Fractions are added easily when their denominators are same. When their denominators are same, fractions are added by adding their numerators (the top numbers) and you get the answer. For example:

2/3 + 5/3 = (2 + 5)/3 = 7/3

On the other hand, if the denominators of two fractions are different, then you need to make them same in order to add them like we did above. To make the denominators of two fractions same, we will generally multiply the numerator and denominator of each fraction with the denominator of the other fraction. This will result in two fractions that have the same denominators but they are equivalent fractions of the original two fractions that you wanted to add.

This will be done like this:

Two fractions with different (unlike) denominators are : 2/3 and 3/7

Multiply the numerator and denominator of the first fraction 2/3 with the denominator 7 of the other fraction;

2/3 * 7/7 = 14/21

Multiply the numerator and denominator of the second fraction 3/7 with the denominator 3 of the other fraction;

3/7 * 3/3 = 9/21

Now we have two fractions with the same denominators: 14/21 and 9/21

Note that 14/21 is same as 2/3 because on reducing it we get 2/3 and 9/21 is same as 3/7 because on reducing it we get 3/7.

Now add the two fractions 14/21 and 9/21: 14/21 + 9/21 = (14 + 9)/21 = 23/21

Therefore the answer is 23/21.

Summary:

We had two fractions with different (unlike) denominators: 2/3 and 3/7. We converted these fractions into 14/21 and 9/21 respectively. 14/21 is same as 2/3 and 9/21 is same as 3/7. So adding 2/3 and 3/7 is same as adding 14/21 and 9/21. On adding 14/21 and 9/21 we get 23/21. Therefore,

2/3 + 3/7 = 14/21 + 9/21 = 23/21

2/3 + 5/3 = (2 + 5)/3 = 7/3

On the other hand, if the denominators of two fractions are different, then you need to make them same in order to add them like we did above. To make the denominators of two fractions same, we will generally multiply the numerator and denominator of each fraction with the denominator of the other fraction. This will result in two fractions that have the same denominators but they are equivalent fractions of the original two fractions that you wanted to add.

This will be done like this:

Two fractions with different (unlike) denominators are : 2/3 and 3/7

Multiply the numerator and denominator of the first fraction 2/3 with the denominator 7 of the other fraction;

2/3 * 7/7 = 14/21

Multiply the numerator and denominator of the second fraction 3/7 with the denominator 3 of the other fraction;

3/7 * 3/3 = 9/21

Now we have two fractions with the same denominators: 14/21 and 9/21

Note that 14/21 is same as 2/3 because on reducing it we get 2/3 and 9/21 is same as 3/7 because on reducing it we get 3/7.

Now add the two fractions 14/21 and 9/21: 14/21 + 9/21 = (14 + 9)/21 = 23/21

Therefore the answer is 23/21.

Summary:

We had two fractions with different (unlike) denominators: 2/3 and 3/7. We converted these fractions into 14/21 and 9/21 respectively. 14/21 is same as 2/3 and 9/21 is same as 3/7. So adding 2/3 and 3/7 is same as adding 14/21 and 9/21. On adding 14/21 and 9/21 we get 23/21. Therefore,

2/3 + 3/7 = 14/21 + 9/21 = 23/21

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