Improper and Unlike Fractions Addition Calculator

Adding fractions, whether they have like (equal) or unlike (different) denominators, requires finding a common denominator to combine the numerators. For mixed numbers, convert them to improper fractions first. The least common multiple (LCM) of all denominators is calculated to find the lowest common denominator, then all numerators are adjusted, added, and simplified to their lowest terms. You can use the step-by-step solved examples below to learn how to find the sum of multiple unlike fractions, mixed numbers, and integers.

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

Problem
Find the sum of three fractions with unlike or different denominators such as 1/2, 2/3 and 4/5.

Step by step workout
step 1 Address formula, input values.
Input values:
1/2,2/3,4/5
1/2+2/3+4/5= ?

step 2 For fractions with different denominators, find the LCM (least common multiple) for all denominators. 30 is the LCM for 2, 3 and 5.

step 3 Multiply LCM 30 with each numerators and denominators
=(1 x 30)/(2 x 30)+(2 x 30)/(3 x 30)+(4 x 30)/(5 x 30)

step 4 Simply the above expression to have same denominators for all fractions.
=15/30+20/30+24/30
=(15 + 20 + 24)/30

step 5 Add all numerators and rewrite it in a single form.
=59/30
1/2+2/3+4/5=59/30

59/30 is the equivalent fraction by adding three fractions 1/2, 2/3 and 4/5.

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

Problem
Find the sum of three fractions with same or equal denominators such as 5/9, 7/9 and 4/9.

Step by step workout
step 1 Address formula and input values.
Input values:
The given fractions :
5/9,7/9,4/9
5/9+7/9+4/9= ?

step 2 For same denominators, add all the numerators directly and rewrite the fraction as below
=5/9+7/9+4/9
=(5 + 7 + 4)/9
5/9+7/9+4/9= 16/9

16/9 is the equivalent fraction for adding three fractions with same denominators 5/9, 7/9 and 4/9.

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

Problem
Find the equivalent fraction for adding 1/2, 1, 5/3, 2, 1/4, 2/5 and 3.
Step by step workout
step 1 Address formula and input values.
Input values:
1/2, 1,5/3, 2 ,1/4,2/5 , 3
1/2 + 1 +5/3 + 2 + 1/4 + 2/5 + 3 = ?

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
1 = 1/1
2 = 2/1
3 = 3/1

step 3 Arrange all the numbers as fractions.
1/2+1/1 + 5/3 + 2/1+ 1/4+2/5+3/1

step 4 Find LCM (least common multiple) for all denominators, if all the denominators are not identical to each other.
60 is the LCM for denominators 2, 1, 3, 1, 4, 5 and 1.

step 5 Multiply LCM 60 with all the numerators and denominators of each fractions
(1 x 60)/(2 x 60) +(1 x 60)/(1 x 60) + (5 x 60)/(3 x 60)+(2 x 60)/(1 x 60)+(1 x 60)/(4 x 60)+(2 x 60)/(5 x 60) +(3 x 60)/(1 x 60)

step 6 Simplify and rewrite the above expression to have the common denominators
30/60+60/60+100/60+ 120/60+25/60+24/60+180/60

step 7 Add all the numerators and simplify
=(30 + 60 + 100 + 120 + 25 + 24 + 180)/60
=539/60
1/2+ 1 +5/3 + 2 + 1/4 + 2/5 + 3 =539/60

539/60 is the equivalent fraction for adding multiple fractions and whole numbers such as 1/2, 1, 5/3, 2, 1/4, 2/5 and 3.

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

Problem
Find the equivalent fraction for adding positive and negative fractions 5/6, 1/3, -2/7, 1/6, -4/7 and 4/5.

step 1 Address formula and input values.
Input values:
5/6,1/3,-2/7,1/6,-4/7,4/5
5/6+1/3+-2/7+1/6+-4/7+4/5= ?

step 2 Find the LCM (least common multiple) for all denominators, if all the denominators are not identical to each other.
210 is the LCM for denominators 6, 3, 7, 6, 7, and 5.

step 3 Multiply LCM 210 with all the numerators and denominators of each fractions
(5 x 210)/(6 x 210)+(1 x 210)/(3 x 210)+-(2 x 210)/(7 x 210)+(1 x 210)/(6 x 210)+-(4 x 210)/(4 x 210)+(4 x 210)/(5 x 210)

step 4 Simplify and rewrite above expression to have the common denominators
175/210+70/210-60/210+35/210-210/210+24/210+168/210

step 5 Add all the numerators and simplify
=(175 + 70 - 60 + 35 - 210 + 24 + 168)/210
=202/210
=101/105
5/6+1/3+-2/7+1/6+-4/7+4/5=202/210

202/210 is the equivalent fraction for adding multiple positive and negative fractions 5/6 + 1/3 + (-2/7) + 1/6 + (-4/7) + 4/5.

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

Problem
Find the equivalent fraction for adding multiple fractions, mixed and whole numbers 1/2, 1/3, 1/4, 6, 7(1/5), 8(1/6) and 1/7.
Step by step workout
step 1 Address formula and input values.
Input values:
1/2,1/3,1/4, 6 ,71/5, 8 1/6,1/7
1/2+1/3+1/4 + 6 + 71/5+ 8 1/6 +1/7 = ?

step 2 Convert whole numbers to fractions and rewrite as below
6 = 6/1

step 3 Convert mixed fractions to fractions and rewrite as below
7 1/5= ((7 x 5) + 1)/5= 36/5
8 1/6= ((8 x 6) + 1)/6= 49/6

step 4 Arrange all the numbers as fractions.
1/2+1/3 + 1/4 + 6/1+ 36/5+ 49/6+1/7

step 5 For fractions with different denominators, find the LCM (least common multiple) for all denominators. 420 is the LCM for 2, 3, 4, 1, 5, 6 and 7.

step 6 Multiply LCM 420 with all the numerators and denominators of each fractions
=(1 x 420)/(2 x 420)+(1 x 420)/(3 x 420)+(1 x 420)/(4 x 420)+(6 x 420)/(1 x 420)+(36 x 420)/(5 x 420)+(49 x 420)/(6 x 420)+(1 x 420)/(7 x 420)

step 7 Simplify and rewrite above expression to have the common denominators
=(1 x 210)/420 +(1 x 140)/420+(1 x 105)/420+(6 x 420)/420+(36 x 84)/420+(49 x 70)/420+(1 x 60)/420
=210/420 +140/420+105/420+2520/420+3024/420+3430/420+60/420

step 8 Add all the numerators and simplify
=(210 + 140 + 105 + 2520 + 3024 + 3430 + 60)/420
=9489/420
=3163/140
1/2+1/3+1/4 + 6 + 71/5+ 8 1/6 +1/7 = 3163/140

3163/140 is the equivalent fraction for adding multiple fractions, mixed and whole numbers 1/2 + 1/3 + 1/4 + 6 + 7(1/5) + 8(1/6) + 1/7.

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