Accuplacer Arithmetic Review - Hennepin Tech
AccuplacerArithmeticReviewHennepin Technical CollegePlacement Testing for SuccessPage 1
OverviewThe Arithmetic section of ACCUPLACER contains 17 multiple choice questions that measureyour ability to complete basic arithmetic operations and to solve problems that testfundamental arithmetic concepts. A calculator is provided by the computer on questionswhere its use would be beneficial. No outside calculators are allowed. Expect to see thefollowing concepts covered on this portion of the test: Operations with whole numbers and fractions such as addition, subtraction, multiplication,division, recognizing equivalent fractions and mixed numbers, and estimating. Operations with decimals and percent, including addition, subtraction, multiplication, anddivision with decimals. Percent problems, recognition of decimals, fraction and percentequivalencies, and problems involving estimation are also given. Problems that involve applications and problem solving are also covered, including rate,percent, and measurement problems, simple geometry problems, and distribution of aquantity into its fractional parts.Testing Tips Solve problems by utilizing basic arithmetic skills and formulas. Then if advancedmathematical skills are required such as algebra, use those skills next. Use resources provided such as scratch paper or the calculator to solve the problem. DONOT attempt to solve problems only in your head. For equations, check your answer by substituting the answer back into the originalproblem. Make an educated guess if you are unsure of the answer.Hennepin Technical CollegePlacement Testing for SuccessPage 2
Arithmetic TipsTest takers should be familiar with the following detailed list of concepts. For additionalpractice exercises using these concepts, please utilize the resources listed at the end of thisguide.Whole Numbers and Money Rounding whole numbers and dollars andcentsAdding (larger numbers, by regrouping,dollars and cents)Subtracting (larger numbers, byregrouping, dollars and cents) Regrouping/borrowingMultiplying (larger numbers, byregrouping, by zeros)Dividing (using long division, remainders,zero as a placeholder, larger numbers)Fractions Like fractions and unlike fractionsAdding and subtracting like fractions andunlike fractionsLowest common denominator (LCD)Estimating with mixed numbersAdding and subtracting mixed numbersSubtracting fractions from whole numbers Subtracting mixed numbers by regroupingMultiplying and dividing fractions byfractionsCanceling to simplify multiplicationMultiplying and dividing fractions bywhole numbers or mixed numbersMultiplying mixed numbers by mixednumbersPercents Changing a fraction to a percentChanging a decimal to a percentChanging a percent to a fractionChanging a percent to a decimalFinding the part, percent, and whole Finding percent increase or decreaseFinding the original priceUnderstanding simple interestComputing interest for part of a yearDecimals Comparing/ordering decimal fractionsReading and writing mixed decimalsEstimating with mixed decimalsRounding to a chosen place valueAdding and subtracting decimalsUsing zeros as placeholdersHennepin Technical College Multiplying decimals by whole numbersMultiplying decimals by decimalsMultiplying by 10, 100, or 1,000Dividing decimals by whole numbersDividing decimals by decimalsDividing by 10, 100, or 1,000Placement Testing for SuccessPage 3
Practice Questions & AnswersFractionsNumerator: tells how many pieces are in part of the whole (number on top)Denominator: tells how many pieces in the whole (number on bottom)3 3 pieces out of 4 are shaded4Example:Proper fraction: numerator is smaller less than denominator. Examples:1 7 9,,3 10 19Improper fraction: numerator is equal to or larger than denominator. Examples:3 8,2 8213Mixed Number: a whole number plus a proper fraction. Examples: 1 , 2 , 10524Common Denominator: a number that is a multiple of each denominator in the problemExample:3 2 1 4 3 2986 2311 112 12 12 1212The number 12 is a multiple of 4, 3, and 2. We call this acommon denominator. Since it is the smallest multiple of all thedenominators, it is called the least common denominator (LCD).To add these fractions, rewrite them using the LCD.Reducing Fractions to Lowest TermsExample:4848 8 6 6464 8 866 2 3 88 2 4Hennepin Technical CollegeStep 1: Find a number that both the numerator anddenominator can be divided by evenly. In this example, theyboth divide evenly by 8 and then by 2.Step 2: Check to see whether both the numerator anddenominator can be divided again by a number. Stop when thereare no more numbers that will divide both the numerator anddenominator evenly.Placement Testing for SuccessPage 4
