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Need further clarifications Understands the 60 as the LCD but do not understand the 2 x 2 x 3 x 5 Prime Numbers 2 3 5 7 11 13 17 19 23 29 31 37 41 43 Learning Objectives Understand the meaning of fractions Identify the numerator and denominator of fraction Write a fraction to represent the shaded area of a figure Recognize the type of fractions Convert improper fraction to mixed numbers Convert mixed numbers to improper fractions Simply fractions in lowest terms Find equivalent fractions Add and subtract the fractions Multiply and divide fractions and mixed numbers Simplify expressions using the order of operations Compere fractions Solved applied problems involving fractions IDENTIFYING NUMERATORS A fraction is one or more of the equal parts into which a whole is divided or numbers There are two parts of fractions the numerator and the simply a ratio of two denominator with a horizontal or number of equal parts being taken into denominator the numbers of equal parts into slanting line between the two numbers The numerator is the consideration It is written above the numerator The separates the numerator from the denominator and which the whole is divided The fraction line stands out for out of or divided by KINDS OF FRACTIONS than the denominator 1 Proper fraction a fraction in which the numerator is less or of lower degree greater than or equal to the 2 Improper fraction A fraction where the numerator the top number is denominator the bottom number 3 Mixed Numbers consist a whole number and a proper fraction and is used to describe a quantity greater than 1 by the of the mixed number mixed number CONVERTING IMPROPER FRACTIONS TO MIXED NUMBERS To change an improper fraction to a mixed number we divide the numerator denominator The quotient the result of division is the whole number The remainder is the numerator of the fractional part of the To convert a mixed fraction to an improper fraction follow these steps 1 Multiply the whole number part by the fraction s denominator 2 Add that to the numerator 3 Then write the result on top of the denominator Homework Notes Expresses a part of a whole number Fraction Numerator Denominator Top of the fraction equal parts of the whole bottom of the fraction total number of equal parts A proper fraction has a value less than 1 it s numerator is smaller than it s denominator improper fraction it s denominator has a value equal to or greater than 1 it s numerator is equal to or greater than Mixed number The sum of a whole number greater than zero and a proper fraction The horizontal line Indicates division Converting improper fractions to whole or mixed number Step 1 Divide the numerator of the improper fraction by the denominator Step 2 a if you have no remainder the quotient is a whole number is the quotient The remainder is placed over the old denominator as the proper fraction of the mixed number b if you have a remainder the whole number part of the mixed number Converting mixed numbers to improper fractions 1 Multiply the denominator of the fraction by the whole number 2 Add the product from step 1 to the numerator 3 Place the total from step 2 over the denominator Step Approach for finding the greatest common divisor Step 1 Divide the smaller number numerator of the fraction into the larger number denominator 2 Divide the remainder of step 1 into the divisor of Step 2 3 Divide the remainder of step 2 into the divisor of step 2 divisor is the greatest common divisor Continue this division process until the remainder is a 0 which means the last Higher terms to the original Expressing a fraction with a new numerator and denominator that is equivalent 2 9 6 27 Reducing fractions to lowest terms might result in More than one division Greatest common divisor denominator The largest possible number that will divide evenly into both the numerator and denominator except the number 1 Expressing a fraction when no number divides evenly into the numerator and Lowest terms 5 10 1 2 Reducing Fractions to lowest terms by inspection will divide evenly into the numerator and denominator does not change the fraction value 1 By inspection find the largest whole number greatest common divisor that 2 Divide the numerator and denominator by the greatest common divisor Now you have reduced the fraction to its lowest terms since no number except 1 can divide evenly into the numerator and denominator Raising fractions to higher terms when the denominator is known 1 divide the new denominator by the old denominator to get the common number that raises the fraction to higher terms as the new numerator over the new denominator 2 multiply the common number from step 1 by the old numerator and place it Like fractions Proper fractions with the same denominators Unlike fractions Proper fractions with different denominators Common denominator To add two or more fractions denominators must be the same Adding like fractions 1 Add the numerators and place total over the denominator whole number if the total numerator is larger than denominator convert to mixed number 2 If the total of your numerators is the same as your denominator convert to Least common denominator LCD Smallest nonzero whole number into which all denominators will divide evenly Finding lcd by inspection ex 3 7 5 21 7 goes into 21 thus 21 is the LCD to the numerator so 3x3 9 7 becomes 21 because and 3 becomes 9 because 7x3 21 and you do the same Adding unlike fractions 1 find the lcd 2 change each fraction to a like fraction with the LCD 3 add the numerators and place the total over the lcd 4 if necessary reduce the answer to lowest terms Prime number Whole number greater than 1 that is only divisible by itself and 1 1 is not a prime number Using prime numbers to find the LCD Ex 1 3 1 8 1 9 1 12 1 copy the denominators and arrange them in a row 3 8 9 12 2 divide the denominators in step 1 by prime numbers start with the smallest number that will divide into at least 2 of the denominators Bring down any number that is not divisible Keep in mind that the lowest prime number is 2 3 Continue step 2 until no more prime number will divide evenly into at least 2 numbers 3 is now used since 2 can no longer divide evenly into at least 2 numbers 2 3 8 9 12 2 3 4 9 6 3 3 2 9 3 1 2 3 1 Now we have 2 3 8 9 12 2 3 4 9 6 3 3 2 9 3 1 2 3 1 4 To find the LCD multiply all the numbers in the divisors 2 2 3 we used 2 as prime number then 2 then 3 and then in the last row 1 2 3 1 fractions numbers 2x2x3 x 1x2x3x1 72 LCD 5

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