**Adding Mixed Numbers with Unlike Denominators : **

In this section, we will learn, how to add fractions with different denominators.

We can use one of the following methods to add fractions with unlike denominators.

1. Cross-Multiplication method

2. LCM Method.

If the denominators of the fractional parts are co-prime or relatively prime, we have to apply this method.

Fro example, let us add the two mixed numbers given below.

5 1/3 and 2 1/8

In the above two mixed numbers, denominators of the fractional parts are 8 and 3.

For 8 and 3, there is no common divisor other than 1. So 8 and 3 are co-prime.

Here we have to apply cross-multiplication method to add the two mixed numbers using the steps given below.

**Step 1:**

First we have to add the integer parts 2 and 5.

2 + 5 = 7

**Step 2 :**

Now, we have to add the fractional parts 1/8 and 1/3 using cross multiplication as given below.

**Step 3 :**

Now, write step 1 value and step 2 together as shown below.

If the denominators of the fraction parts are not co-prime (there is a common divisor other than 1), we have to apply this method.

Fro example, let us add two mixed numbers given below.

2 5/13 and 7 1/20

In the above two mixed numbers, denominators of the fraction parts are 12 and 20.

For 12 and 20, if there is at least one common divisor other than 1, then 12 and 20 are not co-prime.

For 12 & 20, we have the following common divisors other than 1.

They are 2 & 4.

So 12 and 20 are not co-prime.

Here we have to apply L.C.M method to add the two mixed numbers using the steps given below.

**Step 1 :**

First we have to add the integer parts 2 and 7.

2 + 7 = 9

**Step 2 :**

Now, we have to add the fraction parts 5/12 and 1/20 using L.C.M method.

Let us find L.C.M of (Least common multiple) of 12 and 20.

12 = 2^{2} ⋅ 3

20 = 2^{2} ⋅ 5

When we decompose 12 and 20 in to prime numbers, we find 2, 3 and 5 as prime factors for 12 and 20.

To get L.C.M of 12 and 20, we have to take 2, 3 and 5 with maximum powers found above.

So, L.C.M of 12 and 20 is

= 2^{2} ⋅ 3 ⋅ 5

= 4 ⋅ 3 ⋅ 5

= 60

**Step 3 :**

Now we have to make the denominators of both the fractions to be 60 and add the two fractions 5/12 and 1/20 as shown below.

**Step 4 :**

Now, write step 1 value and step 3 together as shown below.

After having gone through the stuff given above, we hope that the students would have understood, how to add two mixed numbers with unlike denominators.

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

You can also visit the following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**