Below is a summary of the common mathematical symbols discussed below, along with the words in English used to describe them.

SYMBOL | SYMBOL NAME | CALCULATION TYPE | CALCULATION WORD |
---|---|---|---|

+ | Plus sign | Addition | ...plus... |

- | Minus sign | Subtraction | ...minus... |

± | Plus-minus sign | N/A | ...plus or minus... |

× ⋅ ∗ | Multiplication sign | Multiplication | ...times... ...multiplied by... |

÷ / | Division sign | Division | ...divided by... |

= | Equals sign | Equation | ...equals... |

≠ | Not-equals sign | N/A | ...is not equal to... |

≈ | Almost-equals sign | Approximation | ...equals... |

> | Greater-than sign | Inequality | ...is greater than... |

< | Less-than sign | Inequality | ...is less than... |

≥ | Greater-than-or-equal-to sign | Inequality | ...is greater than or equal to... |

≤ | Less-than-or-equal-to sign | Inequality | ...is less than or equal to... |

% | Percent sign | Percentage | ...percent |

xy | Exponent | Exponentiation | ...to the power of... ...squared, cubed, etc. ...to the... |

x√ | Radical sign | Root | The square root of… The cube root of... ...root... |

log | Log | Logarithm | Log base...of... |

ln | Natural log | Natural logarithm | The natural log of... |

! | Factorial | Factorial | ...factorial... |

- Addition
- Equation
- Not-equals sign
- Subtraction
- Plus-minus sign
- Multiplication
- Division
- Inequality
- Decimal
- Approximation
- Ratio
- Improper fraction
- Percentage
- Exponential
- Square root
- Imaginary number
- Logarithm
- Per
- Infinity
- Factorial
- Equation of those number

Math can be frustrating enough in your own language. But when learning a new language, you may find that you’ll need to relearn not just numbers, but many of the terms used in the world of math.

For example, it might be difficult for you to calculate a tip at a restaurant out loud for your English-speaking friend, but something like that can definitely come in handy. To help, here are a bunch of terms (and example equations) that English speakers use when rattling their brains with numbers and equations.

**Addition**

6 + 4 = 12

Six plus four equals twelve.

This type of calculation is called **addition**, which is when you add two or more numbers together. When saying the equation out loud, we use the word “plus,” and the “+” symbol is called a **plus sign**. The result of an addition equation is called a **sum**.

**Equation**

Usually, we say that one expression **equals** another, and the “=” symbol is fittingly called an **equals sign**. Though it is fairly common in English to say the word “equals,” it is also fine to use the singular “is.” For example, two plus three *is* five. Any mathematical statement involving an equals sign is called an **equation**.

**Not-equals sign**

6 + 4 ≠ 13

Six plus four is not equal to thirteen.

The “≠” symbol is called a **not-equals sign**, and we say that one expression is **not equal to** another.

**Subtraction**

15 – 8 = 7

Fifteen minus eight equals seven.

This type of calculation is called **subtraction**, which is when you **subtract** one number from the other to get a difference. When saying the equation out loud, we use the word “minus,” and the “-” symbol is called—you guessed it—a **minus sign**. However, the word “minus” is not used when describing negative numbers (as opposed to positive numbers). For example, three minus four is not “minus one,” but “**negative** one.”

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**Plus-minus** **sign**

4 ± 3 = 1 or 7

Four plus or minus three equals one or seven.

The “±” symbol is called the **plus-minus** **sign**, and when used in an equation, we say that one number **plus or minus** another results in two possible sums.

**Multiplication**

5 × 2 = 10

Five times two equals ten.

Five multiplied by two equals ten.

Now we’ve gotten to **multiplication**, and there are two ways to recite such a calculation. One way is to say that one number times another results in a product. The other way is to use the logical term “**multiplied by**.” The “×” symbol is considered to be the **multiplication sign**, although you can also use a dot (⋅) or an asterisk (∗).

**Division**

21 ÷ 7 = 3

Twenty-one divided by seven equals three.

