Subtracting mixed numbers

Subtracting Mixed Numbers

• When subtracting mixed numbers, you can use a similar method to subtracting fractions, but you also need to subtract the whole numbers.
• Remember, a mixed number is a combination of an integer (whole number) and a fraction, like .

Let's explore two methods for subtracting mixed numbers:

Method 1

Partition the mixed numbers into fractions and whole numbers, then subtract them separately.

Example

Solve:
Sol:
Step 1: Partition the mixed numbers so you have whole numbers together and the fractions together.

and
5 - 2
Subtract the whole numbers.
5 - 2 = 3
Step 2: Change one of the fractions into an equivalent fraction so both fractions have the same denominator.
You can't simplify 2/9 any further so you have to change 2/3. 3 is a factor of 9 so multiply the numerator and denominator by 3.
2/3 = 6/9
Step 3: Subtract the numerator.

Step 4: Put the two answers from the whole numbers and fractions back together:

Therefore:

Method 1: Checklist

• Partition and subtract whole numbers
• Check and change denominators
• Subtract the numerators
• Whole numbers answer + fractions answer = final answer

Method 2

• Change the mixed numbers into improper fractions.
• Remember, an improper fraction is a fraction where the numerator is greater than the denominator, like 9/5.

Example

Solve: 
Sol: Step 1: Convert the fractions so that they have the same denominator.
The denominators are 5 and 25.
5 goes into 25, so 5/15 is equivalent to 1/5.

Step 2: Convert the mixed numbers into improper fractions.
To do this, multiply the integer (whole number) by the denominator, and then add that to the numerator.

becomes
Step 3: Subtract the numerators.

5/5 is one whole, so it can be written as 1. So:

Method 2: Checklist

• Check and change denominators
• Convert to improper fractions
• Subtract the numerators
• If needed, convert answer back to a mixed number