Basic Math and Pre-Algebra - Word Problems - Quick Guides | Mathematics

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Study GuideBasic Math and Pre-Algebra–Word Problems1. Key WordsWhen you solve word problems, certainkey wordsgive you clues about which math operation touse. Learning to spot these words makes problem-solving much easier.1.1AddiƟon Key WordsThese words usually mean you need toaddnumbers together:•Addition–“The team needed the addition of three new players.”•Sum–“Find the sum of 5, 6, and 8.”•Total–“What is the total of the last two games?”•Plus–“Three chairs plus five chairs.”•Increase–“Her pay was increased by $30.”If something is being combined or made bigger, you are probably adding.1.2SubtracƟon Key WordsThese words suggest you shouldsubtract:•Difference–“What is the difference between 8 and 5?”•Fewer–“There were ten fewer girls than boys.”•Remainder–“What is the remainder when…?”•Less–“A number is six less than another number.”•Reduced–“His allowance was reduced by $5.”•Decreased–“What number decreased by 7 is 5?”•Minus–“Seven minus a number is…”

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Study Guide1.3MulƟplicaƟon Key WordsThese words usually meanmultiply:•Product–“Find the product of 3 and 6.”•Of–“One-half of the people in the room.”•Times–“Six times as many men as women.”•At–“The cost of five yards at $9 a yard.”•Total–“If you spend $20 per week on gas, what is the total for two weeks?”•Twice–“Twice the value of a number.” (multiply by 2)If something is repeated equal groups or scaled up, multiplication is usually the operation.1.4Division Key WordsThese words point todivision:•Quotient–“Find the final quotient.”•Divided by–“Some number divided by 5.”•Divided into–“The coins were divided into groups.”•Ratio–“What is the ratio of…?”•Half–“Half of the cards.” (divide by 2)If something is being shared, split, or separated into equal parts, division is needed.Example 1:SolveLet’s see how this works in a real problem.Problem:Jack bowled four games for a total score of 500. What was his average score for a game?Step 1: Understand the QuestionWhat are we trying to find?Jack’s average score per game.

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Study GuideStep 2: Pull Out Important Information•4 games•Total score = 500Step 3: Decide What to DoTo find an average, we divide the total by the number of games.So we set up:500 ÷ 4Step 4: Solve Carefully500 ÷ 4 = 125Step 5: Answer in a SentenceJack’s average score for a game is125.Step 6: Check Your AnswerDoes it make sense?If Jack scored 125 in each of 4 games:125 × 4 = 500Example 2:Finding an AverageProblem:Judy scored 85, 90, and 95 on her last three algebra tests. What was her average score?Step 1: Understand the QuestionWe are asked to find Judy’saverage score.

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Study GuideStep 2: Identify Important InformationThe three test scores are:•85•90•95There are3 tests total.Step 3: Set Up the MathTo find an average:1.Add the scores.2.Divide by the number of scores.So we write:(85 + 90 + 95) ÷ 3Step 4: Solve CarefullyFirst, add:85 + 90 + 95 = 270Now divide:270 ÷ 3 = 90Step 5: Write the Answer in a SentenceJudy’s average test score was90.Step 6: Check if the Answer Makes SenseThe scores were 85, 90, and 95.The average should be somewhere in the middle.Since 90 is halfway between 85 and 95, the answer is reasonable.

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Study GuideExample 3:Finding Change After ShoppingProblem:Frances buys:•Two boxes of cereal at $4 each•Three bottles of milk at $2 each•Two cans of soup at $1 eachShe pays with a $20 bill. How much change will she get?Step 1: Understand the QuestionWe need to find how muchchangeFrances gets from $20.Step 2: Pull Out Important Information•2 boxes × $4•3 bottles × $2•2 cans × $1•Paid with $20Step 3: Set Up the MathMultiply to find the total cost:2 × 43 × 22 × 1Then subtract from $20.

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Study GuideStep 4: Solve Carefully2 × 4 = 83 × 2 = 62 × 1 = 2Now add the costs:8 + 6 + 2 = 16Now subtract from 20:20−16 = 4Step 5: Write the Answer in a SentenceFrances will receive$4 in change.Step 6: Check Your AnswerHer total spending was $16.If she gave $20, getting back $4 makes sense.The answer is correct.Example 4:Comparing Payment OptionsProblem:Sarah can buy a television for:•$275 cash•OR•$100 down payment plus ten monthly payments of $30How much money can Sarah save by paying cash?

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Study GuideStep 1: Understand the QuestionWe need to find how muchmorethe payment plan costs compared to paying cash.Step 2: Identify Important InformationCash price = $275Payment plan:•$100 down payment•10 payments of $30Step 3: Set Up the MathFirst find the total cost of the payment plan:100 + (10 × 30)Then subtract the cash price:Total payment plan−275Step 4: Solve Carefully10 × 30 = 300100 + 300 = 400Now subtract:400−275 = 125Step 5: Write the Answer in a SentenceSarah can save$125by paying cash.

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Study GuideStep 6: Check Your AnswerThe payment plan costs $400.The cash price is $275.The difference is $125.The answer is reasonable.Example 5:Buying ApplesProblem:Apples cost $3.25 per dozen. How many apples can Maria buy for $13.00?Step 1: Understand the QuestionWe need to find how manyapplesMaria can buy with $13.Step 2: Identify Important Information•$3.25 per dozen•$13.00 to spend(Remember: 1 dozen = 12 apples.)Step 3: Set Up the MathFirst, figure out how many dozens she can buy:13 ÷ 3.25 = number of dozensThen convert dozens into apples.Step 4: Solve Carefully13 ÷ 3.25 = 4So Maria can buy4 dozenapples.Now convert to apples:4 × 12 = 48

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Study GuideStep 5: Write the Answer in a SentenceMaria can buy48 applesfor $13.00.Step 6: Check Your AnswerIf one dozen (12 apples) costs about $3, then $12 would buy about 4 dozen.So 4 dozen (48 apples) for $13 makes sense.The answer is reasonable.Example 6:Finding a PercentageProblem:Sequoia Junior High School has 2,000 students. If 30% of the students are seventh graders, howmany seventh graders are there?Step 1: Understand the QuestionWe need to find30% of 2,000 students.Step 2: Identify Important Information•Total students = 2,000•30% are seventh gradersStep 3: Set Up the MathTo find 30% of 2,000:30% × 2,000Convert 30% to a decimal:30% = 0.30So we calculate:0.30 × 2,000

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Study GuideStep 4: Solve Carefully0.30 × 2,000 = 600Step 5: Write the Answer in a SentenceThere are600 seventh gradersat Sequoia Junior High.Step 6: Check Your Answer10% of 2,000 is 200.30% would be 3 × 200 = 600.The answer is reasonable.Example 7:Free Throw PercentageProblem:Jim Chamberlain makes 75% of his free throws. If he attempts 80 free throws in a season, how manydoes he make?Step 1: Understand the QuestionWe need to find75% of 80.Step 2: Identify Important Information•Makes 75%•Attempts 80 shots

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