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Algebraic Translations of English Phrases Front Range Community College Alan Dinwiddie – Mathematics Dept. The following is to help you get the correct operation in application problems. Warning: some of the words or phrases can have different meanings. Example: 5 greater than a number (expression) x+5 5 is greater than x (inequality) 5>x Variable x is used in the examples, but any letter could be used. Words or phrases that suggest: Addition 7 added to a number a number added to 6 the sum of a number and 9 the sum of 12 and a number a number increased by 5 15 increased by a number increasing a number by 12 16 more than a number a number plus 3 7 plus a number 5 greater than a number x+7 6+x x+9 12 + x x+5 15 + x x + 12 x + 16 x+3 7+x x+5 (x + 6 is also correct) (x + 12 is also correct) (x + 15 is also correct) (x + 7 is also correct) Subtraction a number minus 15 6 minus a number 7 subtracted from a number a number subtracted from 8 -4 subtracted from a number the difference between a number and 7 the difference between 12 and a number 5 less than a number -3 less than a number a number decreased by 8 -6 decreased by a number 11 fewer than a number x – 15 6–x (not x – 6 ) x–7 8–x (not x – 8 ) x – (-4) x-7 12 – x (not x – 12 ) x–5 x – (-3) x–8 -6 – x x - 11 Multiplication A number multiplied by 7 6 times a number a number times 12 the product of 8 and a number the product of a number and –4 eight percent of a number 7x 6x 12x 8x -4x 3 x 4 0.08x twice a number 2x three-fourths of a number (12 x also correct) (when taking a fractional part) (percent of – write as decimal or fraction.) Division the quotient of a number and 6 the quotient of –3 and a number a number divided by 7 the ratio of a number and 5 the reciprocal of a number x x 6 x/6 6 3 3 x 3 / x x x 7 x 5 1 x