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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 atleast 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)." is the same as OPERATION KEY WoRD/PHRASE | EXAMPLE TRANSLATION Addition (+) plus A number plus three x+3 more than Ten more than a number x+10 the sum of The sum of a number and five x+5 the total of The total of six and some number 6+x increased by A number increased by two x+2 added to Eleven added to a number x+11 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 x-6 Multiplication (x) | times Eight times a number z 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 3 x 4 Division (+) the quotient of The quotient of a number and seven : ‘ ; ae 10 divided by Ten divided by a number = x the ratio of The ratio of a number to fifteen = a the square of, 7 2 Powers (x") erred The square of a number; a number squared x the cube of, cubed | The cube of a number; a number cubed x Equals (=) equals Seven less than a number equals ten is Three times a number is negative six. Eight is the same as twice a number yields Twelve added to a number yields five. amounts to Nine less a number amounts to twenty 
