Accuplacer Arithmetic Review

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1 Accuplacer Arithmetic Review Hennepin Technical College Placement Testing for Success Page

2 Overview The Arithmetic section of ACCUPLACER contains 7 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 beneficial. No outside calculators are allowed. Expect to see the following 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, and division with decimals. Percent problems, recognition of decimals, fraction and percent equivalencies, 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 a quantity into its fractional parts. Testing Tips Solve problems by utilizing basic arithmetic skills and formulas. Then if advanced mathematical skills are required such as algebra, use those skills next. Use resources provided such as scratch paper or the calculator to solve the problem. DO NOT attempt to solve problems only in your head. For equations, check your answer by substituting the answer back into the original problem. Make an educated guess if you are unsure of the answer. Hennepin Technical College Placement Testing for Success Page

3 Arithmetic Tips Test takers should be familiar with the following detailed list of concepts. For additional practice exercises using these concepts, please utilize the resources listed at the end of this guide. Whole Numbers and Money Rounding whole numbers and dollars and cents Adding (larger numbers, by regrouping, dollars and cents) Subtracting (larger numbers, by regrouping, dollars and cents) Regrouping/borrowing Multiplying (larger numbers, by regrouping, by zeros) Dividing (using long division, remainders, zero as a placeholder, larger numbers) Fractions Like fractions and unlike fractions Adding and subtracting like fractions and unlike fractions Lowest common denominator (LCD) Estimating with mixed numbers Adding and subtracting mixed numbers Subtracting fractions from whole numbers Subtracting mixed numbers by regrouping Multiplying and dividing fractions by fractions Canceling to simplify multiplication Multiplying and dividing fractions by whole numbers or mixed numbers Multiplying mixed numbers by mixed numbers Percents Changing a fraction to a percent Changing a decimal to a percent Changing a percent to a fraction Changing a percent to a decimal Finding the part, percent, and whole Finding percent increase or decrease Finding the original price Understanding simple interest Computing interest for part of a year Comparing/ordering decimal fractions Reading and writing mixed decimals Estimating with mixed decimals Rounding to a chosen place value Adding and subtracting decimals Using zeros as placeholders Decimals Multiplying decimals by whole numbers Multiplying decimals by decimals Multiplying by 0, 00, or,000 Dividing decimals by whole numbers Dividing decimals by decimals Dividing by 0, 00, or,000 Hennepin Technical College Placement Testing for Success Page

4 Practice Questions & Answers Fractions Numerator: tells how many pieces are in part of the whole (number on top) Denominator: tells how many pieces in the whole (number on bottom) Example: = pieces out of are shaded Proper fraction: numerator is smaller less than denominator. Examples: 7 9,, 0 9 Improper fraction: numerator is equal to or larger than denominator. Examples:, Mixed Number: a whole number plus a proper fraction. Examples:,, 0 Common Denominator: a number that is a multiple of each denominator in the problem Example: 9 The number is a multiple of,, and. We call this a common denominator. Since it is the smallest multiple of all the denominators, it is called the least common denominator (LCD). To add these fractions, rewrite them using the LCD. Reducing Fractions to Lowest Terms Example: Step : Find a number that both the numerator and denominator can be divided by evenly. In this example, they both divide evenly by and then by. Step : Check to see whether both the numerator and denominator can be divided again by a number. Stop when there are no more numbers that will divide both the numerator and denominator evenly. Hennepin Technical College Placement Testing for Success Page

5 Changing Mixed Numbers to Improper Fractions Example: Change to an improper fraction. Step : = Step : + = Step : Multiply the denominator by the whole number. Step : Add the result to the numerator. Step : Step : Place the total over the original denominator. Adding and Subtracting Fractions with Different Denominators Example : Add Use LCD of 0 Use LCD of 0 Now add: Step : Find a common denominator for the fractions. Step : Multiply each fraction by a form of to get to the LCD. Step : Now add or subtract numerators and keep the common denominator. Example : 7 Add 9 Use LCD of Use LCD of Now subtract: 7 9 Multiplying Fractions Example: Multiply Step : No need for common denominators when multiplying. Step : Multiply numerators across and multiply denominators across. Step : Reduce to lowest terms. Hennepin Technical College Placement Testing for Success Page

6 Multiplying with Mixed Numbers Example: Multiply and 7 7 Step : Change each mixed number to an improper fraction. Step : Multiply numerators across and multiply denominators across. Step : Reduce to lowest terms by writing as a mixed number. Dividing Fractions Example: Divide Step : Change problem to multiplying by the reciprocal. Step : Multiply numerators across and multiply denominators across. Step : Reduce to lowest terms. Now You Try:. Change to an improper fraction.. Change to a mixed number. Hennepin Technical College Placement Testing for Success Page

