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    Multiple Fractions Average


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    Average of Fractions & Mixed Numbers Calculator

    getcalc.com's Fractions & Mixed Numbers Average calculator is an online basic math function tool to find an equivalent fraction for the average between two or more fractions with same or different (equal or unlike) denominators, positive or negative fractions, regular or irregular fractions, mixed numbers and whole numbers. This calculator also featured to generate the complete work with steps for any given valid input values to assist elementary or grade school students to solve the fractions average worksheet or homework problems effectively. Thus, users can generate the step by step calculation for the corresponding input values or verify the similar calculation results by using this fractions & mixed numbers average calculator.

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    Multiple Fractions Average & Formula

    Average of Multiple Fractions is a basic arithmetic operation used to find the average between two or more fractions with same or different (equal or unlike) denominators, positive or negative fractions, regular or irregular fractions, mixed numbers and whole numbers. The below formula is the mathematical representation for average of multiple fractions with like or unlike denominators, positive or negative fractions or mixed or whole numbers.

    average of multiple fractions
    Formula to find the average of multiple positive & negative fractions with like & unlike denominators

    How to Find the Average of Two or More Fractions

    The average of fractions is the sum of all fractions divided by the count of total number of fractional numbers. Any whole number in the group of fractions considered as a fraction with denominator 1. For fractions with same or equal denominators, the sum is the simplified fraction of sum of numerators divided by the common denominators, whereas, for fractions with unlike, unequal or different denominators, the LCM (least common multiple) of all denominators must be multiplied with both numerators & denominators of each fractions to bring the common denominator to perform the addition between them. By using this tool & associated information, users may refer the below solved examples with step by step calculation to learn how to find the average of two, three or more fraction numbers with same or different denominators, or the average of regular, irregular, positive or negative fractions and whole numbers. user may found the answers for the following queries

    Average of Three Fractions with Different Denominators

    The below solved example with step by step calculation or workout may help users to learn how to find the average of three fractions with unlike, unequal or different denominators.
    Problem
    Find the average of fractions 1/2, 1/3 & 1/4.

    Step by step workout
    step 1 Address formula, input parameters & values.
    Input parameters & values:
    1/2, 1/3 , 1/4
    Total count = 3
    (1/2 + 1/3 + 1/4)/3 = ?

    step 2 To find the sum for fractions with different denominators, find the LCM (least common multiple) for all denominators. 12 is the LCM for 2, 3 and 4.

    step 3 Multiply LCM 12 with each numerators & denominators
    = (1 x 12)/(2 x 12) + (1 x 12)/(3 x 12) + (1 x 12)/(4 x 12)

    step 4 Simplify the above expression to bring same denominators for all fractions.
    = 6/12 +4/12+3/12
    = (6 + 4 + 3)/12

    step 5 Add all numerators and rewrite it in a single form.
    = 13/12
    1/2+1/3+1/4= 13/12

    step 6 Divide the sum by total count of fractions.
    (1/2 + 1/3 + 1/4)/3 = (13/12)/3

    Thus, 13/12is the average of three fractions 1/2, 1/3 & 1/4.

    Average of Three Fractions with Same Denominators

    The below solved example with step by step calculation or workout may help users to learn how to find the average of three fractions with same, equal or common denominators.
    Problem
    Find the average of fractions 5/9, 6/9 & 7/9.
    Step by step workout

    step 1 Address formula, input parameters & values.
    Input parameters & values:
    5/9,6/9,7/9
    Total count = 3
    (5/9 + 6/9 + 7/9)/3 = ?

    step 2 Find the sum of all fractions.
    (5 + 6 + 7)/9=18/9
    =18/9

    step 3 Divide the sum by total count of fractions & simplify
    = (18/9)/3
    (5/9 + 6/9 + 7/9)/3 = 2/3 in fraction form
    (5/9 + 6/9 + 7/9)/3 = 0.66 in decimal form

    Thus, 2/3 or 0.66 is the average of three fractions 5/9, 6/9 & 7/9.

    Average of Multiple Fractions & Whole Numbers

    The below solved example with step by step workout may help users to learn how to find the average of multiple regular or irregular fractions with like or different denominators and whole numbers.
    Problem
    Find the average of fractions & whole numbers 2/3, 3/4, 6, 4/5, 3, 5/6 & 8/9.

    Step by step workout
    step 1 Address formula, input parameters & values.
    Input parameters & values:
    2/3,3/4,6,4/5, 3 ,5/6,8/9
    Total count = 7
    2/3,3/4,6,4/5, 3 ,5/6,8/9 = ?

    step 2 Convert whole numbers to fractions and rewrite as below
    Any whole number or integer is a rational number (quotient of 1), hence the denominators for all whole numbers is 1 and can be written as
    6 =6/1
    3 =3/1

    step 3 Arrange all the numbers as fractions
    2/3+3/4+6/1+4/5+ 3/1+5/6+ 8/9

    step 4 To find the sum for fractions with different denominators, find the LCM (least common multiple) for all denominators. 180 is the LCM for 3, 4, 1, 5, 1, 6 and 9.

    step 5 multiply LCM 180 with each numerators & denominators
    =(2 x 180)/(3 x 180)+(3 x 180)/(4 x 180) +(6 x 180)/(1 x 180)+ (4 x 180)/(5 x 180)+(3 x 180)/(1 x 180)+(5 x 180)/(6 x 180)+(8 x 180)/(9 x 180)

    step 6 simplify the above expression to bring same denominators for all fractions.
    =120/180+135/180+1080/180+144/180+540/180+150/180+160/180
    =(120 + 135 + 1080 + 144 + 540 + 150 + 160)/180

    step 7 add all numerators and rewrite it in a single form.
    =2329/180
    =2/3+3/4+6/1+4/5+ 3/1+5/6+ 8/9=2329/180

    step 8 Divide the sum by total count of fractions.
    (2/3 + 3/4 + 6/1 + 4/5 + 3/1 + 5/6 + 8/9)/7 = (2329/180)/7
    = 2329/1260

    Thus, 2329/1260 is the average of fractions & whole numbers 2/3, 3/4, 6, 4/5, 3, 5/6 & 8/9.