Changing Mixed Numbers to Improper FractionsExample: Change 23to an improper fraction.4Step 1: 2 4 8Step 1: Multiply the denominator by the whole number.Step 2: 8 3 11Step 2: Add the result to the numerator.Step 3: Place the total over the original denominator.114Step 3:Adding and Subtracting Fractions with Different DenominatorsExample 1:2 1Add 5 4Use LCD of 202 4 8 5 4 20Use LCD of 201 5 5 4 5 20Now add:85 13 20 20 20Example 2:Step 1: Find a commondenominator for the fractions.7 1Add 15 9Step 2: Multiply eachUse LCD of 45fraction by a form of 1 to getto the LCD.Step 3: Now add or subtractnumerators and keep thecommon denominator.7 3 21 15 3 45Use LCD of 451 5 5 9 5 45Now subtract:21 5 16 45 45 45Multiplying FractionsExample: Multiply3 5 4 63 5 15 4 6 2415 3 5 24 3 8Hennepin Technical CollegeStep 1: No need for common denominators when multiplying.Step 2: Multiply numerators across and multiply denominatorsacross.Step 3: Reduce to lowest terms.Placement Testing for SuccessPage 5
Multiplying with Mixed Numbers2 2Example: Multiply 2 13 522 72 8and 1 5 53 38 7 56 3 5 155611 31515Step 1: Change each mixed number to an improper fraction.Step 2: Multiply numerators across and multiply denominatorsacross.Step 3: Reduce to lowest terms by writing as a mixed number.Dividing FractionsExample: Divide1 1 4 21 11 2 4 24 11 2 2 4 1 42 2 1 4 2 2Step 1: Change problem to multiplying by the reciprocal.Step 2: Multiply numerators across and multiply denominatorsacross.Step 3: Reduce to lowest terms.Now You Try:1. Change 41to an improper fraction.6Hennepin Technical College2. Change42to a mixed number.16Placement Testing for SuccessPage 6
Now You Try (continued):323. Add: 5 2535. Subtract: 9124. Add: 5 323111 2132736. Subtract: 10 2871 57. Multiply: 3 7 99. Divide:Answers:378. Multiply: 3 2796 1411256256) 8561)Hennepin Technical College4510. Divide: 3 55658477) 1632) 2415118) 9213) 81639)774) 9Placement Testing for Success92611410)1755) 7Page 7
DecimalsAdding and Subtracting DecimalsExample 1:Step 1: Line up decimalpoints vertically.Add: 28.5 44.47 3075.6Example 2:Subtract: 380.53 – 75Step 2: Add zeros whenneeded to the right of thedecimal point so each numberhas the same number ofdecimal places.28.5044.47 3075.603148.57Step 3: Then add orsubtract.Check:380.53– 75.00305.53305.53 75.00380.53Correct!Multiplying DecimalsExample: Multiply 1.89 5.03Step 1: Multiply the decimal numbers as you would wholenumbers.1.89 5.03Step 2: Count the total number of decimal places (numbers to theright of the decimal point) in all decimal numbers. In this example,there are four total decimal places.567 945009.5067Step 3: Since there were 4 total decimal places in the originalproblem, place the decimal point 4 places from the right in theanswer.Dividing a Decimal by a Whole NumberExample: Divide 2.701 730.03773 2.701219511– 5110Step 1: Place the decimal point directly above its original position.Step 2: Divide using the same method as dividing whole numbers,making sure to place each digit in the correct position so the decimalpoint stays in the correct place.Step 3: Check by multiplying.Hennepin Technical CollegePlacement Testing for SuccessPage 8
Dividing a Decimal by a Decimal NumberExample: Divide 4.374 0.03Step 1: Move decimal point in the divisor (number dividing by) to make it awhole number.0.03 3145.83 437.43131217152424Step 2: Move decimal point in the dividend (number dividing into) thesame number of places as the divisor.4.374 437.4Step 3: Follow regular steps for dividing.Step 4: Check by multiplying.0Now You Try:1. Multiply: 18.1 0.042. Multiply: 0.97 5.63. Add:4. Add: 83.0097 124.9 9.043123 2.6 9.045. Subtract: 0.07 – 0.0026. Subtract: 96 – 0.39927. Divide: 27.36 48. Divide: 0.2601 99. Divide: 7.055 0.8310. Divide: 4.466 2.03Answers:1) 0.7246) 95.6008Hennepin Technical College2) 5.4327) 6.843) 134.648) 0.02894) 216.95279) 8.5Placement Testing for Success5) 0.06810) 2.2Page 9
PercentsPercents are another way to express part of a whole. With percents, the part is expressed asparts per hundred. For example, 89% means 89 parts of 100. Percents are commonly used tocalculate sales discounts or to determine the amount of interest someone will pay on a loan.Changing Decimals to Percents or Percents to DecimalsSince percents can be written as a fraction with a 100 for the denominator, one can convert apercent to a decimal by dividing by 100. For example, to convert 35% to a decimal, drop the %symbol and then divide 35 by 100. The result is 35% 0.35. From this example, we arereminded that dividing by 100 results in moving the decimal point 2 places left.Likewise, to convert a decimal to a percent, multiply by 100 and add a % symbol. This results inmoving the decimal point 2 places right, such as 0.07 7%.Examples:30% .30.9% .0090.6 60%0.002 0.2%Converting Fractions to Percent FormDivide the numerator by the denominator of the fraction. The result will be in decimal form.Then convert to a percent using the steps above.Example:340.754 3.002820200Then convert 0.75 75%Alternate Method: Multiply the fraction by 100.3 100 300 0.754 14Then convert 0.75 75%Percent to FractionExample: 85%8585 5 17 100 100 5 20Hennepin Technical CollegeStep 1: Write the percent as a fraction with 100 as thedenominator.Step 2: Reduce the fraction to lowest terms.Placement Testing for SuccessPage 10
