# Adding Mixed Numbers with Different Denominators

Adding and subtracting mixed numbers can become complicated when the fractions have different denominators, such as 7 3/4 + 2 1/5. One way to solve this equation is to convert each side of the equation into one improper fraction by multiplying the denominator by the whole number and add the numerator. Using the previous example, (4*7) + 1 = 31. This gives you 31/4 for the first improper fraction. (5*2) + 1 = 11, which gives you 11/5 for the second improper fraction. Now your equation is 31/4 + 11/5, which still needs a common denominator. The LCM between 4 and 5 is 20, so multiply the improper fractions in a way that results in a denominator of 20. Your result will be 155/20 and 44/20, which you will add together to reach 199/20 and reach your final answer of 9 19/20.

## Adding Mixed Numbers with Different Denominators

Adding and subtracting mixed numbers becomes a little more complicated when the fractional parts have different denominators. **I’ll demonstrate the improper fraction method for solving each of these examples.** First we have 7 and 3/4 plus 2 and 1/5.

**The first thing we need to do is convert each of these terms to an improper fraction.** From this one we have 4 times 7 is 28, plus 3 is 31, over 4. Plus, 5 times 2 is 10, plus 1 is 11, over 5. **Now these do not have a common denominator, so we need to create one.**

The least common multiple between 4 and 5 is 20, so we’ll multiply these to get a denominator of 20, the first fraction by 5 over 5, and the second fraction by 4 over 4. Multiplying this you get 155 over 20, plus 44 over 20. 155 plus 44 is 199, and we keep the same denominator, 20.

20 goes into 199 9 times, with the remainder of 19, so this is equal to 9 and 19/20. In the second example we have 8 and 1/3 minus 3 and 1/2, so we’ll solve it the same way. 3 times 8 is 24, plus 1 is 25, 25 over 3. Minus 2 times 3 is 6, plus 1 is 7, 7 over 2. Again, we have to create a common denominator.

The least common multiple between 2 and 3 is 6, so multiply the first term by 2 over 2, and the second term by 3 over 3. This gives us 2 times 25 is 50, over 6. Minus 7 times 3 is 21, over 6. 50 minus 21 is 29, and we keep the denominator of 6. 6 goes into 29 4 times with the remainder of 5, so we have 4 and 5/6.