Fractions and Mixed Numbers Addition Calculator
Two or More Fractions Addition and Formula
Multiple Fractions Addition is a basic arithmetic operation which combines two or more fractions together. The below formula is the mathematical representation to add any number of fractions with like or unlike denominators, positive and negative fractions or fractions with whole or mixed numbers. Use this fractions and mixed numbers calculator to verify the results of addition between two or more fractions, mixed numbers and whole numbers.
How to Find the Sum of Multiple Fractions
For fractions which are having same or equal denominators, the sum of fractions is equals to the sum of numerators divided by the common denominators, while for fractions with unlike, unequal or different denominators, the sum of fractions is calculated by using the LCM (least common multiple) method. Users may refer the below solved examples with step by step calculation to learn how to find the equivalent fraction by adding two, three or more fraction numbers with same or unlike denominators.
- How to find sum of two, three or more fractions
- How to find sum of multiple fractions and whole numbers
- How to find sum of multiple positive and negative fraction numbers.
Adding Three Fractions with Unlike Denominators
The below solved example with step by step calculation or workout may help users to know how to find the equivalent fraction by adding three fractions (with unlike or different denominators) 1/2, 2/3 and 4/5.
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.
Adding Three Fractions with Same Denominators
The below solved example with step by step calculation or workout may help users to know how to find the equivalent fraction by adding three fractions (with same or equal denominators) 5/9, 7/9 and 4/9.
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.
Adding Multiple Fractions and Whole Numbers
The below solved example with step by step calculation may help users to know how to find the equivalent fraction by adding multiple fractions (with unlike or different denominators) and whole numbers.
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.
Adding Multiple Positive and Negative Fractions
The below solved example with step by step calculation may help users to know how to find the equivalent fraction by adding multiple positive and negative fractions (with unlike or different denominators).
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.
Two or More Fractions and Mixed Numbers Addition
The below solved example for addition between two or more fractions, mixed numbers and 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 adding multiple fractions, mixed and whole numbers 1/2, 1/3, 1/4, 6, 7(1/5), 8(1/6) and 1/7.
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 5 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.
