In order to write algebraic expressions and equations, assign a variable to represent the unknown number. In the table below, the letter “x” is used to represent the unknown.
Like,
Operation: Addition ( + )
Key word/phrase: plus, more than, the sum of, the total of, increased by, and added to.
Example: A number plus three, Ten more than a number, The sum of a number and five, The total of six and some number, A number increased by two, Eleven added to a number.
Translation: x + 3, x + 4, x + 10, x + 5, x + 2, 6 + x, x + 11 and so on.
Subtraction ( − ) minus A number minus seven X – 7
less than Four less than a number X – 4
the difference of The difference of a number and three X – 3
less Nine less a number 9 – X
decreased by A number decreased by twelve X – 12
subtracted from Six subtracted from a number
Multiplication ( x ) times Eight times a number 8x
the product of The product of fourteen and a number 14x
twice; double Twice a number; double a number 2x
multiplied by A number multiplied by negative six −6x
of Three fourths of a number
Division ( ÷ ) the quotient of The quotient of a number and seven divided by Ten divided by a number the ratio of The ratio of a number to fifteen
Powers ( x^n
) the square of;
squared The square of a number; a number squared x^2
the cube of; cubed The cube of a number; a number cubed x^3
Equals ( = ) equals Seven less than a number equals ten. x − 7 = 10
is Three times a number is negative six. 3x = −6
is the same as Eight is the same as twice a number. 8 = 2x
yields Twelve added to a number yields five. x + 12 = 5
amounts to Nine less a number amounts to twenty. 9 – x = 20