ACCUPLACER Study Guide For Arithmetic Review

ACCUPLACER Study Guide for Arithmetic Review1. FractionsVocabularyNumerator: The top part of a fraction – tells us how many equal pieces we have.Denominator: The bottom part of the fraction – tells us how many equal pieces are in the whole.Example:We have 3 equal pieces. The whole pie had 4 equal3pieces. So we have of a pie!4Proper Fractions: When the numerator is smaller than the denominatorExamples:137,910,17Improper Fractions: When the numerator is bigger than or equal to the denominatorExamples:32,9411,11Mixed Number: The sum of a whole number and a proper fractionExamples:17123, 49, 82Common Denominator: A number that can be divided evenly by all denominators in theproblemExample:A common denominator of the fractions13 412,34 912,52 13,34,52is 12.3012Note: 24 is also a common denominator of the fractions. In this case, 12 iscalled the least common denominator.Page 1 of 8

Changing Mixed Numbers into Improper Fractions3Example: Change 2 into an improper fraction.41. Multiply the whole number by the denominator of the fraction.2. Add this to the numerator of the fraction.3. This result is the numerator of the improper fraction. The denominator stays the same.1. 2 4 82. 8 3 11113. Answer:4Changing an Improper Fraction Into a Mixed NumberExample: Change143into a mixed number1. Long divide the numerator by the denominator.2. The quotient becomes the whole number and the remainder becomes the numerator of thefraction. The new denominator is the same as that of the original improper fraction.43 141.2.423122Reducing Fractions to Lowest TermsExample: Reduce4864to lowest terms1. Divide both the numerator and denominator by a common factor.2. Repeat until the numerator and denominator have no more common factors.Example:1.2.4864688688 2324 Page 2 of 8

Multiplying Fractions6Example: Multiply1.2. 734Multiply numerators and denominators straight across.Reduce the fraction to lowest terms.61.7182.318428 2829214 Dividing FractionsExample: Divide6 7341. Take the reciprocal of the fraction on the right and change the division sign to a multiplicationsign.2. Follow the rules of multiplication.1.2.67673647 4 3244 3 2124213837 87 117Adding and Subtracting Fractions1. Find a common denominator for all fractions.2. Add/Subtract the numerators of these fractions, keeping the same denominator in your answer.Example 1:2 31.2.23Example 2:3344433844312 812 912 1712931245151220 1 Page 3 of 8255241555420 820 720 820

NOTE: To multiply/divide/add/subtract mixed numbers, you must first change them intoimproper fractions!Example 1:1223Add 3 21. Change both mixed numbers to improper fractions, and find a common denominator.2. Add and reduce1 77 3 211. 3 2 22 368 2 162 8 2 3 263 312 21 16 3712. 3 2 𝑜𝑟 6236666Practice Problems:61.52 32115. 1 3 4 2 2222 432.56.33.6 77.42427 43231 638. Which of the following is not equivalent to 13or 1 151or 8 62.6.43617211or 7 63.7.Page 4 of 8121224. 5 74.1458. e4or 2 5

2. DecimalsAdding and Subtracting DecimalsExample 1 : Add 28.5 2.64 105.3Example 2: Subtract 230.43 25.1To add/subtract decimals, we line up the decimal points, then add/subtractExample 1:Example 2:28.502.64 105.30136.44230.43- 25.10205.33Multiplying DecimalsExample 1: Multiply 1.57 32.1Example 2: Multiply 4.1 .23To multiply decimals, you don’t have to line up the decimals. Just multiply the two numbers as youwould without any decimals. Then count the number of digits to the right of all decimals in the problem.This number is the same as the number of digits to the right of the decimal in your answer!Example 1:1.57X 32.115731404710050.397Example 2:4.1X .23123820.943Dividing a Decimal By a Whole NumberExample: Divide 2.701 73To divide a decimal, put a decimal directly above the position of the decimal in the problem. Divide likenormal filling in any gaps with zeros.03773 2.701- 219511-5110Page 5 of 8

Dividing a Decimal By a DecimalExample: Divide 4.374 .03To divide by a decimal, move the decimal point of the divisor (outside the brackets) to the right until it isno longer needed. Then move the decimal of the dividend (inside the brackets) the same number ofplaces to the right. Now, divide like normal.03 4.374 3 437.4 We moved the decimal 2 places to the right.145.83 437.4-313-1217-1524-240Practice Problems:1.18.1 .042. 97 5.63.123 2.6 9.044.83.0097 124.9 9.0435. 07 .0026.96 .39927.4 27.368.0.2601 99.7.055 5.60087.6.848.02899.8.5Page 6 of 8

3. Word ProblemsA good percentage of accuplacer math problems are word problems. It’s important to know that you’reprobably more likely to see a problem phrased12“You have 3 pizzas. Bill eats 1 4 pizzas and Tom eats 3 of a pizza. How much pizza is left?”than you are to see the same problem worded12“Find 3 1 4 3 . ”Solving word problems just takes a lot of practice, focus, and critical thinking. Many students like to usea list of “key words” to help them translate words into math. Here is a chart of some key words:Addition ( )Subtraction (-)Multiplication ( )Division ( )Equality ( Is equal toAdded toSubtracted fromMultiplyShared equallyamongIs/wasMore thanLess ThanTwicePerYieldsIncreased byDecreased byProductDivided byAmounts toTotalLessDouble/tripleDivided intogivesOf course, these key words won’t help in every problem, so we have to think hard about what eachproblem gives us and what it is asking for. Let’s try some out!Page 7 of 8

1. A 127.42 acre area of rain forest is beginning to be cut down. So far, 82.5 acres have beenremoved. How many acres of this area of rain forest are left?2. Heather is collecting money for a charity bike ride. So far, she’s been given donations of 12.50, 9.25, and 44. 10 of this money goes to fund the event and the rest goes to charity. Howmuch of her collected money will go to charity?3. The number of people that hiked Mt. Evans in 2006 was 2/3 the number of people that hiked MtEvans in 2005. 12,000 people hiked Mt. Evans in 2005. How many people hiked Mt. Evans in2006?4. Chuck gets paid an hourly rate of 7.15/hr. If he works 4.3 hours, how much is he paid?135. Terry purchaces 2 packages of ground beef. One package weighs 2 pounds. The other weighs41 5 pounds. How many pounds of ground beef did Terry buy?56. Marty’s Indian Head penny is made of copper and nickel only. If 32 of the coin is nickel, whatfraction of the coin is copper?Answers:1.2.3.4.127.42 82.5 44.92 𝑎𝑐𝑟𝑒𝑠12.50 9.25 44 10 55.75212000 3 8000 𝑝𝑒𝑜𝑝𝑙𝑒7.15 4.3 30.745 𝑟𝑜𝑢𝑛𝑑𝑠 𝑡𝑜 30.75147935276225. 2 3 1 5 3 5 15 15 15 𝑝𝑜𝑢𝑛𝑑𝑠 or 4 15 𝑝𝑜𝑢𝑛𝑑𝑠6. 1 532 3232 532 2732of the coin is copper.Page 8 of 8

ACCUPLACER Study Guide for Arithmetic Review 1. Fractions Vocabulary Numerator: The top part of a fraction – tells us how many equal pieces we have. Denominator: The bottom part of the fraction – tells us how many equal pieces are in the whole. Example: We have 3 equal pieces. T