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

KEY WORD/PHRASE EXAMPLE

TRANSLATION

Addition ( + )

plus

more than

the sum of

the total of

increased by

added to

Subtraction ( - )

minus

less than

the difference of

less

decreased by

subtracted from

Multiplication ( x ) times

the product of

twice; double

multiplied by

of

Division ( ? )

the quotient of

divided by

Powers ( xn )

the ratio of

the square of; squared

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

x + 3 x + 10 x + 5 6 + x x + 2 x + 11 X ? 7 X ? 4 X ? 3 9 ? X X ? 12 X ? 6

8x 14x 2x -6x

3 x

4 x 7 10 x x 15

x2

the cube of; cubed The cube of a number; a number cubed

x3

Equals ( = )

equals is is the same as yields amounts to

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.

x - 7 = 10 3x = -6 8 = 2x

x + 12 = 5 9 ? x = 20

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