Academic Skills - Math Terminology

 

Translating Words into Mathematical Symbols

English Phrase	Mathematical Phrase
The sum of a number n and 4	n + 4
6 more than a number n	6 + n
A number n increased by 9	n + 9
15 less than a number n	n – 15
A number n subtracted from 7	7 – n
A number n decreased by 9	n – 9
Twice the number n	2n
The sum of 5 times a number n and 8	5n + 8
The sum of p and q less the sum of n and m	(p + q) – (n + m)
The product of n and m	nm
A number n divided by 6	n/6
7 divided by the number n	7/n
The quotient of a number n and 5	n/5
The ratio of two numbers n and m	n/m
20% of a number n	0.20n
The sum of x and y is 8	x + y = 8
The sum of x and y is 4 more than twice the product of x and y	x + y = 4 + 2xy
The square of a number n	n²
The square root of a number n	√n
The absolute value of a number n	|n|
The absolute value of the difference between x and y	|x – y|

 

Common Vocabulary Used in Mathematics:

• Sum. The result of adding numbers
• Difference. The result of subtracting numbers
• Terms.  Quantities that are added or subtracted. In the expression 3x – 6y + 4, there are three terms: 3x, 6y, and4.
• Product.  The result of multiplying numbers
• Factors. Quantities that are multiplied. In the expression m(a + b), there are two factors: m and (a + b).
• Factor. The word factor is used in a few different ways including the example above. “n is a factor of a number” means n divides exactly into the number.  “To factor” means to write a number as the product of its factors.
• Multiple of n. A number that is exactly divisible by n
• Quotient. The result of dividing two numbers. In the division x ÷ y = z, x is the dividend, y is the divisor, and z is the quotient.
• Ratio. The quotient of two numbers  The ratio of a to b is a/b.
• Natural numbers. The set of numbers used for counting: {1, 2, 3, 4, 5,…}
• Whole numbers. The natural numbers and zero: {0, 1, 2 , 3, 4,…}
• Integers. The set: {…,-3, -2, -1, 0, 1, 2, 3,…}
• Rational numbers. The set of all numbers which can be represented as a fraction using integers
• Irrational numbers. The set of numbers with non-repeating, non-terminating decimals
• Real numbers. The set of rational and irrational numbers
• Variable.  A symbol (usually a letter) which stands for a number
• Literal part of a term. Non-numerical part of a term (for example, in the term 3xy, xy is the literal part of the term and 3 is called the coefficient)
• Like terms. Terms with identical literal parts
• Asymptote. An asymptote is a line or curve that approaches a given curve arbitrarily closely

 

Binomial Theorem:

• (a + b) ¹ = a + b
• (a + b) ² = a ² + 2ab + b ²
• (a + b) ³ = a ³+ 3a ² b + 3ab ² + b ³
• (a + b) = a + 4a ³ b + 6a ² b ² + 4ab ³ + b ...and so on...

Difference of Squares:

• a² - b² = (a - b)(a + b)

Difference of Cubes:

• a³ – b³ = (a - b)(a²– ab + b²)

Sum of Cubes:

• a³ + b³ = (a + b)(a²– ab + b²)

Rules of Zero:

• 0/x = 0 where x is not equal to 0.
• a º = 1
• 0a = 0
• a x 0 = 0
• a/0 is undefined (you can't do it)

Laws of Exponents: