How do you add mixed fractions? such as 4 1/3 + 3 3/7

Expert Answers
pohnpei397 eNotes educator| Certified Educator

To do this, you have to find a way to get the fractions to have the same denominator.  Once you have done that, you will be able to just add them together.

Looking at these two fractions, the least common multiple of the two is 21.  You can easily change both of these to fractions with 21 as the denominator.

To do that, you must mutliply the first fraction (only the fraction part, not the whole number) by 7 and the second by 3.  That will give you

4 7/21 + 3 9/21

Now you just add those together and get

7 16/21

giorgiana1976 | Student

To add the mixed ratios, we'll introduce the integer into the fraction:

Let's start with 4 1/3.

The first step is to multiply 4 by the denominator, 3:

4*3 = 12

Now, we'll add the numerator 1, to the value of 12:

12 + 1 = 13

So, the mixed ratio became:

4 1/3 = 13/3

Now, we'll calculate the mixed ratio, 3 3/7.

The first step is to multiply 3 by the denominator, 7:

3*7 = 21

Now, we'll add the numerator 3, to the value of 21:

21 + 3 = 24

So, the mixed ratio has transformed into the ratio: 

3 3/7 = 24/7

Now, we'll add the 2 quotients:

13/3 + 24/7

As we can notice, they don't have the same denominator, so we'll calculate the least common denominator of the 2 ratios:

LCD = 3*7 = 21

In order to obtain the same denominator, we'll multiply the 1st ratio by 7 and the 2nd ratio by 3:

13*7/21 + 24*3/21

(13*7 + 24*3)/21 = (91+72)/21

(91+72)/21 = 163/21

4 1/3 + 3 3/7 = 163/21

We'll write the result as a mixed ratio:

We'll divide 163 by 21 and we'll get:

163 = 21*7 + reminder

reminder = 163 - 21*7

reminder = 163 - 147

reminder = 16

163 = 21*7 + 16

We'll divide by 21 the expression:

163/21 = 7 16/21

So, the result of the addition:

4 1/3 + 3 3/7 = 7 16/21