    Average of Multiple Positive & Negative Fractions

    The below solved example with step by step calculation may help users to learn how to find the average of multiple whole numbers, positive & negative fractions (with unlike or different denominators).
    Problem
    Find the average of multiple whole numbers, positive & negative fractions 2/3, 2/4, -2/5, 6, 2/7, -3/9 & 2/9.

    Step by step workout
    step 1 Address formula, input parameters & values.
    Input parameters & values:
    2/3,2/4,-2/5, 6 ,2/7,-3/9
    Total count = 6
    (2/3 + 2/4 + -2/5 + 6 + 2/7 + -3/9)/6 = ?

    step 2 Convert the whole numbers to fractions, if any
    6 = 6/1

    step 3 Arrange all the numbers as fractions.
    2/3+2/4+-2/5+6/1+2/7+-3/9

    step 4 To find the sum for fractions with different denominators, find the LCM (least common multiple) for all denominators. 1260 is the LCM for 3, 4, 5, 1, 7 and 9.

    step 5 Multiply LCM 1260 with each numerators & denominators
    =(2 x 1260)/(3 x 1260)+(2 x 1260)/(4 x 1260)-(2 x 1260)/(5 x 1260)+(6 x 1260)/(1 x 1260)+(2 x 1260)/(7 x 1260)-(3 x 1260)/(9 x 1260)

    step 6 Simplify the above expression to bring same denominators for all fractions.
    =(2 x 420)/(1260)+(2 x 315)/(1260)-(2 x 252)/(1260)+(6 x 1260)/(1260)+(2 x 180)/(1260)-(3 x 150)/(1260)
    =840/1260+ 630/1260- 504/1260 + 7560/1260 + 360/1260 - 450/1260

    step 7add all numerators and rewrite it in a single form.
    =(840 + 630 + 504 + 7560 + 360 + 450)/1260
    =10344/1260
    =862/105
    (2/3 + 2/4 + -2/5 + 6 + 2/7 + -3/9) = 862/105

    step 8 Divide the sum by total count of fractions.
    (2/3 + 3/4 + 6/1 + 4/5 + 3/1 + 5/6 + 8/9)/6 = (862/105)/6
    = (431/105)/3
    =431/315

    Thus, 431/315 is the average of multiple whole numbers, positive & negative fractions 2/3, 2/4, -2/5, 6, 2/7, -3/9 & 2/9.

    Average of Two or More Fractions & Mixed Numbers

    The below solved example for average of two or more fractions, mixed numbers & whole numbers. The fraction numbers include regular, irregular, negative or positive fractions with same or unlike denominators. The below step by step work guides how to find equivalent fraction for the average between multiple fractions, mixed & whole numbers 2/3, 4/5, 6/7, 3(8/9), 6(1/2) & 9. Problem
    Find the average between multiple fractions, mixed & whole numbers 2/3, 4/5, 6/7, 3(8/9), 6(1/2) & 9.

    Step by step workout
    step 1 Address formula, input parameters & values.
    Input parameters & values:
    2/3,4/5,6/7, 3 8/9, 6 1/2, 9
    Total count = 6
    (2/3 + 4/5 + 6/7 + 3(8/9) + 6(1/2) + 9)/6 = ?

    step 2 Convert the whole numbers to fractions, if any
    9 = 9/1

    step 3 Convert the mixed fractions to fractions, if any
    38/9= ((3 x 9) + 8)/9= 35/9
    61/2= ((6 x 2) + 1)/2= 13/2

    step 4 Arrange all the numbers as fractions.
    2/3+4/5+6/7+35/9+13/2+9/1

    step 5 To find the sum for fractions with different denominators, find the LCM (least common multiple) for all denominators. 630 is the LCM for 3, 5, 7, 9, 2 and 1.

    step 6 Multiply LCM 630 with each numerators & denominators
    =(2 x 630)/(3 x 630)+(4 x 630)/(5 x 630)+(6 x 630)/(7 x 630)+(35 x 630)/(9 x 630)+(13 x 630)/(2 x 630)+(9 x 630)/(1 x 630)

    step 7 Simplify the above expression to bring same denominators for all fractions.
    =(2 x 210)/(630)+(4 x 126)/(630)+(6 x 90)/(630)+(35 x 70)/(630)+(13 x 315)/(630)+(9 x 630)/(630)
    =420/630+504/630+54/630+2450/630+4095/630+5670/630

    step 8 Add all numerators and rewrite it in a single form.
    =(420 + 504 + 54 + 2450 + 4095 + 5670)/630
    =13193/630
    (2/3 + 4/5 + 6/7 + 3(8/9) + 6(1/2) + 9) = 13193/630

    step 9 Divide the sum by total count of fractions.
    (2/3 + 4/5 + 6/7 + 3(8/9) + 6(1/2) + 9)/6 = (13193/630)/6
    =13193/3780

    Thus, 13193/3780 is the average of multiple fractions, mixed & whole numbers 2/3, 4/5, 6/7, 3(8/9), 6(1/2) & 9.

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