When dealing with **division**, we say that one number is **divided by** another number to get a **quotient**. We call the “÷” symbol a **division sign**, but it is also common to use a slash (/), a symbol also used for fractions. If an answer contains a remainder, then you simply say “**remainder**” where the “r” is. For example, 22 ÷ 7 = 3r1 would be “twenty-two divided by seven equals three remainder one.”

**Inequality**

18.5 > 18

Eighteen point five is greater than eighteen.

This type of equation is called an **inequality**, and it is usually read from left to right. So logically, the “>” symbol is called a “**greater-than sign**” and the “<” symbol is called a “**less-than sign**.” You can also use the “≥” or “≤” symbols if a number, usually a variable, may be **greater than or equal to** another number, or **less than or equal to** it.

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**Decimal**

3.141

three point one four one

18.5 is considered a **decimal**, and the period used to write this number is called a **decimal point**.

When said out loud, we usually use the word “point,” followed by a string of individual numbers. For example, 3.141 would be pronounced “three point one four one.” However, with simpler numbers, it is common to use a fraction like “five-tenths.” Don’t worry, this will be covered next.

Money tends to be recited a little differently. For example, if something costs $5.75, you wouldn’t say “five point seven five dollars.” Instead you would say “five dollars and seventy-five cents” or simply “five seventy-five.”

### Approximation

π ≈ 3.14

Pi is approximately equal to 3.14

This type of equation is called an **approximation**, where one value is **approximately equal to** another value. The “≈” symbol is called an **almost-equals sign**.

The fields of math and science tend to borrow a lot of letters from the Greek alphabet as commonplace symbols, and English tends to put a twist on the pronunciation of these letters. For example, the letter π is not pronounced /pi/ as it normally would be, but rather as /paj/, like the word “pie.”

Be careful about pronouncing Greek letters in English because oftentimes, it won’t be the same.

### Ratio (numerator, denominator)

1 ÷ 3 = ⅓

One divided by three equals a third.

In a fraction, the top number is called the **numerator** and the bottom number is called the **denominator**. When saying fractions out loud, we usually treat the denominator like an ordinal number. That means ⅓ is pronounced “a third,” ¼ is pronounced “a fourth,” etc. One exception is ½, which is usually called “a **half**,” not “a second.” Similarly, ¼ can be called “a** quarter**,” as well as a fourth, but those are the only irregularities.

With all of these fractions, it’s acceptable to use the word “one” instead of “a,” so ½ can be called “one half” as well as “a half.” And if the numerator is a number greater than one, simply say that number out loud. ¾ would be “three-fourths,” ⅖ would be “two-fifths,” etc. Notice the use of a hyphen when writing out the fraction.

With any fraction, it is also possible to simply say that one number is “over” another. While ⅖ can be pronounced “two-fifths,” it is also perfectly fine to say “two over five.” In fact, when dealing with **variables** (letters that represent numbers), it is actually the only convenient way to say it. For example, x/y would be said as “x over y,” while nobody would ever say “x-yth.”

**Improper fraction**

2 ÷ 3 = 1½

Two divided by three equals one and a half.

An **improper fraction** is a combination of a whole number (**integer**) and a fraction and involves the use of the word “and.” So 1½ would be one *and *a half, 2¾ would be two *and* three-fourths, etc. As stated before, decimals can occasionally be stated as an improper fraction. While it is normal to pronounce 0.7 as “zero point seven” or “point seven,” it can also be said as “seven-tenths,” since it is technically equal to 7/10. Similarly, 0.75 can be said as “seventy-five hundredths.”

However, this method of reading decimals can become clunky and confusing, and so it is much more common and convenient to stick with the “point” method.

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### Percentage

20 × 40% = 8

Twenty times forty percent equals eight.

Forty percent of twenty is eight.

The **percent sign** (%) is used to indicate a **percentage**. When reading a percentage, you simply say the number and the word “**percent**” after it, so 50% would be read as “fifty percent.” When calculating something that involves a percentage, you can simply pronounce it as a standard multiplication equation, or you can say that a certain percent of another number results in a product.

In computer science, the percent sign tends to have a different function and is actually used as the **modulo operator**, which acts as a division calculation but outputs only the remainder. Where the percent sign is, you would say “**modulo**” or “**mod**” for short. For example, 15 % 6 == 3 would be “fifteen mod six equals three” (a double percent sign is usually used in computer languages, but it is read the same).

