LESSON: Adding and Subtracting Fractions with Unlike Denominators

READ: Adding and Subtracting Mixed Number with Unlike Denominators

Adding and Subtracting Mixed Numbers with Unlike Denominators

Do you remember adding mixed numbers with like denominators? Adding & subtracting mixed numbers with unlike denominators is very similar, but with one extra step. When we add mixed numbers with different denominators, we need to rename the fraction part of the mixed number with a common denominator FIRST. Then we can add the mixed numbers.

Example

$& \quad \ \ 6\frac{7}{8}\\ & \underline{+ \quad 4\frac{2}{4}\;}$

Our first step here is to rename both fractions with a common denominator. The common denominator for 8 and 4 is 8.

$\frac{7}{8}$ can stay the same. It already has a denominator of 8.

$\frac{2}{4}=\frac{4}{8}$

Let’s rewrite the problem.

$& \quad \ \ 6\frac{7}{8}\\ & \underline{+ \quad 4\frac{2}{4}\;}=\frac{4}{8}\\ & \qquad \frac{11}{8}$

When we add these two fractions now, we get an improper fraction. Seven eighths and four-eighths is equal to Eleven-eighths.

Now we can change $\frac{11}{8}$ . $\frac{11}{8}=1\frac{3}{8}$

This is the first part of the answer. Now we can add the whole numbers and then find the sum of both quantities.

$6 + 4 &= 10\\ 10 + 1\frac{3}{8} &= 11\frac{3}{8}$

This is our final answer.