Mathematical operations are actions you do to numbers to get a result. The four core operations are addition, subtraction, multiplication, and division. Each operation has a symbol, a common verb you say in English, and a name for its result. Learning these lets you understand and describe most basic calculations clearly.

Word/Phrase	Definition	Example
addition	Putting numbers together to get a total	7 + 5 is addition
subtraction	Taking one number away from another to find the difference	10 − 3 is subtraction
multiplication	Repeated addition to get a product	4 × 6 is multiplication
division	Splitting into equal parts to get a quotient	20 ÷ 4 is division

In English, you often describe operations with verbs instead of only symbols. These verbs appear in spoken math, word problems, and instructions. Many verbs have close meanings, but some fit certain operations better than others. Knowing the common verb for each operation helps you translate a sentence into an equation.

Word/Phrase	Definition	Example
add	Do addition	Add 2 and 8
plus	Added to	3 plus 9 equals 12
subtract	Do subtraction	Subtract 5 from 12
minus	Subtracted from	15 minus 4 equals 11
multiply	Do multiplication	Multiply 7 by 3
times	Multiplied by	6 times 5 is 30
divide	Do division	Divide 24 by 6
divided by	Separated into equal parts	18 divided by 3 is 6

English uses specific nouns for the result of an operation. These words show up in textbooks, instructions, and explanations. Using the correct result word makes your math writing sound precise. Some result words are used more in formal math than in everyday speech.

Word/Phrase	Definition	Example
sum	Result of addition	The sum of 4 and 9 is 13
total	Final amount after adding	The total is 27
difference	Result of subtraction	The difference between 10 and 6 is 4
product	Result of multiplication	The product of 3 and 8 is 24
quotient	Result of division	The quotient of 20 and 5 is 4
remainder	Amount left over after division	17 divided by 5 has a remainder of 2

The equals sign shows that two expressions have the same value. In English you can say equals, is, is equal to, or results in, depending on context. In equations, both sides must balance, even if they look different. This idea is important for reading and writing math statements correctly.

Word/Phrase	Definition	Example
equals	Has the same value as	8 + 1 equals 9
is	Informal way to state equality	2 times 6 is 12
is equal to	More formal way to state equality	3 + 4 is equal to 7
results in	Focuses on the outcome	9 − 2 results in 7

When an expression has multiple operations, English follows a standard order to avoid confusion. Parentheses come first, then exponents, then multiplication and division, then addition and subtraction. Multiplication and division share the same level, so you work left to right. Addition and subtraction also share a level, so you work left to right.

Rule	Example
Do parentheses first	(3 + 5) × 2
Do exponents next	2^3 + 1
Do multiplication and division left to right	12 ÷ 3 × 2
Do addition and subtraction left to right	10 − 4 + 1

Word problems often use prepositions that change the order of numbers in an operation. The pattern subtract A from B means B − A, not A − B. The phrase divide A by B means A ÷ B. Learning these fixed patterns prevents common interpretation errors when turning English into equations.

Rule	Example
Subtract A from B means B − A	Subtract 3 from 10 means 10 − 3
Divide A by B means A ÷ B	Divide 20 by 4 means 20 ÷ 4
Multiply A by B means A × B	Multiply 6 by 7 means 6 × 7
Add A to B means B + A	Add 5 to 12 means 12 + 5

English connects division and fractions closely: a fraction bar can mean divided by. You may hear over to describe a fraction, especially in spoken math. You also need language for numerator and denominator to describe fraction parts clearly. This vocabulary helps when reading formulas and simplifying expressions.

Word/Phrase	Definition	Example
fraction bar	The line meaning division in a fraction	3/4 means 3 divided by 4
over	Spoken way to read a fraction	5/8 is five over eight
numerator	Top number in a fraction	In 7/9, 7 is the numerator
denominator	Bottom number in a fraction	In 7/9, 9 is the denominator

Beyond the four core operations, English frequently uses exponent and root vocabulary. Exponents describe repeated multiplication, and roots undo powers. You will see terms like squared and cubed often in geometry and measurement. Knowing these words helps you read expressions with superscripts and radical symbols.

Word/Phrase	Definition	Example
exponent	A power showing repeated multiplication	In 2^5, 5 is the exponent
squared	Power of 2	7^2 is seven squared
cubed	Power of 3	4^3 is four cubed
square root	A number that squared gives the original number	The square root of 25 is 5
cube root	A number that cubed gives the original number	The cube root of 27 is 3

Operations with negative numbers use clear sign language in English. You may say negative five for −5, and you may also hear minus five in casual speech. When reading expressions, minus can mean subtraction or a negative sign, depending on position. Being careful with these terms helps you interpret equations correctly.

Rule	Example
Negative describes the sign of a number	Negative 6 means −6
Minus often describes subtraction between two numbers	8 minus 3 means 8 − 3
A negative sign can appear inside parentheses	4 × (−2)
You can say plus negative to show addition with a negative number	7 + (−3) is seven plus negative three

Math in real life often uses approximate answers. English uses words like round, estimate, and approximately to show you are not giving an exact value. You also need phrases for decimal places to explain how you rounded. This language is common in measurement, money, and data.

Word/Phrase	Definition	Example
round	Change a number to a nearby simpler number	Round 3.47 to 3.5
estimate	Find a close value without exact calculation	Estimate 198 × 5 as about 200 × 5
approximately	Not exact, close to	The result is approximately 62
decimal place	A position after the decimal point	4.736 rounded to two decimal places is 4.74