Exponents, Factors, and Fractions. Chapter 3

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1 Exponents, Factors, and Fractions Chapter 3

2 Exponents and Order of Operations Lesson 3-1

3 Terms An exponent tells you how many times a number is used as a factor A base is the number that is multiplied is the base, 5 is the exponent. It means 4 x 4 x 4 x 4 x 4 It does NOT MEAN 4 x 5

4 Simplify Using Order of Operations Simplify 3 4 (7-2) 3 First: Parentheses = Second: Exponents = Third: Multiply = 10,125

5 Simplify Powers with Negatives -5 4 and (-5) 4 are not equivalent means the negative of 5 4, so the base is 5, not = -( ) = -625 But watch out for: here the base is the number in the parentheses (-5) 4 = (-5)(-5)(-5)(-5) = 625

6 Partner Practice Exponents and Order of Operations

7 Scientific Notation Lesson 3-2

8 Definition A number in scientific notation is written as the product of two factors, one greater than or equal to 1 but less than 10, and the other as a power of 10 7,500,000,000,000 = 7.5 x 10 12

9 Example The moon orbits the earth at a distance of 384,000 km. Write the number in scientific notation First: move the decimal point to get a factor greater than 1 but less than ,000. becomes Then: rewrite as 3.84 x 10 5 because I moved the decimal point 5 places

10 From Scientific Notation to Standard Form Mars is 2.3 x 10 8 miles from Earth Write in standard form: Move the decimal point to the right 8 places 230,000,000

11 Think, Pair, Share dc46f73b98/worksheetworks_scientific_nota tion_1.pdf

12 Divisibility Tests Lesson 3-3

13 Definition Facts/Characteristics A whole number is all even numbers are divisible by another if divisible by 2 the remainder is zero Vocabulary Word Divisible 48 4 = 12 Examples 47 4 = 11 r 3 Non-Examples

14 Divisibility of Whole Numbers A whole number is divisible by 2 if it ends in 0, 2, 4, 6 or 8 3 if the sum of its digits is divisible by 3 5 if it ends in 0 or 5 0 if the sum of the digits is divisible by 9 10 if it ends in 0

15 Prime Factorization Lesson 3-4

16 Definition Factors are numbers that are multiplied Facts/Characteristics When divided there is no remainder Vocabulary Word Factor 3 x 4 = = = 2 r2 Examples Non-Examples

17 Definition Facts/Characteristics A whole number numbers that can be greater than 1 with more divided evenly by more than two factors than just 1 and itself Vocabulary Word Composite number 1 x 20 1 x 19 2 x 10 4 x 5 Examples Non-Examples

18 Definition Facts/Characteristics A whole number with The whole numbers 0 exactly two factors, 1 and 1 are neither prime and the number itself nor composite Vocabulary Word Prime number x 19 1 x 20 2 x 10 4 x 5 Examples Non-Examples

19 Prime Factorization What does this mean??? Writing a composite number as a product of prime numbers gives the prime factorization.ok, so what does that mean??? And how do I do it??

20 Method One: Division Ladder Find the prime factorization of 84 Divide 84 by prime numbers starting with 2 and work your way up. 2) 84 2) 42 3) 21 7 Divide 84 by the prime number 2. Work down. The result is 42. Since 42 is even, divide by 2, again. The result is 21. Divide by the prime number 3. The prime factorization of 42 is 2 x 2 x 3 x 7

21 Some things to remember When using division ladders, start by first dividing with the smallest prime number. For even numbers, that divisor will be 2. Keep dividing until you reach a prime number as the quotient.

