Subtracting Mixed Numbers

How to subtract mixed numbers?
We will look at two methods that can be used to subtract mixed numbers.

Method 1: Convert to Improper Fractions
We can convert the mixed numbers to improper fractions and then subtract them as fractions.
This method is often preferred because it avoids the “borrowing” step which can confuse some people.

The following example shows how to subtract mixed numbers by first converting them to improper fractions. Scroll down the page for more examples and solutions.

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Steps:

1. Convert each mixed number to an improper fraction.
2. Find a Common Denominator (if necessary).
3. Rewrite both improper fractions with this common denominator.
4. Subtract the Improper Fractions.
5. Simplify the Result.

The following video gives another example of subtracting mixed numbers by converting to improper fractions.

• Show Step-by-step Solutions

Method 2: Subtracting Whole Numbers and Fractions Separately (with Regrouping/Borrowing)
We can subtract the whole number part and the fractional part of the mixed numbers separately. This may require a regrouping or borrowing step.

The following example shows how to subtract mixed numbers by subtracting the whole number part and the fractional part separately. Scroll down the page for more examples and solutions.

Steps:

1. Find a Common Denominator (if necessary) for the fractional parts.
   Rewrite both mixed numbers with the common denominator.
   
2. Compare the Fractional Parts:
   If the first fraction (from which you are subtracting) is smaller than the second fraction, you will need to “borrow” or “regroup”.
   Regroup (if needed):
   Take 1 from the whole number part of the first mixed number.
   Convert that 1 into a fraction with the common denominator.
   Add this fraction to the existing fractional part of the first mixed number.
   
3. Subtract the Fractional Parts:
   Subtract the numerators. Keep the common denominator.
   
4. Subtract the Whole Numbers:
   Subtract the whole numbers.
   
5. Combine and Simplify:
   Combine the new whole number and fraction.
   
6. Simplify the fraction if possible.

The following video gives another example of subtracting mixed numbers using method 2.

• Show Step-by-step Solutions

Subtracting mixed numbers with borrowing
If the fractional part of the second mixed number is bigger than the fractional part of the fixed number then it would be necessary to “borrow” from the whole part before subtracting.

The following example shows how to subtract mixed numbers with borrowing. Scroll down the page for more examples and solutions.

The following video shows how to subtract mixed numbers with borrowing.

• Show Step-by-step Solutions

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