Algebra Expressions in Word Problems

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Algebra Expressions in Word Problems

  1. 1. It depends how fast she walks : Time = d / s Image Source: http://camsp.net
  2. 2. Word Problems need to be turned into Algebra Expressions so thatwe can do mathematics on them, and work out number answers.(Or write a Computer App that gets the answer).Little Red Riding Hood has to walk 5 miles.If she hops on 1 leg at 1 mile per hour, it will take her 5 hours.If she walks at 5 miles per hour it will take her 1 hour.If she runs at 10 miles per hour, it will take her half an hour.The Algebra Expression that gets the time for any speed shetravels at is : 5 divided by Speed or the “expression” 5 / S .
  3. 3. An Algebra Expression is made up of Numbers andLetters (or “Pronumerals”) as well as + - x symbols. Examples of Algebra Expressions are: Y+7 2m 4k / 3 3g – 4k 5–L
  4. 4. The Algebra Expression for the “Momentum” of a moving object is mass x velocity or mvA light object travelling slowly, like a party balloon, willhave low momentum, and will not hurt you if it bumpsinto you. (small mass x low speed = small momentum).However, a fast runningAmerican Footballplayer, who has bodyweight, and considerablespeed, will make therecipient of his tackledefinitely feel some bigmomentum ! Image Source: http://btfl.tripod.com
  5. 5. Algebra Expressions are used to make descriptions ofmathematical situations a lot shorter. It is much easier to write “mv”, than “mass x velocity”Think of it like this:On a Calculator it would take a long time to type in words: “Six times twelve divided by three equals”and it is much easier to type in: 6 x 12 2=
  6. 6. To translate word problems into Algebra Expressions,containing letters and numbers, we need to know how totranslate the key words in the problem into mathematicalsymbols.Consider these examples: “Two added to Four” becomes 2 + 4 “Four multiplied by V” becomes 4VThe following slides provide some translation rules for thekey words that are found in word problems.
  7. 7. Words that translate to Addingplus added to the sum ofsum more than combined togetherand increased by heavier thantotal next year the total ofcombined longer than older thanstill gain bigger thanperimeter together older than
  8. 8. Words that translate to Subtractless subtracted subtracted fromdifference less than taken awayremoved decreased by lighter thantotal last year the difference ofseparated shorter than younger thanfewer smaller than shorter thanloss differ by how many more
  9. 9. Words that translate to DivisionPer quotient split so many waysout of halved divided byover ratio fractionsplit half into equal parts
  10. 10. Words that translate to Multiplicationtimes multiplied by three times asof doubled increased by a factor ofproduct tripled quadrupledarea twice as volume
  11. 11. Words that translate to Equalsequals results in to obtaingives will be has a value ofwas makes is the same asis becomes is equivalent to
  12. 12. "the quotient of n and 3" n/3“four less than x" x–4"the sum of ten and y" y + 10“Two less than the total of a number and five" n + 5 – 2 which simplifies to n + 3 "x multiplied by 22“ 22x
  13. 13. “Alex has C chocolates, and D drinks. Miley has four fewer chocolates than Alex, but twice as many drinks. Write an expression for Miley’s snacks”.Replace the words with Numbers and Maths symbols.Four 4fewer Chocolates C - 4 (Remember minus Reverses)Twice 2xas many Drinks 2xD Answer: C – 4 + 2 x D C - 4 + 2D
  14. 14. “In a fruit bowl there are ‘a’ apples and ‘b’ bananas. In a paper bag there are 6 apples and 8 bananas. What is the total number of pieces of fruit?”Replace the words with Numbers and Maths symbols.‘a’ apples and ‘b’ bananas a+b6 apples and 8 bananas 6 + 8 ( Not 6a + 8b ) Combining our two expressions we have: a+b +6+8 Final Answer: a + b + 14
  15. 15. “Brad takes ‘h’ hours and ‘m’ minutes to complete a mini-triathlon. His friend Leonardo takes twice as long to finish the race. Write an algebra expression for Leo’s race time.”‘h’ hours and ‘m’ minutes h+mTwice ‘h’ hours and ‘m’ minutes 2x h+m2 x (h + m) 2xh+2xm 2h + 2m [ Not 2h + m ] Final Answer: 2h + 2m
  16. 16. “Johnny has ‘r’ red marbles and ‘b’ blue marbles. Pete keeps losing his marbles, and has half as many red marbles, and 5 less blue marbles than Johnny. Write an expression for Pete’s total marbles”Half as many red marbles r/2Five less blue marbles b–5 Source: ipadwallpapers.orgCombining our two expressions we have: r/2 +b-5 Final Answer: r/2 + b - 5
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