Mathematical operations are the basic processes used to calculate, solve, and manipulate numbers. In English, these operations have specific names, symbols, and related vocabulary that help you follow instructions, explain your work, and understand problems. This page covers the main operations and some common related terms.
- Mathematical operations are fundamental actions like adding, subtracting, multiplying, and dividing numbers.
- Each operation has a standard name, symbol, and set of related words in English.
- Knowing this vocabulary helps you understand math problems, follow instructions, and communicate your solutions clearly.
Addition
Addition is the operation of combining two or more numbers to get a total sum. It answers the question "How many in all?" The symbol for addition is +.
- Addition means putting numbers together to find the total.
- The result is called the "sum."
- Common words: plus, add, total, increase, more than.
```
+ (plus) - used between numbers (e.g., 3 + 2)
add - to combine numbers
sum - the result of adding
total - the final amount
increase - to make a number larger
more than - indicates addition
together - combining numbers
both - referring to two amounts
combine - put numbers together
count up - add numbers
```
| English Word | English Example | Explanation |
|---|---|---|
| plus | plus 3 equals 8. | Use “plus” between numbers. |
| add | Add 7 and 2. | To combine numbers. |
| sum | The sum is 10. | Result of adding. |
| total | The total is 15. | Final amount after adding. |
| increase | Increase 4 by 6. | Make a number larger. |
| more than | is 4 more than 5. | Shows addition. |
| together | Add them together. | Combine numbers. |
| both | Both numbers are 3. | Refers to two items. |
| combine | Combine 2 and 7. | Put numbers together. |
| count up | Count up to 10. | Add numbers gradually. |
Subtraction
Subtraction is the operation of taking one number away from another. It answers "How many left?" or "What is the difference?" The symbol is −.
- Subtraction means removing or taking away.
- The result is called the "difference."
- Common words: minus, subtract, less, take away, decrease.
```
- (minus) - used between numbers (e.g., 5 - 3)
subtract - to take away one number from another
difference - the result of subtracting
less - smaller amount or fewer
take away - remove from a number
decrease - make a number smaller
reduce - lower the amount
remain - what is left
left - remaining quantity
fewer - smaller number of items
```
| English Word | English Example | Explanation |
|---|---|---|
| minus | minus 2 equals 4. | Use “minus” between numbers. |
| subtract | Subtract 3 from 9. | Take away a number. |
| difference | The difference is 5. | Result of subtracting. |
| less | is 2 less than 9. | Indicates a smaller amount. |
| take away | Take away 4. | Remove from a number. |
| decrease | Decrease 10 by 3. | Make a number smaller. |
| reduce | Reduce the total by 1. | Lower the amount. |
| remain | remain after 8 − 3. | What is left. |
| left | are left. | Remaining quantity. |
| fewer | Fewer than 6. | Smaller number of items. |
Multiplication
Multiplication means repeated addition. It shows how many times to count a number. The symbol is × or sometimes *.
- Multiplication means "times" or groups of a number.
- The result is called the "product."
- Common words: multiply, times, product, double, triple.
```
× (times) - used between numbers (e.g., 4 × 3)
multiply - to take one number times another
product - the result of multiplying
double - multiply by 2
triple - multiply by 3
once, twice, thrice - number of times
factor - a number multiplied
multiple - a number in the multiplication table
repeat - do again
groups of - sets of a number
```
| English Word | English Example | Explanation |
|---|---|---|
| times | times 4 equals 12. | Use “times” between numbers. |
| multiply | Multiply 5 by 2. | Take one number times another. |
| product | The product is 20. | Result of multiplying. |
| double | Double 7 is 14. | Multiply by 2. |
| triple | Triple 3 is 9. | Multiply by 3. |
| once | Multiply once. | One time. |
| twice | Multiply twice. | Two times. |
| factor | is a factor of 12. | A number multiplied in. |
| multiple | is a multiple of 5. | Product of a number and an integer. |
| groups of | groups of 4 = 12. | Sets of a number. |
Which symbol is commonly used for multiplication?
×
The symbol × (times) is used for multiplication.
Division
Division splits a number into equal parts or groups. It answers "How many in each group?" or "How many groups?" The symbols are ÷ or /.
- Division means sharing or splitting into equal parts.
- The result is called the "quotient."
- Common words: divide, quotient, share, split, half.
```
÷ (divided by) - used between numbers (e.g., 8 ÷ 2)
/ (slash) - alternative division symbol (e.g., 8/2)
divide - to split into equal parts
quotient - the result of dividing
share - distribute equally
split - divide into parts
half - divide by 2
third, quarter - divide by 3, 4
remainder - what is left over
equal parts - same size pieces
```
| English Word | English Example | Explanation |
|---|---|---|
| divided by | divided by 2 equals 5. | Use “divided by” between numbers. |
| divide | Divide 12 by 3. | Split into equal parts. |
| quotient | The quotient is 4. | Result of dividing. |
| share | Share 8 equally. | Distribute evenly. |
| split | Split 10 into 5 parts. | Divide into pieces. |
| half | Half of 6 is 3. | Divide by 2. |
| third | One-third of 9 is 3. | Divide by 3. |
| quarter | A quarter of 8 is 2. | Divide by 4. |
| remainder | Remainder is 1. | Leftover after division. |
| equal parts | Divide into equal parts. | Same-size pieces. |
If you share 10 apples among 5 people, what operation are you using?
division
Sharing equally involves division.
