# Adding and Subtracting Mixed Fractions

In two of previous lessons, we saw how to add and subtract two fraction with like or unlike denominators. But what about two mixed fractions? How to add and subtract it?

Before we see how we do it, you first need to know how to convert a mixed fraction into an improper fraction. Then I advise you to go to this lesson first if you are not familiar with how to convert mixed fraction to improper fraction.

There are two different methods to add and subtract mixed fractions.

Method 1: by converting all mixed fractions to improper fractions

• Step 1: Convert all mixed numbers into improper fractions.

• Step 2: Check! Do they have a common denominator? If not, find a common denominator.

• Step 3: When necessary, create equivalent fractions.

• Step 4: Add or subtract the numerators and keep the denominator the same.

• Step 5: If the answer is an improper form, reduce the fraction into a mixed number.

The following examples showing you hwo to apply the steps above.

#### Solution:

• Step 1: Convert both mixed fractions into improper fractions

For the mixed fraction: :

For the mixed fraction: :

• Step 2: Find a common denominator

The common denominator is the lowest common multiple of 7 and 4.

By listing the multiples of 7 and 4, we fin that .

• Step 3: Create equivalent fraction
• Step 4: Add the fractions obtained in the step 3 (Fractions with like denominators)
• Step 5: Reduce the resulting fraction into a mixed fraction

• Divide 165 by 28

• Quotient = 5 (then 5 is the whole part)

• Remainder = 25 (then is the fraction part)

hence the answer is final is:

#### Solution:

• Step 1: Convert both mixed fractions into improper fractions

For the mixed fraction: :

For the mixed fraction: :

• Step 2: Find a common denominator

The common denominator is the lowest common multiple of 3 and 4.

By listing the multiples of 7 and 4, we fin that .

• Step 3: Create equivalent fraction
• Step 4: Add the fractions obtained in the step 3 (Fractions with like denominators)
• Step 5: Reduce the resulting fraction into a mixed fraction

• Divide 191 by 12

• Quotient = 15 (then 15 is the whole part)

• Remainder = 11 (then is the fraction part)

hence the answer is final is:

Method 2: by adding or subtracting the whole number parts.

• Step 1: Add or subtract the whole number part.

• Step 2: Check! Does the fraction part share a common denominator? If not, find one.

• Step 3: When necessary, create equivalent fractions.

• Step 4: Add or subtract the numerators of the fraction part and keep the denominator the same.

• Step 5: If the answer is an improper form, reduce the fraction into a mixed number.

The following examples showing you hwo to apply the steps above.

#### Solution:

• Step 1: Add the whole number part
• Step 2: The fraction part withe unlike denominator, so we must find the common denominator

The lowest common multiple of 5 and 8 is 40. Hence, the common denominator is 40.

• Step 3: Creat equivalent fractions of the fraction part
• Step 4: Add the two fraction obtained in step 3. (Fractions with like denominatots)
• Step 5:

The fraction is reduced to its lowest term.

#### Solution:

• Step 1: Add the whole number part
• Step 2: The fraction part withe unlike denominator, so we must find the common denominator

The lowest common multiple of 3 and 6 is 6. Hence, the common denominator is 6.

• Step 3: Creat equivalent fractions of the fraction part
• Step 4: Add the two fraction obtained in step 3. (Fractions with like denominatots)
• Step 5:

The fraction isn't reduced to its lowest term. We must convert it to the mixed fraction.

By Applying the steps in this lesson, we get:

The new whole part is :