Percent of a NumberDecimal Method:Example: What is 25% of 6500 ?Fraction Method:Example: What is 25% of 6500 ?1Change 25% to416500Multiply 6500 162544Result: 1,625Multiply 25% 6500Multiply (0.25) 6500Result: 1,625Finding What Percent One Number Is of AnotherThere are key words to remember that will help you solve a problem involving percents.The word ‘of’ in the sentence means to multiply and the word ‘is’ means equals.Example: 9 is what percent of 45?Example: 12 is what percent of 70?Translate to: 9 (x)(45)Translate to: 12 (x)( 70)Solve for x:9 45 x 45 45Result:x 99 9 1 45 45 9 5Convert fraction to decimal1 0.20 20%5Answer: 9 is 20% of 45.Solve for x:12 70 x 70 70Result:x 12 12 2 6 70 70 2 35Convert fraction to decimal6 0.17 17%35Answer: 12 is about 17% of 70.Finding a Number When a Percent of It is GivenExample: 20% of what number is 16?Translate to: 0.20 x 16Solve for x:0.20 x16 0.20 0.20Result:x 16 800.20Answer: 20% of 80 is 16.Hennepin Technical CollegeExample: 15% of what number is 30?Translate to: 0.15 x 30Solve for x:0.15 x30 0.15 0.15Result:x 30 2000.15Answer: 15% of 200 is 30.Placement Testing for SuccessPage 11
Now You Try:1. Write 0.12 as a percent.3. Write2. Write2as a percent.53as a percent.44. Write 0.233 as a percent.5. Write 1.15 as a percent.6. What is 11% of 3,000?7. 60 is what percent of 1200?8. 28 is 40 % of what number?Answers:1) 12%5) 115%Hennepin Technical College2) 75%6) 3303) 40%7) 5%4) 23.3%8) 70Placement Testing for SuccessPage 12
The Arithmetic section of ACCUPLACER contains 17 multiple choice questions that measure your ability to complete basic arithmetic operations and to solve problems that test fundamental arithmetic concepts. A calculator is provided by the computer on questions where its use would be benefici
3.2 Arithmetic series: the sum of an arithmetic sequence Analysis, interpretation and prediction where a model is not perfectly arithmetic in real life. 7C 7D Arithmetic Sequence Arithmetic Series 6C 6D Arithmetic sequences Arithmetic series 3.1 3.2 Arithmetic sequence Arithmetic s
the test administers questions based on how you are performing on each question. This allows ACCUPLACER to accurately score and provide a placement based on your result. ACCUPLACER TEST SETUP At Hennepin Technical College, students generally take the following sections: Reading Comprehension, Sentence Skills, Arithmetic, Elementary Algebra .
Sep 17, 2019 · English as a Second Language ACCUPLACER Students who do not speak English or whose second language is English may be given the ACCUPLACER LOEP exam. Based on the student's background, ACCUPLACER will automatically essay as part of the LOEP exam. We encourage all ESL students to review our ACCUPLACER Prep Guide and the required ESL
ACCUPLACER, or you may only be asked to write specific sections of the test. Here is a summary of the various portions of ACCUPLACER: -Arithmetic o Measures a student’s ability to perform basic arithmetic operations and to solve problems involving fundamental arithmetic con
advocacy on behalf of students, educators, and schools. For further information, visit . w.collegeboard.org. ACCUPLACER Arithmetic Sample Questions . The next-generation ACCUPLACER Arithmetic placement test is a computer . adaptive assessment of test-takers' ability for selected mathematics content.
arithmetic sequence finds the nth term of an arithmetic sequence lists down the first few terms of an arithmetic sequence given the general term and vice-versa solves word problems involving arithmetic mean applies the concepts of mean and the nth term of an arithmetic sequence
Arithmetic Series: A series whose terms form an arithmetic sequence. 11 4 Arithmetic Series 7 April 27, 2009 Apr 21 4:18 PM. 11 4 Arithmetic Series 8 April 27, 2009 Apr 21 4:19 PM. 11 4 Arithmetic Series . Homework: page 622 (2 32 even, 37, 40) Title: 11-4 Arithmetic Series Subject: SMART Board Interactive Whiteboard Notes
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