Translating Key Words and Phrases Into Algebraic Expressions
TRANSLATING KEY WORDS AND PHRASES INTO ALGEBRAIC EXPRESSIONS
The table below lists some key words and phrases that are used to describe common mathematical operations. 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. In translation problems, the words sum, total, difference, product and quotient imply at least two parts – use parentheses when a sum or difference is multiplied. For example, the phrase "the sum of three times a number and five" translates to "3x + 5," while the phrase "three times the sum of a number and five" translates to "3(x + 5)." OPERATION Addition ( + ) KEY WORD/PHRASE plus more than the sum of the total of increased by added to
Subtraction ( − )
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 A number minus seven Four less than a number The difference of a number and three Nine less a number A number decreased by twelve Six subtracted from a number Eight times a number The product of fourteen and a number Twice a number; double a number A number multiplied by negative six Three fourths of a number The quotient of a number and seven Ten divided by a number The ratio of a number to fifteen The square of a number; a number squared The cube of a number; a number cubed Seven less than a number equals ten. Three times a number is negative six. Eight is the same as twice a number. Twelve added to a number yields five. Nine less a number amounts to twenty.
TRANSLATION x+3 x + 10 x+5 6+x x+2 x + 11
X–7 X–4 X–3
minus less than the difference of less decreased by subtracted from
9–X
X – 12 X–6
Multiplication ( x )
times the product of twice; double multiplied by of
8x 14x 2x −6x
3 4 x
Division ( ÷ )
the quotient of divided by the ratio of
x 7
10 x x 15
Powers ( xn )
the square of;
The table below lists some key words and phrases that are used to describe common mathematical operations. 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. In translation problems, the words sum, total, difference, product and quotient imply at least two parts – use parentheses when a sum or difference is multiplied. For example, the phrase "the sum of three times a number and five" translates to "3x + 5," while the phrase "three times the sum of a number and five" translates to "3(x + 5)." OPERATION Addition ( + ) KEY WORD/PHRASE plus more than the sum of the total of increased by added to
Subtraction ( − )
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 A number minus seven Four less than a number The difference of a number and three Nine less a number A number decreased by twelve Six subtracted from a number Eight times a number The product of fourteen and a number Twice a number; double a number A number multiplied by negative six Three fourths of a number The quotient of a number and seven Ten divided by a number The ratio of a number to fifteen The square of a number; a number squared The cube of a number; a number cubed Seven less than a number equals ten. Three times a number is negative six. Eight is the same as twice a number. Twelve added to a number yields five. Nine less a number amounts to twenty.
TRANSLATION x+3 x + 10 x+5 6+x x+2 x + 11
X–7 X–4 X–3
minus less than the difference of less decreased by subtracted from
9–X
X – 12 X–6
Multiplication ( x )
times the product of twice; double multiplied by of
8x 14x 2x −6x
3 4 x
Division ( ÷ )
the quotient of divided by the ratio of
x 7
10 x x 15
Powers ( xn )
the square of;