LCM method to find the sum of two fractions

If you want to add two fractions with different denominators, then you will can use the LCM method to do so.

In this method, you find the LCM (Lowest Common Multiple) of the denominators of the two fractions. Then for each of the two fractions, you use the following method:
  • Divide the LCM by the denominator.
  • Multiply the result by the numerator.
  • Note down the result.
By following the above procedure for both the fractions, you will get two numbers. On adding these two numbers you will get the numerator of the resultant fraction (that is, the sum of the two fractions). The denominator of the resultant fraction will be the LCM calculated above.

For example, there are two fractions 2/3 and 3/7. To add them, first you find the LCM (Least Common Multiple) of the denominators 3 and 7 of the two fractions.

LCM of denominators 3 and 7 = 21
Now for each fraction, we follow the above mentioned process:
For 2/3:
  • Divide the LCM by the denominator: 21 divide by 3 = 7
  • Multiply the result with the numerator: 7 * 2 = 14
  • Note down the result: 14
For 3/7:
  • Divide the LCM by the denominator: 21 divided by 7 = 3
  • Multiply the result with the numerator: 3 * 3 = 9
  • Note down the result: 9
Now add the two results obtained above: 14 + 9 = 23
Therefore 23 is the numerator of the resultant fraction (that is, the sum of the two fractions). Denominator of the resultant fraction will be the LCM 21 as calculated above, so we get 23/21

Therefore 2/3 + 3/7 = 23/21

Summary:
In the LCM method, we calculate the LCM (Least Common Multiple) of the denominators of two fractions. Then for each fraction, we divide this LCM by the denominator and then multiply the result with the numerator. Then we add the two results obtained from the two fractions together to get the numerator of the resultant fraction. The denominator of the resultant fraction is the LCM calculated above.

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