22 Method Two: Factor Trees Gets us to the same result, just a different way Circle the prime numbers Prime factorization of 84: 2 x 2 x 3 x 7

23 GCF The greatest common factor of two or more numbers is the greatest factor shared by all the numbers. Find the GCF three different ways: Use a list of factors Use a division ladder Use factor trees

24 Simplifying Fractions Lesson 3-5

25 Definition Equivalent fractions are fractions that name the same amount Form equivalent fractions by multiplying the numerator and denominator by the same nonzero number

26 Simplest Form Fractions are in simplest form when the only common factor of the numerator and denominator is 1 Example: 2 is on simplest form since 2 and 3 3 only have the number 1 as a common factor

27 Partner Practice Get the fractions into simplest form Write the Fraction in Simplest Form Fractions Puzzlers Task Cards

28 Comparing and Ordering Fractions Lesson 3-6

29 Least Common Denominator To compare fractions, start with the LCD The Least Common Denominator of two or more fractions is the Least Common Multiple of the denominators Ex: compare 3/4 and 5/6

30 Compare ¾ and 5/6 Step One: Find LCM for 4 and 6 Option 1: Use a List of Multiples Multiples of 4: 4, 8, 12, 16, 20, 24 Multiples of 6: 6, 12, 18, 24, 30, is the least common multiple for 4 and 6

31 Compare ¾ and 5/6 Step Two: Write equivalent fractions using LCM as the common denominator 3/4 = 9/12 5/6 = 10/12 3/4 < 5/6

32 How to Find LCM Find LCM for 8, 10 and 20 Option 2: Use Prime Factorization Prime Factorization for 8 = 2 x 2 x 2 Prime Factorization for 10 = 2 x 5 Prime Factorization for 20 = 2 x 2 x 2 x 5 Circle each different factor: 2 x 2 x 2 x 5 = 40 LCM for 8, 10 and 20 is 40

33 Partner Practice Use either method for practice Find the LCM for each pair What Happens If You Watch TV All Day?

34 Mixed Numbers and Improper Fractions Lesson 3-8

35 Key Terms A proper fraction has a numerator that is less than its denominator: ⅜ An improper fraction has a numerator that is greater than or equal to its denominator: 8 / 5 A mixed number is a number written with both a whole number and a fraction: 2⅔

36 Write Mixed Numbers as Improper Fractions Write 6⅔ as an improper fraction First: Multiply the whole number by the denominator (6 x 3 thirds = 18 thirds) Second: Add the numerator (18 thirds + 2 thirds = 20 thirds) Example: 6⅔ = (6 x 3) + 2 =

37 Write Improper Fractions as Mixed Numbers Write 9 6 as a mixed number First: divide the numerator by the denominator Second: write the remainder as a fraction Third: simplify 1 6) = 1 3/ 6 6 = 1⅟ 2

38 Partner Practice With your partner, convert Mixed Numbers to Improper Fractions Convert Mixed Numbers and Fractions Cryptic Quiz

39 Fractions and Decimals Lesson 3-9

40 Terminating Decimals Write fractions as decimals by dividing the numerator by the denominator. A decimal that stops, or terminates, is a terminating decimal Ex: 5/8 = 5 8 = 0.625

41 Repeating Decimal If when we divide, we discover the same digit or group of digits in the quotient repeats without end, that decimal is a repeating decimal Ex: 3/11 = 3 11 = = 0.27

42 convert Practice

43 Rational Numbers Lesson 3-10

44 Rational Number A rational number is a number that can be written as a quotient of two integers, where the divisor is not 0. Examples: ⅝, 0.46, -6 and 3⅟ 2 All integers are rational numbers as all integers can be written with a denominator of 1

45 Negative Rational Numbers Negative Rational Numbers can be written in three ways 6 = 6 =

46 Compare Negative Rational Numbers Compare -⅟ 2 and - 3 / 4 Option 1: Use a number line. Since - 3 / 4 is farther to the left, it is the smaller number

47 Compare Negative Rational Numbers Compare -⅟ 2 and - 3 / 4 Option 2: make equivalent fractions -⅟ 2 = - 2 / 4 Since - 3 / 4 < - 2 / 4, then - 3 / 4 < -⅟ 2

48 Ordering Rational Numbers Order these numbers from greatest to least ⅟ 4, -0.2, - 2 / 9, 1.1 Step One: convert the fractions to decimals by dividing ⅟ 4 = 0.25 and - 2 / 9 = Now order: -0.22, -0.2, 0.25, 1.1

49 Partner Practice at/ip.pdf

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