Chapter 2

  prime number  composite number  prime factorization  factor tree  common factor  equivalent fractions  simplest form  multiple  least common multiple  least common denominator  improper fraction  mixed number Words To Know

 2.1 Prime Factorization 2.2 Greatest Common Factor 2.3 Fundamental Fraction Concepts 2.4 Fractions in Simplest Form 2.5 Least Common Multiple 2.6 Comparing and Ordering Fractions 2.7 Mixed Numbers and Improper Fractions Overview

2.1

 A nonzero whole number that divides another nonzero whole number evenly Or A number that divides another without remainders What is a factor? 1)What would the factors of 14 be?

 A number whose only whole number factors are 1 and itself Or A number whose factors are only 1 and itself Define: Prime Number 1)What would the factors of 3 be? 2)What would the factors of 2 be?

 A number that has factors other than 1 and itself Define: Composite Number 1)What would the factors of 10 be? 2)What would the factors of 20 be?

 What is 1? It is neither a prime nor a composite number Something to Ponder

 1)12 2)8 3)15 4)21 5)35 Practice What are the factors of?

 This means writing the number as a product of prime numbers Prime Factorization Write the prime factorization of … 1)6 2)15 3)12

 Find the prime factorization of each Practice

2.2

 The largest number that is a factor of two or more nonzero whole numbers. (GCF) [also can be called greatest common divisor (GCD) ] Greatest Common Factor This will be helpful to know how to do when simplifying fractions.

 Find the Greatest Common Factor by listing all the factors of the numbers. 1.14, , , 27, , , 96 Practice

2.3

 = Part of a Whole Fractions 3434 = Numerator = Denominator Top Number? Bottom Number?

 Numerator = number of objects that are being looked at Denominator = number of total equal parts that make up the Whole What do they mean? Note: the fraction bar means to divide the numerator by the denominator

 N umerator = N orth Easy Way To Remember! 3434 D enominator = D own What you have Whole Amount Divided by

 = one part of the whole Or a fraction where the numerator is one What is a Unit Fraction?

 = a comparison of two quantities What is a Ratio? Examples: Miles per gallon Girls to Boys Write it like a fraction Know the denominator does not have to = the Whole

2.4

 Different fractions that name the same value What are Equivalent Fractions? Examples: === = = The numbers are different but the value is the same!

 Multiply the numerator AND denominator by the same non zero whole number Creating Equivalent Fractions x= 36 Example: They look different but they have the same value

 Three methods  Simplify all fractions  Cross Multiply  Get a common denominator Are they Equivalent?

 Simplify all Fractions = = 2 x 3 5 x 3 = x 5 10 x 5 = x 1 2 x 5 = Reduced to different numbers Not Equivalent

 Cross Multiply = Not Equivalent

 Common Denominators x x= = Not Equivalent

 How do you know if … A fraction is in its simplest form? The numerator and denominator have a greatest common factor of 1.

  Can it be reduced by 2?  Can it be reduced by 3?  Can it be reduced by 5?  Can it be reduced by 7, 11 etc.? Simplifying Fractions

 Reducing by 2 Are both numbers even? Yes No

 Reducing by 2 Divide both top and bottom by ÷ = If answer comes out even repeat this step

 Reducing by Do both the numbers add up to a number divisible by 3? No = = = 5 13 No Can’t be reduced by 3

 Reducing by 3 Do both the numbers add up to a number divisible by 3? No = = = 13 Can’t be reduced by 3 13 No

 Reducing by 5 Do both numbers end in either 5 or 0? Yes No

 Reducing by Divide both top and bottom by ÷ = If answer comes out with a 5 in the top and bottom repeat this step

 Reducing by 7… etc. Divide the top and bottom by ÷ = Can’t be reduced by 7

 Reducing by 7… etc. Divide the top and bottom by ÷ = Can’t be reduced by 7

 Reducing Simplified

 Simplifying Improper Fractions Divide the numerator by the denominator 7919 = x

 Simplifying Improper Fractions The remainder becomes the new numerator 7919 = x

 3 19 Simplifying Improper Fractions The mixed number is 4

 3 19 Check your Answer! Multiply the Whole number by the denominator 4 = x 76 + =79 19 Add the answer to the numerator

