelve over three
a fraction bar	division written as a fraction	12 over 3 equals 4
long division bracket	layout for step by step division	3 goes into 12

English has several natural sentence patterns for division, and each highlights a different viewpoint. Choose the pattern that matches what you want to emphasize, such as the operation, the result, or the equal sharing idea. Being consistent with wording makes explanations easier to follow.

Word/Phrase	Definition	Example
divided by	standard way to read ÷	Twelve divided by three equals four
over	common for / and fractions	Twelve over three equals four
split into	focuses on dividing into equal groups	Split 12 into 3 equal groups
shared equally among	focuses on fair sharing	12 cookies shared equally among 3 kids
goes into	common in long division speech	Three goes into twelve four times
per	expresses a unit rate from division	12 dollars for 3 items is 4 dollars per item

Division results in English are described differently depending on whether the division is exact. If a remainder appears, English often names it explicitly, especially in school math. The same remainder can also be expressed as a fraction or a decimal, so you should recognize these as equivalent ways to report the result.

Rule	Example
If the divisor divides the dividend exactly, say the quotient with no remainder	12 ÷ 3 = 4, the division is exact
If something is left, state the remainder using remainder or r	14 ÷ 3 = 4 remainder 2, or 4 r 2
You can convert a remainder to a mixed number	14 ÷ 3 = 4 2/3
You can convert a remainder to a decimal when appropriate	14 ÷ 3 ≈ 4.67

Long division uses special spoken vocabulary to describe each step. English explanations often follow a predictable sequence so listeners can track where each number comes from. Understanding these phrases helps you follow classroom instruction and written solution walkthroughs.

Word/Phrase	Definition	Example
goes into	asks how many times the divisor fits	4 goes into 20 five times
times	multiplication step inside division	5 times 4 is 20
subtract	remove the product to find what remains	Subtract 20 from 20
bring down	move the next digit into the working number	Bring down the 6
repeat the steps	continue until all digits are used	Repeat until you reach the last digit

Word problems often describe division without showing a symbol, so you must recognize division meaning from vocabulary. Some problems ask for the number of groups, while others ask for the size of each group. Identifying which quantity is unknown helps you set up the correct division expression.

Rule	Example
If the problem says shared equally, it signals division	15 stickers shared equally among 5 friends
If it asks how many each, it usually asks for the quotient	How many stickers does each friend get
If it asks how many groups, divide to find the number of groups	How many boxes can you fill with 24 apples if each holds 6
Words like per often mean division to find a unit rate	120 miles in 3 hours is 40 miles per hour

In English math language, division is the inverse of multiplication, meaning one operation undoes the other. This relationship is used to check answers and to explain why division facts connect to multiplication facts. Understanding inverse language helps you follow explanations about fact families and checking work.

Rule	Example
If a ÷ b = c, then c × b = a	If 12 ÷ 3 = 4, then 4 × 3 = 12
Use multiplication to check a division result	Check 14 ÷ 3: 4 × 3 = 12, plus remainder 2 makes 14
Exact division means the divisor is a factor of the dividend	3 is a factor of 12 because 12 ÷ 3 is an integer

English often treats a fraction as a division statement, where the numerator is divided by the denominator. This connects division vocabulary to fraction vocabulary like numerator and denominator. Recognizing this equivalence helps when rewriting expressions and interpreting math text.

Word/Phrase	Definition	Example
numerator	top number in a fraction, the dividend	In 3/4, 3 is the numerator
denominator	bottom number in a fraction, the divisor	In 3/4, 4 is the denominator
fraction equals division	a/b means a divided by b	3/4 means three divided by four
simplify	reduce a fraction by dividing by a common factor	6/8 simplifies to 3/4

When division produces decimals, English explanations often mention place value and rounding. In real life contexts, you may also hear approximation language to show the result is not exact. Knowing these terms helps you interpret calculator results and measurements.

Word/Phrase	Definition	Example
decimal point	dot that separates whole and fractional parts	4.5 has a decimal point
terminate	decimal ends after a certain place	1 ÷ 4 = 0.25, it terminates
repeat	decimal pattern continues	1 ÷ 3 = 0.333..., it repeats
round to	shorten a decimal to a place value	Round 4.666... to 4.67
approximately	indicates an estimate close to the value	14 ÷ 3 is approximately 4.67