HFCC Math Lab Beginning Algebra 13 TRANSLATING ENGLISH INTO ALGEBRA: WORDS, PHRASE, SENTENCES

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1 HFCC Math Lab Beginning Algebra 1 TRANSLATING ENGLISH INTO ALGEBRA: WORDS, PHRASE, SENTENCES Before being able to solve word problems in algebra, you must be able to change words, phrases, and sentences into algebraic form. WORDS: Here is a list of commonly used words and the operations they corresponds to in mathematics. ADDITION WORDS 5 more than increased by 5 The sum of and 5 plus 5 5 added to ALGEBRAIC EXPRESSION + 5 SUBTRACTION less than decreased by The difference of and minus subtracted from MULTIPLICATION times of The product of and multiplied by twice or or ( ) DIVISION divided by 4 The ratio of to 4 The quotient of and 4 per 4 4 or 4 EXPONENT The square of The cube of Note: less than means BUT is less than means < Revised 0/09 1

2 NOTE: Many students believe that the word and always means to add. But as we have seen in the above eamples, and could mean to add, subtract, multiply, or divide, depending on the words that come before it. The sum of and + The difference of and The product of and The quotient of and PHRASES: Sometimes more than one of the key words in the lists above will be used in a phrase. You must read the phrase very carefully, perhaps several times, to see what is being said before translating to an algebraic EXPRESSION Eamples: REMEMBER: In English, a phrase is a group of words without a verb (a word showing action or eistence) THEREFORE: A phrase will become an algebraic epression, not an equation. 1) Seven more than twice + Since: more than means + and twice means times ) Five less than the square of 5 Since: less than means and the square of means raising to the second power ) more than the product of a number and + 4) 5 times the sum of a number and 5( + ) 5) The sum of 5 times a number and 5+ NOTE: eamples 4 & 5 are easy to confuse. Be sure you understand how they are different before you go on. Revised 0/09

3 SENTENCES: When two phrases are connected by a verb, the English word translate into an algebraic EQUATION. Here are some words that mean is equal to : is was yields is the some as result in gives becomes The words that translate to = divide the word sentence into the two side of the equation. The phrase before the = makes up the left side of the equation. The phrase after the = makes up the right side of the equation. Eamples: 1) The sum of a number and is 1 + = 1 ) Twice a number is the same as 8 more than the number = + 8 ) Seven less than three times a number yields si more than the number. = + 6 4) The square of a number plus 8 gives si times the number. + 8 = 6 5) Two times the sum of a number and is less than si times the number. ( ) + = 6 Revised 0/09

4 EXERCISES: I) Translate the following phrases to algebraic epressions: 1) Five more than a number. ) Ten less than a number. ) Three times a number. 4) Twice a number increased by. 5) Seven added to half a number. 6) Two less than the quotient of and 5. ) The difference of three times a number and. 8) Three times the difference of a number and. 9) Half the sum of 5 and twice a number. 10) The sum of half of 5 and twice a number. II) Translate the following sentences to algebraic epressions: 11) A number decreased by 4 yields. 1) Four more than a number gives the product of the number and 5. 1) The sum of twice a number and three is the number decreased by. 14) If you subtracted from the product of a number and 5, it results in 5 more than the number. 15) Five times a number is the square of the number increased by 4. 16) A number plus 6 is the same as three times the number. III) Determine whether each of the following is a phrases or sentence, and translate to the correct algebraic form: 1) Si less than three times a number 18) Four more than a number is twice the number minus 19) Five times a number yields less than four times the number. 0) A number increased by 4 1) Five times the sum of a number and ) Three times the difference of a number and is one less than twice the number. Answers: 1) + 5 ) 10 ) Revised 0/09 4

5 4) + 5) 1 + 6) 5 ) 8) ( ) 1 5 9) ( + ) 10) ) 4= 1) 4+ = 5 1) + = 14) 5 = 5+ 15) 5= ) + 6= 1) 6 18) 4+ = 19) 5= 4 0) + 4 1) 5( + ) ) ( ) = 1 Revised 0/09 5

6 NOTE: you can get additional instruction and practice by going to the following web site: This website gives eplanation and eamples. This website gives instruction along with practice problems, including answers. Revised 0/09 6

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