Unlike and Improper Fractions Average Calculator

Finding the average (arithmetic mean) of multiple fractions requires summing all the fractions together and then dividing that sum by the total count of fractions. Whole numbers are converted to fractions by placing them over 1, and mixed numbers are converted to improper fractions first. The addition step involves finding a common denominator (using the least common multiple), and the final result is divided by the total number count. You can use the step-by-step solved examples below to learn how to find the average of multiple unlike fractions, mixed numbers, and integers.

The solved example below shows the step-by-step workout for finding the average of three unlike fractions (fractions with different denominators). You can use our unlike fractions average calculator to find the average of any number of like, unlike and improper fractions to generate the step by step workout like the one below.

Problem
Find the average of fractions 1/2, 1/3 and 1/4.

Step by step workout
step 1 Address formula and input values.
Input 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 and 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

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

The solved example below shows the step-by-step workout for finding the average of three like fractions (fractions with equal denominators). You can use this unlike fractions average calculator to find the average of any number of like, unlike, and improper fractions.

Problem
Find the average of fractions 5/9, 6/9 and 7/9.
Step by step workout

step 1 Address formula and input values.
Input 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 and 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

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

The solved example below shows the step-by-step workout for finding the average of multiple unlike fractions with whole numbers. You can use this unlike fractions average calculator to find the average of any number of like, unlike, improper fractions and whole numbers to generate the step by step workout like the below.

Problem
Find the average of fractions and whole numbers 2/3, 3/4, 6, 4/5, 3, 5/6 and 8/9.

Step by step workout
step 1 Address formula and input values.
Input 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 and 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

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

The solved example below shows the step-by-step workout for finding the average of multiple positive and negative unlike fractions. You can use this unlike fractions average calculator to find the average of any number of like and unlike positive and negative fractions to generate the step by step workout below.

Problem
Find the average of multiple whole numbers, positive and negative fractions 2/3, 2/4, -2/5, 6, 2/7, -3/9 and 2/9.

Step by step workout
step 1 Address formula and input values.
Input 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 and 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

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

The solved example below shows how to find the average of a set of mixed numbers, integers, and unlike fractions using the step-by-step common denominator method. You can use this unlike fractions average calculator to find the average of any number of mixed numbers, whole numbers and proper fractions.

Problem
Find the average between multiple fractions, mixed and whole numbers 2/3, 4/5, 6/7, 3(8/9), 6(1/2) and 9.

Step by step workout
step 1 Address formula and input values.
Input 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 and 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

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

Whether you are working with proper, improper, like, or unlike fractions, mixed numbers, or integers, this mixed numbers average calculator, unlike fractions average calculator, and improper fractions average calculator is designed to make finding the average simple and efficient. Enter your math problems in the input field above to instantly compute the simplified average and view detailed step-by-step calculations today!