HOW TO ADD AND UNLIKE FRACTIONS

Unlike fractions are the fractions that have different denominators.

Example :

The picture below practically illustrates unlike fractions.

Adding and Subtracting Unlike Fractions

The following steps would be useful to add/subtract unlike fractions.

Step 1 :

Find the least common multiple of the denominators either by prime factorization or division method.

Step 2 :

Using multiplication, make each denominator as the value of the least common multiple found in step 2.

Step 3 :

At the end of step 2, you will have the same denominator. Take the denominator once and add/subtract the numerators. 

Least Common Multiple by Prime Factorization

The following steps would be useful to find the least common multiple of the given numbers using prime factorization.

Step 1 :

Find the prime factors of the given numbers 

Step 2 :  

Take each prime factor with its maximum times of repetitions.

Step 3 :  

Multiply all the prime factors in step 2 to get the least common multiple of the given numbers.

Least Common Multiple by Division Method

Finding the least common multiple for two numbers :

Using L division, divide both the numbers by a common divisor.

Continue this process, until you get a common divisor for both the numbers.

At one stage, there will be no common divisor for both the numbers.

Then, multiply all the common divisors and the numbers at the last stage to get the least common multiple of the given two numbers.

Finding the least common multiple for more than three numbers :

Consider the least common multiple for three numbers.

Try to get a common divisor for all the given three numbers.

If you get a common divisor for all the three numbers, using L division, divide all the the three numbers by it.

If you don't get a common divisor for all the three numbers, try to get a common divisor for at least two numbers and divide those two numbers by it. Write the third number as it is.

Continue this process, until you get a common divisor for at least two numbers.

At one stage, there will be no common divisor even for two numbers.

Then, multiply all the common divisors and the numbers at the last stage to get the least common multiple of the given three numbers.

You can follow the same process to find the least common multiple for than three numbers.

Note :

Usually prime numbers are being used as divisors.

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