# Fractions & Mixed Numbers Addition Calculator

**use the mixed numbers directly in the format of X(Y/Z)**; where X is an integer, Y and Z are the numerator and denominator of the fraction. For example, a mixed number 3 1/2 should be provided as 3(1/2) in the calculator.

## Two or More Fractions Addition & 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 & mixed numbers calculator to verify the results of addition between two or more fractions, mixed numbers & 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 & 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 & 4/5.

**Problem**

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

**Step by step workout**

step 1 Address *formula*, input parameters & values.

Input parameters & 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 & 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

Thus, **59/30** is the equivalent fraction by adding three fractions 1/2, 2/3 & 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 & 4/9.

**Problem**

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

**Step by step workout**

step 1 Address formula, input parameters & values.

Input parameters & 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

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

### Adding Multiple Fractions & 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 & 3.
**Step by step workout**

step 1 Address formula, input parameters & values.

Input parameters & 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 & 1.

step 5 Multiply LCM 60 with all the numerators & 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

Thus, **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 & 3.

#### Adding Multiple Positive & 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 & negative fractions (with unlike or different denominators).

**Problem**

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

step 1 Address formula, input parameters & values.

Input parameters & 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, & 5.

step 3 Multiply LCM 210 with all the numerators & 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

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

#### Two or More Fractions & Mixed Numbers Addition

The below solved example for addition between 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 adding multiple fractions, mixed & whole numbers 1/2, 1/3, 1/4, 6, 7(1/5), 8(1/6) & 1/7.
**Problem**

Find the equivalent fraction for adding multiple fractions, mixed & whole numbers 1/2, 1/3, 1/4, 6, 7(1/5), 8(1/6) & 1/7.
**Step by step workout**

step 1 Address formula, input parameters & values.

Input parameters & 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 & 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

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