### Exponential

3

^{3}= 27

Three cubed equals twenty-seven.

Three to the third equals twenty-seven.

Three to the power of three equals twenty-seven.

An **exponent** is when you take a number and multiply it by itself a certain number of times, an operation called **exponentiation**. In other words, you take one number **to the power** **of** another number. This is the easiest way to read an exponent out loud, since it works easily with decimals and fractions (“four to the seven point five,” “three to the four-fifths,” etc.).

However, it is also common to use an ordinal number when reading aloud an exponent. For example, x^{3} reads “x to the third,” x^{4} reads “x to the fourth,” etc. Note that this is different from saying “x-thirds” or “x-fourths,” which would turn the number into a fraction.

It is not common to say x^{2} as “x to the second.” Instead, the convention is to say “x squared,” which relates to concepts of geometry. Similarly, it is common to say x^{3} as “x cubed.”

However, there is no equivalent for x^{4} and numbers beyond that. “Squared” and “cubed” are also used when talking about units of length in two or three dimensions. For example, 5 ft^{2} would be read as “five feet squared,” and 50 km^{3} would be read as “fifty kilometers cubed.

### Square root

√16 = 4

The square root of sixteen is four.

The result of this equation is called a **square root**, and the “√” symbol is called a **radical sign** (“radical” literally means “root”). It is typical to state that the square root of one number equals another number.

A square root is essentially a number to the power of a half. In other words, √16 is the same as 16^{1/2}. However, if the number is to the power of a different fraction, say ⅓, then the root becomes a **cube root**, written as ^{3}√16.

For this, you can say “the cube root of sixteen,” but you can also say “sixteen root three.” Similarly, ^{4}√16 would be “sixteen root four,” etc.

### Imaginary number

√(–4) = 2i

The square root of negative four is two i.

An **imaginary number** is the result of taking the square root of a negative number. When reading an imaginary number aloud, simply pronounce the letter “i” as it is. 2i is pronounced “two i,” 3i is “three i,” etc.

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### Logarithm

log

_{2}8 = 3

Log base two of eight equals three.

A **logarithm** is basically an inverse of an exponential equation, and though it seems complicated, reading one may actually be easier and more consistent.

In the case of log_{2}8, since the “2” is considered to be the base of the logarithm, you would say that log base two of eight equals three. An expression containing “ln” is called a **natural log**. For example, lnx would be stated as “the natural log of x.”

### Per

12m / 4s = 3m/s

Twelve meters divided by four seconds equals three meters per second.

When dealing with rates, we use the word **per** between units. This applies to even mundane rates that don’t require the use of scientific units. For example:

- This class will meet five times
**per**(Five times a week) - I usually assist ten customers
**per**(Ten customers every shift)

The word “**per**” also appears in the abbreviation “**mph**,” which stands for “miles per hour.” Instead of using a slash like most scientific rates, this abbreviation shortens the word “**per**” with the letter “p.”

- I usually go 80mph on the highway.

### Infinity

0 < x < ∞

X is greater than zero and less than infinity.

**Infinity** (∞) is an abstraction of the largest number imaginable, the opposite of which is **negative infinity** (–∞). The “∞” symbol is called the **infinity symbol**, sometimes called a **lemniscate** because of its figure-eight shape. Notice that it’s different from the word “infinite,” which is an adjective that describes something that is endless or limitless.

### Factorial

5! = 120

Five factorial equals 120.

A **factorial** is represented by an exclamation point, and you simply say the word “factorial” after the number. Things don’t get much easier…

### Equation of those number

5 x (4 + 3) = 35

Five times the quantity of four plus three equals thirty-five.

Saying equations out loud can get a bit tricky when there are parentheses involved.

One method is to take short pauses before saying numbers grouped in parentheses. But a more effective way would be to call them **the quantity of** those numbers, almost as if you’re making a calculation within a calculation, which is essentially what you’re doing.

This phrase also comes in handy when you’re dealing with complex fractions. For example, an easy way to say x / (y + z) would be “x over the quantity of y plus z.”

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