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Basic Math and Pre-Algebra - Graphs - Document preview page 1

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Basic Math and Pre-Algebra - Graphs

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Basic Math and Pre-Algebra - Graphs - Page 1 preview imageStudy GuideBasic Math and Pre-AlgebraGraphs1. Bar Graphs1.1What Is a Bar Graph?Abar graphshows information using rectangular bars.Each bar represents a category (like a city, year, or company). The length or height of the bar showsthe amount.Usually:One side lists thecategories(cities, companies, years).The other side showsnumbers(like totals or amounts).When reading a bar graph, always ask:• What does each bar represent?• What units are being used?• What relationship is the question asking about?Example 1:Comparing CitiesThe bar graph shows thenumber of billboards in each city.The scale increases in increments of 100.From the graph:City W500 billboardsCity Y150 billboardsTo find how many more billboards City W has than City Y:So,City W has about 350 more billboards than City Y.Always estimate carefully using the scale shown.
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Basic Math and Pre-Algebra - Graphs - Page 2 preview imageStudy GuideFigure 1Example 2:Books Sold by PublishersFigure 2
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Basic Math and Pre-Algebra - Graphs - Page 3 preview imageStudy GuideThis bar graph shows thenumber of books sold (in millions)for three publishers from 1990 to1992:Mystery MysteryReference UnlimitedAll SportsEach bar represents one year.Since the values are already inmillions, you do not need to add extra zeros.Question 1How many more books did Mystery Mystery sell than All Sports (total for 19901992)?Mystery Mystery Sales (in millions):1990: 2.51991: 2.51992: 3.4Total:All Sports Sales (in millions):1990: 11991: 2.11992: 3Total:Now subtract:So,Mystery Mystery sold 2.3 million more books than All Sportsover those three years.
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Basic Math and Pre-Algebra - Graphs - Page 4 preview imageStudy GuideQuestion 2Which publisher had the greater percent increase from 1991 to 1992?To find percent increase, use this formula:Mystery Mystery1991: 2.51992: 3.4Change:Percent increase:All Sports1991: 2.11992: 3Change:Percent increase:
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Basic Math and Pre-Algebra - Graphs - Page 5 preview imageStudy GuideNow compare:So,All Sports’ percent increase exceeded Mystery Mystery’s by about 7%.Question 3What caused the 1992 decline in Reference Unlimited's book sales?This cannot be answered from the graph.The graph only shows numbers soldit does not explainwhysales changed.Important rule:Never assume information that is not shown in the graph.Helpful Tips for Reading Bar Graphs• Check the scale carefully.• Estimate only to the level of precision shown.• Do not assume extra information.• Use formulas when percent change is required.• Remember that “in millions” means the numbers are already largeno extra zeros needed.SummaryBar graphs organize data into visual bars, making comparisons easier.From this lesson, you learned:How to compare totals using subtraction.How to calculate percent increase usingHow to avoid assuming information not shown.How to carefully read scales and units.
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Basic Math and Pre-Algebra - Graphs - Page 6 preview imageStudy Guide2. Quiz: Bar Graphs1. QuestionThe maximum number of traffic lights for any city exceeded the minimum number of traffic signals byhow many?Answer Choices458Correct Answer8Why This Is CorrectFrom the graph, identify the city with the greatest number of traffic signals and the city with the fewest.Subtract the smallest value from the largest value.The difference between these two values is8.2. QuestionWhich city had 25% more traffic signals than City C?Answer ChoicesCity ACity BCity D
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Basic Math and Pre-Algebra - Graphs - Page 7 preview imageStudy GuideCorrect AnswerCity DWhy This Is CorrectTo find 25% more than City C, multiply City C’s value by 1.25.The city whose number matches that result isCity D.3. QuestionIn which city is traffic congestion the worst?Answer ChoicesCity BCity Dcannot answer based on the graphCorrect Answercannot answer based on the graphWhy This Is CorrectThe graph only shows thenumber of traffic signals, not the amount of traffic congestion.More traffic lights does not necessarily mean worse congestion.So, this questioncannot be answered from the graph alone.4. QuestionIf City B decreased the number of traffic signals by 1/4, it would have the same number of trafficsignals as which city?
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Basic Math and Pre-Algebra - Graphs - Page 8 preview imageStudy GuideAnswer ChoicesACDCorrect AnswerCWhy This Is CorrectDecreasing City B’s number by 1/4 means multiplying by 3/4 (or 0.75).After calculating, the new value matches the number of traffic signals inCity C.5. QuestionHow does the average number of traffic signals for cities B, C, and D compare with the number oftraffic signals in City A?Answer ChoicesThey are the same number.The average number of traffic signals for cities B, C, and D exceeds the number of trafficsignals in city A by 1.The average number of traffic signals for city A exceeds the number of traffic signals in citiesB, C, and D by 1.Correct AnswerThe average number of traffic signals for cities B, C, and D exceeds the number of traffic signalsin city A by 1.Why This Is CorrectAdd the numbers for cities B, C, and D.Divide by 3 to find the average.Comparing that average with City A shows it is1 greater.
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Basic Math and Pre-Algebra - Graphs - Page 9 preview imageStudy Guide6. QuestionIn 2010, the number of degrees in Science exceeded the number of degrees in Math by how many?Answer Choices330300Correct Answer30Why This Is CorrectLook at the 2010 values for Science and Math.Subtract the Math value from the Science value.The difference is30 degrees.7. QuestionWhich of the following is true about the number of degrees awarded from 2008 to 2009?Answer ChoicesScience and Math increased in numberEnglish and Math increased in numberScience and English increased in numberCorrect AnswerScience and English increased in numberWhy This Is CorrectComparing the 2008 and 2009 bars on the graph shows that Science and English increased, whileMath did not increase during that period.
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Basic Math and Pre-Algebra - Graphs - Page 10 preview imageStudy Guide8. QuestionWhich of the following had the greatest percent change?Answer ChoicesOther from 2008 to 2009Math from 2009 to 2010Science from 2009 to 2010Correct AnswerMath from 2009 to 2010Why This Is CorrectPercent change is calculated by:(Change ÷ Original) × 100Comparing the relative increases shows thatMath from 2009 to 2010had the greatest percentageincrease.9. QuestionBy approximately what percent did the number of English degrees awarded change from 2009 to2010?Answer Choices3%10%15%Correct Answer10%
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