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: If same signs, add & keep the sign. If different signs, subtract smaller from larger and give sign of the larger.

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

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: Multiplication of Fractions Division of Fractions If same signs, result is positive. If different signs, result is negative.

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. Definition of Exponents B. Place Value & Base Place value increases moving left of units place, and decreases moving right of 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 average is between the highest and lowest.

15. 1.3 Estimation & Operations B. Operations with Decimals: To add or subtract: line up dec. pts. To multiply: number of dec. places in the product is the sum of the number of dec. places in the factors. To divide: if divisor is whole number, bring decimal pt. up. If divisor is not, 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. 1.3 Decimal Examples 7. 14.22 - 1.761= A.12.459 B.13.459 C.11.459 D.12.261 14.220 -1.761 It is smaller than 14.22 - 1.22=13 It is larger than 14.22 -2=12.22

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

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

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

22. 1.4 Equivalence Examples 1. 0.19= 100 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. 1.4 Equivalence Examples 100 92 A. 0.92 3. B. 0.092 C. 9.2% D. 0.92%

25. 1.4 Order Examples 100~260 smlg B. < sm lg < < 5. 8. A. = C. > B. < A. = 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 256 x 4 = 1024 Thus, positive

27. 1.5 Percents Percent problems Real-world problems with percent R S T U V Method Percent increase or decrease

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

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. B. $380 Find the cost of renting this 1.6 Word Problems 1. A car rents for $180 per A. $280 week plus $0.25 per mile. car for a two week trip of 400 miles for a family of 4. D. $760 C. $460

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

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