 Give 2 equivalent fractions for each: Practice

 Is the fraction in it’s simplest form? Practice

2.5

  Define:  Multiple = the product of a number and any nonzero whole number  Common Multiple = a multiple shared by two or more numbers  Least Common Multiple (LCM) = the smallest of all the common multiples of two or more numbers Least Common Multiple

  Two ways to find them: 1.List the first several multiples of each number and then compare the lists for the common multiples and choose the lowest one. 2.Compare their prime factorization How to find LCM

 Find the LCM of LCM Listing 1.8, 10 8 = 16, 24, 32, 40, 48, 56, 64, 72, = 20, 30, 40, 50, 60, 70, 80 Answer: 40

 Find the LCM of Practice Listing 1.7, , 6 3.6, 8 4.9, , 25

 LCM Prime Factorization Find the LCM of 1.12, = 2 x 2 x 3 16 = 2 x 2 x 2 x 2 Circle the factors the two have in common Write out the factors of both, writing out the ones they have in common only once 2 x 2 x 3 x 2 x 2 = 48 Answer: 48

 Practice Prime Factorization Find the LCM of 1.10, , , , , 9, 15

2.6

 1 10 Sequence Fractions that have the same denominator? The numerator with the highest number is the greatest fraction

 1 10 Sequence So… Is the proper order

 5 24 Sequence Fractions with unlike denominators (and unlike numerators)? Convert them to equivalent fractions with common denominators in order to compare them

 5 24 Sequence To find the least common denominator (LCD) you have to find the least common multiple of the denominators.

 24 Denominators x x x x = = = = 600

 5 Numerators 3 7 9x x x x = = = =

 Sequence Compare: Set in order

 Sequence

 1818 Sequence Fractions with all the same numerator As the denominator gets bigger the fraction gets smaller.

 1818 Sequence Fractions with all the same numerator As the denominator gets bigger the fraction gets smaller.

 Cheat Sheet!

 Compare Fractions: Practice

2.7

 A fraction in which the numerator is less than the denominator. What is a Proper Fraction? 3434 Example:

 A fraction in which the numerator is greater than or equal to the denominator. What is an Improper Fraction? 4444 Examples: 7474

 A whole-number and a fraction What is a Mixed Number? Examples:

 Cheat Sheet!

 Write as a proper fraction: Practice

2.8

 Convert Fractions to Decimals = = = =0.009

 Convert Fractions to Decimals If you can turn the denominator into 10, 100, 1,000 (any power of 10) then it’s simple: = = = x x x = = =

 Convert Fractions to Decimals x 2 = x 25 = = x 5 x 5 = x 2222 = =.06

 Convert Fractions to Decimals What about this? That 3 makes it so you can’t use this method, but there is another way… 7 75 = 7 3 x 5 x 5

 Terminating Decimals Decimals that stop! Notice that these denominators are easily turned into powers of = = =

 Repeating Decimals Decimals that do not stop! The dot dot dot means it goes on forever … … … … = = = =

  a/solving-linear-equations-and- inequalities/conv_rep_decimals/v/coverting -repeating-decimals-to-fractions-1 a/solving-linear-equations-and- inequalities/conv_rep_decimals/v/coverting -repeating-decimals-to-fractions-1

 Writing a Fraction as a Decimal To write a fraction as a decimal, divide the numerator by the denominator

 Convert Fractions to Decimals So let’s address these kinds of fractions x 5 x 5 = 7 75 = … =

 Convert Fractions to Decimals =.1818… =.18

 Convert Decimals to Fractions Remember to Simplify! = ÷ =

 Convert Decimals to Fractions =÷=

 Convert Decimals to Fractions You can check your answer by… =÷ = 13 ÷ 40=.325

 Practice

 Practice

 Practice

 Practice