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ARITHMETIC

ARITHMETIC. CHAPTER 1. ARITHMETIC. 1.1 Operations with Rational Numbers 1.2 Exponents, Base & Decimals 1.3 Estimation & Decimal Operations 1.4 Equivalence, Order & Sequences 1.5 Percents 1.6 Word Problems. 1.1 Rational Numbers. Types of Numbers:

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ARITHMETIC

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  1. ARITHMETIC CHAPTER 1

  2. ARITHMETIC 1.1 Operations with Rational Numbers 1.2 Exponents, Base & Decimals 1.3 Estimation & Decimal Operations 1.4 Equivalence, Order & Sequences 1.5 Percents 1.6 Word Problems

  3. 1.1 Rational Numbers Types of Numbers: natural, whole, integers, rational, prime, composite, fractions, mixed Addition Sign Rules: Ifsame signs,add&keep the sign. Ifdifferent signs,subtractsmaller from largerand givesign of the larger.

  4. Rational Numbers Addition continued Change mixed numbers to fractions. Find Least Common Denominators

  5. 1.1 Adding & Subtracting 1. Remember to find common denominators first. Did you forget the 2

  6. 1.1 Adding & Subtracting 3. It is subtraction! Subtract smaller from larger and give same sign as larger. (Thus result is negative) We need to get 4/4 from 2: 2 = 1 and 4/4

  7. 1.1 Adding & Subtracting 4. First let us change the -(-1) to a +1 Remember: bigger minus smaller, sign bigger! (result must be positive)

  8. 1.1 Multiplying & Dividing Multiplication & Division Rules of Signed Numbers: Ifsame signs, result ispositive. Ifdifferent signs, result isnegative. Multiplication of Fractions Division of Fractions

  9. 1.1 Multiplication & Division 2 5. 1

  10. 1.1 Multiplication & Division 7. Same signs means positive result!! Remember to invert the second fraction!

  11. 1.2 Exponent; Base; Decimal A. Definitionof Exponents B. Place Value & Base Place valueincreases moving leftof units place, anddecreases moving rightof units place.

  12. 1.2 Examples 1.

  13. 1.2 Examples 5. Select the place value associated with the underlined digit 83,584.02

  14. 1.3 Estimation & Operations A. Estimating Sums, Averages or Products: An estimate of the averageisbetweenthe highestandlowest.

  15. 1.3 Estimation & Operations B. Operations with Decimals: Toadd or subtract:line updec. pts. Tomultiply:number of dec. places in the product is thesumof the number of dec.places in the factors. Todivide:if divisor iswhole number,bring decimal pt. up. If divisor isnot, move decimal point as needed.

  16. 1.3 Estimation Examples 1. If a unit of water costs $1.82 and 40.435 units were used, which is a reasonable estimate? (Water is sold…) A. $80,000 B. $800 C. $8000 D.$80

  17. 1.3 Estimation Examples 4. 500 students took an algebra test. All scored less than 92 but more than 63. Which of the following could be a reasonable estimate of the avg. score? A. 96 B. 63 C. 71 D. 60

  18. 14.220 -1.761 1.3 Decimal Examples 7. 14.22 - 1.761= It is smaller than 14.22 - 1.22=13 A.12.459 B.13.459 It is larger than 14.22 -2=12.22 C.11.459 D.12.261

  19. 1.3 Decimal Examples 10. 3.43 x 2.8 A. 0.9604 Estimate 3 x 3 = 9 B. 8.504 Larger than 3 x 2.8 = 8.24 C. 7.1344 D. 9.604

  20. 1.3 Decimal Examples 735 12. A. 735 Dividing by a number between 0 and 1 will cause the result to be larger than original number B. 73.5 C. 7.35 D. 0.0735

  21. 1.4 Equivalence; Order; Seq. Rational numbers can be written as fractions, mixed numbers, dec. or % Tocomparetwo rational numbers, express them in the same way Asequence of numbersis arranged according to some law. Look for the pattern to find the next number.

  22. 19 100 1.4 Equivalence Examples 1. 0.19= % 0.19 is not greater than 1 % “means divided by 100” 19/100 %=0.19/100=0.0019

  23. 1.4 Equivalence Examples 2. 350%= A. 0.350 B. 3.50 C. 350.0 D. 3500

  24. 92 100 1.4 Equivalence Examples 3. A. 0.92 B. 0.092 C. 9.2% D. 0.92%

  25. 1.4 Order Examples 100 ~260 A. = 5. B. < sm lg < C. > < 8. sm lg A. = B. < C. >

  26. 1.4 Sequence Examples 10. Identify the missing term in the following geometric progression PATTERN: Multiply each denom. by 4 to get the next Signs alternate Thus,positive 256 x 4 = 1024

  27. 1.5 Percents Percentincreaseordecrease Percentproblems Real-worldproblems with percent R S T U VMethod

  28. 1.5 Percent Examples 1. If 30 is decreased to 6, %decrease? 4 5 p = 80 5p = 400 A. 8% B. 24% C. 20% D. 80%

  29. 1.5 Percent Examples 5. What is 120% of 30? 10x = 360 x = 36 A. 0.25 B. 25 C. 36 D. 3.6

  30. 1.6 Word Problems • A car rents for $180 per week plus $0.25 per mile. Find the cost of renting this car for a two week trip of 400 miles for a family of 4. D. $760 A. $280 B. $380 C. $460

  31. 1.6 Word Problems 6. Find the smallest positive multiple of 6 which leaves a remainder of 6 when divided by 10 and a remainder of 8 when divided by 14. B. 18 A. 36 D. 53 C. 48

  32. REMEMBER MATH IS FUN AND … YOU CAN DO IT

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