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1 Math 090 Exam 1 Review- Chapter 1, 2.2 & 2.3 Section 1.1 Whole Numbers: Writing, Rounding, and Inequalities Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 Natural numbers (counting numbers): 1, 2, 3, 4, 5, and so on Whole numbers: 0, 1, 2, 3, 4, 5, 6, and so on. Place value notation: numbers larger than 9 are written in place value notation by writing the digits in positions having standard place value Less than symbol < Greater than symbol > Round – to give a number an approximate value by rounding to an indicated place. Name the place value of the indicated digit in the number 15,287,654 1. the 1 2. the 6 Write the word name for: 3. 23, 001 4. 5, 408, 325 Write the place value notation for: 5. Thirty-five thousand, four hundred six 6. Twelve million, seventy-six thousand, five Compare the numbers using < or > 7. 6507____6570 8. 1410____1140 2 Round to the indicated place value: 9. Round 985,237 to the ten thousand’s place 10. Round 3, 999 to the hundred’s place Section 1.2 Adding and Subtracting Whole Numbers Addends - the numbers that are added Sum - the answer to an addition exercise Difference - the answer in a subtraction exercise Term - numbers or variables that are added. Ex. In the expression 3 + 4, 3 and 4 are both terms. Properties of Addition: Commutative Property of Addition: a + b = b + a Associative Property of Addition: (a + b) + c = a + (b + c) ** Note that the commutative and associative properties do not apply to subtraction. Find the sum of: 11. 65, 4,432 and 908, 324 12. 35, 532, 6,859 and 3,001 Subtract (Find the difference of): 13. 36,123 and 5,987 14. 598,225 and 16, 549 3 Section 2.2 Perimeter Polygon – any closed figure whose sides are line segments Perimeter – the distance around the outside of a polygon. Find the perimeter: (Include proper unit values.) 15. Perimeter of a rectangle = 2(length) + 2(width) 16 cm 9 cm 16. 14 in. 12 in. Section 1.3 Multiplying and Dividing Whole Numbers Factors – the numbers being multiplied in a multiplication exercise. Product – the answer to a multiplication exercise. Ex. In the equation 4 5 = 20 4 and 5 are the factors, and 20 is the product. Properties of Multiplication: Commutative Property of Multiplication: a b b a Associative Property of Multiplication: a (b c) (a b) c Distributive Property: a (b c) a b a c Multiplication Property of Zero: a 0 0 a 0 Multiplication Property of One: a 1 1 a a **Note that the commutative and associate properties do not apply to division. Dividend – the number being divided Divisor - the number we are dividing by Quotient – the answer to a division exercise 4 Remember: 0 0 any number any number is undefined 0 Multiply (or Find the product of): 17. 435 169 = 18. 925 728 = Distribute: 19. 5 (34 + 26) = 20. 13 (16 + 20) = Divide (or Find the quotient of): 21. 5,688 18 = 22. 55, 269 = 13 23. What is the remainder of 200 divided by 10? 5 Match the letter of the property that was used with the corresponding equation. 24. 4 1 = 4 __________________________ A. Associative 25. 2 + 9 = 9 + 2______________________ ___ B. Commutative 26. 3(2 + 1) = 6 + 3_______________________ C. Distributive 27. 3 6 7 3 6 7 ___________________ D. Multiplicative Identity Section 2.3 Area Area – a measure of surface (measured in square units) Base – the side of a geometric figure that is parallel to the horizon Altitude or Height – the perpendicular distance from the base to the highest point of the figure Formulas: Area of a rectangle = length width Area of a triangle = base height 2 A l w A bh 2 Find the area of the following figures: (Include proper unit values.) 28. Area of a rectangle = length width 15 ft 6 ft 29. Area of a triangle = 6 cm 10 cm base height 2 6 Section 1.4 Whole Number exponents and Powers of Ten Base – a number used as a repeated factor Exponent – indicates the number of times the base is used as factor Ex. With 53 5 is the base and 3 is the exponent Properties of Exponents: 1. If 1 is used as an exponent, the value is equal to the base. x1 x 2. If 0 is used as an exponent, the value is 1 (unless the base is also 0). x 0 1 Evaluate: 30. 53 31. 500 Multiply as indicated: 32. 34 105 33. 356 107 Divide as indicated: 34. 3, 256,000 103 35. 55,879,000,000 10 4 Section 1.5 Operations with Exponents Rules of Exponents: 1. To multiply powers with the same base, add the exponents and keep the common base. Ex. x a x b x a b 2. To divide powers with the same base, subtract the exponents and keep the common base. Ex. xa x a b xb 3. To raise a power to a power, multiply the exponents. Ex. x a b x ab 4. To raise a product to a power, raise each factor to the power. Ex. x y a xa y a 5. As covered in section 1.4, any number to the power of 0 = 1. 0 Ex. x 1 7 Use the rules of exponents to simplify, but DO NOT EVALUATE! 36. 154 1510 157 37. 615 69 38. 5 7 39. 40. 4 5 3 85 87 83 87 63 62 4 6 65 41. 40 45 42. 58 54 36 53 32 Section 1.6 Order of Operations and Average To simplify an expression with more than one operation follow these steps: Step 1: Parentheses Step 2 : Exponents Step 3: Multiply and Divide – do only multiplication and division as they appear from left to right Step 4: Add and Subtract - do addition and subtraction as they appear from left to right. Story Problem Review: 1. Read the problem 2. Determine which math function to use 3. Set up the equation 4. Solve and label your answer 5. Reread the problem to make sure that you have answered the question. 8 Evaluate: 43. 34 3 10 2 6 44. 4 6 2 8 3 16 2 45. 13 13 33 6 13 0 Find the average of: 46. 23, 15, 22 47. 56, 27, 9, 28 Story Problems: 48. Christie took four tests in her math class. She scored a 95 on the first and the third test, a 79 on the second test, and an 87 on the fourth test. What was her average score? 49. Ben went out jogging. It took him 7 minutes to run 2 laps. How long would it take him to run 22 laps? 9 Answers to 090 Exam 1 Review 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. ten million’s place hundred’s place Twenty-three thousand, one Five million, four hundred eight thousand, three hundred twenty-five 35,406 12,076,005 < > 990,000 4,000 912,821 10,427 30,136 581,676 50 centimeters 52 inches 73,515 673,400 300 468 316 4251 R 6 0 D B C A 90 square feet 30 square centimeters 125 1 3,400,000 3,560,000,000 3,256 5,587,900 36. 1521 37. 66 12 15 38. 5 7 2 39. 8 5 40. 6 41. 45 42. 59 34 43. 43 44. 64 45. 22 46. 20 47. 30 48. Christie’s average score was an 89. 49. It would take Ben 77 minutes to run 22 laps.