7 Now You Try (continued):. Add:. Add:. Subtract: 7 9. Subtract: Multiply:. Multiply: Divide: 0. Divide: Answers: ) ) ) 7) ) 7 ) ) 9 9) 77 9 ) 9 7 0) 7 Hennepin Technical College Placement Testing for Success Page 7

8 Decimals Adding and Subtracting Decimals Example : Add: Step : Line up decimal points vertically. Example : Subtract: 0. 7 Step : Add zeros when.0 needed to the right of the Check: decimal point so each number.7 has the same number of decimal places Step : Then add or subtract Correct! Multiplying Decimals Example: Multiply Step : Multiply the decimal numbers as you would whole numbers. Step : Count the total number of decimal places (numbers to the right of the decimal point) in all decimal numbers. In this example, there are four total decimal places. Step : Since there were total decimal places in the original problem, place the decimal point places from the right in the answer. Dividing a Decimal by a Whole Number Example: Divide Step : Place the decimal point directly above its original position Step : Divide using the same method as dividing whole numbers, 9 making sure to place each digit in the correct position so the decimal point stays in the correct place. 0 Step : Check by multiplying. Hennepin Technical College Placement Testing for Success Page

9 Dividing a Decimal by a Decimal Number Example: Divide Step : Move decimal point in the divisor (number dividing by) to make it a 7. whole number Step : Move decimal point in the dividend (number dividing into) the same number of places as the divisor Step : Follow regular steps for dividing. Step : Check by multiplying. Now You Try:. Multiply:.0.0. Multiply: Add: Add: Subtract: Subtract: Divide: 7.. Divide: Divide: Divide:..0 Answers: ) 0.7 ). ). ).97 ) 0.0 ) ). ) ). 0). Hennepin Technical College Placement Testing for Success Page 9

10 Percents Percents are another way to express part of a whole. With percents, the part is expressed as parts per hundred. For example, 9% means 9 parts of 00. Percents are commonly used to calculate sales discounts or to determine the amount of interest someone will pay on a loan. Changing Decimals to Percents or Percents to Decimals Since percents can be written as a fraction with a 00 for the denominator, one can convert a percent to a decimal by dividing by 00. For example, to convert % to a decimal, drop the % symbol and then divide by 00. The result is % = 0.. From this example, we are reminded that dividing by 00 results in moving the decimal point places left. Likewise, to convert a decimal to a percent, multiply by 00 and add a % symbol. This results in moving the decimal point places right, such as 0.07 = 7%. Examples: 0% =. 0. = 0% 0.9% = = 0.% Converting Fractions to Percent Form Divide the numerator by the denominator of the fraction. The result will be in decimal form. Then convert to a percent using the steps above. 0.7 Alternate Method: Multiply the fraction by 00. Example: Then convert 0.7 = 7% Then convert 0.7 = 7% Percent to Fraction Example: % Step : Write the percent as a fraction with 00 as the denominator. Step : Reduce the fraction to lowest terms. Hennepin Technical College Placement Testing for Success Page 0

11 Percent of a Number Decimal Method: Fraction Method: Example: What is % of $00? Example: What is % of $00? Multiply % 00 Change % to 00 Multiply (0.) 00 Multiply 00 = = Result: $, Result: $, Finding What Percent One Number Is of Another There 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? Example: is what percent of 70? Translate to: 9 = (x)() Translate to: = (x)( 70) Solve for x: 9 x Solve for x: 70x Result: x = Result: x = Convert fraction to decimal 0. 0 = 0% Convert fraction to decimal % Answer: 9 is 0% of. Answer: is about 7% of 70. Finding a Number When a Percent of It is Given Example: 0% of what number is? Example: % of what number is 0? Translate to: 0.0 x = Translate to: 0. x = 0 Solve for x: 0.0x Solve for x: 0.x Result: x = 0 Result: x = Answer: 0% of 0 is. Answer: % of 00 is 0. Hennepin Technical College Placement Testing for Success Page

12 Now You Try:. Write 0. as a percent.. Write as a percent.. Write as a percent.. Write 0. as a percent.. Write. as a percent.. What is % of $,000? 7. 0 is what percent of 00?. is 0 % of what number? Answers: ) % ) 7% ) 0% ).% ) % ) $0 7) % ) 70 Hennepin Technical College Placement Testing for Success Page

Accuplacer Arithmetic Study Guide

Accuplacer Arithmetic Study Guide I. Terms Numerator: which tells how many parts you have (the number on top) Denominator: which tells how many parts in the whole (the number on the bottom) Example: parts