What word means to split a number into equal parts?
divide
The word "divide" means to split a number into equal parts.
Exponents and Roots
Exponents mean multiplying a number by itself a certain number of times. Roots are the opposite, finding a number that was multiplied by itself. Symbols include ^ (caret), superscript numbers, and √.
- Exponents show repeated multiplication.
- The result is called a "power."
- Roots find the original number before multiplying.
- Common words: power, square, cube, root, square root, cube root.
```
^ (caret) - exponent symbol (e.g., 2^3)
power - result of exponentiation (e.g., 2³)
square - power of 2 (e.g., 4²)
cube - power of 3 (e.g., 3³)
root - opposite of power
square root - √ number (e.g., √9 = 3)
cube root - number × itself × itself (e.g., ∛8 = 2)
raise to - to the power of
exponent - the small number showing power
root sign (√) - symbol for root
```
| English Word | English Example | Explanation |
|---|---|---|
| power | to the power of 3 = 8. | Exponentiation result. |
| square | squared is 25. | Number to the power of 2. |
| cube | cubed is 64. | Number to the power of 3. |
| root | The root of 16 is 4. | Opposite of exponent. |
| square root | √36 = 6. | Number times itself equals 36. |
| cube root | ∛27 = 3. | Number × itself × itself = 27. |
| raise to | Raise 3 to the power of 4. | Exponentiation phrase. |
| exponent | In 2³, 3 is the exponent. | Shows how many times to multiply. |
| radical | Radical means root. | Symbol √ is called radical. |
| base | In 2³, 2 is the base. | Number being multiplied. |
Fractions and Decimals
Fractions represent parts of a whole using two numbers separated by a slash. Decimals use a dot to show parts of one. These forms often involve division.
- Fraction means "part of a whole" (e.g., ½).
- Decimal means "tenths, hundredths, etc." (e.g., 0.5).
- Words include numerator, denominator, decimal point.
```
fraction - part of a whole (e.g., 3/4)
numerator - top fraction number
denominator - bottom fraction number
decimal - number with a dot (e.g., 0.75)
decimal point - the dot in decimals
percent - out of 100
half, third, quarter - common fractions
simplify - reduce fraction
convert - change form (fraction↔decimal)
mixed number - whole + fraction (e.g., 1½)
```
| English Word | English Example | Explanation |
|---|---|---|
| fraction | /2 is a fraction. | Part of a whole. |
| numerator | In 3/4, 3 is numerator. | Top fraction number. |
| denominator | In 3/4, 4 is denominator. | Bottom fraction number. |
| decimal | .5 is a decimal. | Part of a whole with a dot. |
| decimal point | .75 has a decimal point. | Dot separating whole and part. |
| percent | % means 50 out of 100. | Fraction of 100. |
| half | Half means 1/2. | Divide by 2. |
| third | One-third is 1/3. | Divide by 3. |
| quarter | A quarter is 1/4. | Divide by 4. |
| simplify | Simplify 4/8 to 1/2. | Reduce fraction. |
Order of Operations
Order of operations tells us which part to calculate first in a math expression. The common rule is PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction).
- Follow the order to get the correct answer.
- Operations inside parentheses come first.
- Then exponents, then multiplication/division, then addition/subtraction.
- Common words: parentheses, brackets, evaluate, simplify.
```
parentheses ( ) - calculate inside first
brackets [ ] - another grouping symbol
exponents - powers come next
multiply/divide - left to right
add/subtract - last step, left to right
evaluate - work out the answer
simplify - make the expression easier
order of operations - rules for calculation
expression - a math phrase with numbers/symbols
calculate - find the result
```
| English Word | English Example | Explanation |
|---|---|---|
| parentheses | (3 + 4) × 2 = 14. | Calculate inside ( ) first. |
| brackets | [5 − 2] + 3 = 6. | Another grouping symbol. |
| exponents | ³ + 1 = 9. | Powers come after grouping. |
| multiply/divide | ÷ 2 × 3 = 9. | Left to right. |
| add/subtract | + 3 − 2 = 6. | Last step, left to right. |
| evaluate | Evaluate 4 × (2 + 1). | Find the answer. |
| simplify | Simplify 2 + 3 × 4. | Make easier to solve. |
| order of operations | Follow PEMDAS rules. | Correct sequence for calculation. |
| expression | − (3 + 2). | Math phrase to calculate. |
| calculate | Calculate 8 ÷ 4. | Find the result. |
Mathematical operations vocabulary includes addition, subtraction, multiplication, division, exponents, fractions, and more. Each category has specific terms that help you describe, understand, and perform calculations in English.
Flashcards (1 of 70)
- Explanation: Use “plus” between numbers.
- English Word: plus
- English Example: 5 plus 3 equals 8.
Last updated: Wed Jun 18, 2025
