Mixed Number Subtraction Practice Test Worksheets
Mixed number subtraction questions test whether you can turn whole-number-and-fraction parts into one clean calculation. Once the numbers are converted, the problem becomes a standard fraction subtraction with a final simplifying step.
For students who understand fractions, but get stuck regrouping mixed numbers before subtracting.
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What Do Mixed Number Subtraction Questions Look Like?
Mixed number subtraction questions test whether you can turn whole-number-and-fraction parts into one clean calculation. Students are given two mixed numbers to subtract, requiring them to convert to improper fractions, find a common denominator, subtract the numerators, and simplify the result. Here is a worked example.
Subtract Using a Common Denominator
Question: Work out 212 - 114, giving your answer in its simplest form.
Worked Method
Step 1: Convert to improper fractions: 212 = 52 and 114 = 54.
Step 2: Use denominator 4: 52 = 104.
Step 3: Subtract: 104 - 54 = 54.
Step 4: Divide 5 by 4: the quotient is 1 with remainder 1, so 54 = 114.
Answer: 114.
Tip: Converting a mixed number to an improper fraction keeps its denominator. Make the denominators match before subtracting.
Rules to Help You Solve Mixed Number Subtraction Questions
To solve mixed number subtractions like the example above, convert the mixed numbers into improper fractions before finding a common denominator.
🧮 Rule 1: Write mixed numbers as improper fractions
For the method used here, multiply the whole number by the denominator, add the numerator, and keep the denominator.
Example: 212 = (2 x 2 + 1)2 = 52.
🔢 Rule 2: Use a common denominator
If the denominators are different, rewrite the fractions using a common denominator. Multiply the numerator and denominator of each fraction by the same number to keep its value unchanged. Use the lowest common denominator to keep the calculations manageable.
Example: 52 - 54 = 104 - 54.
âž– Rule 3: Subtract the numerators
Once the denominators match, subtract the top numbers and leave the denominator unchanged.
Example: 104 - 54 = 54.
✅ Rule 4: Simplify the final answer
Simplify by dividing the numerator and denominator by their greatest common factor. Convert an improper fraction to a mixed number, or a whole number if there is no remainder. Answers below 1 stay as proper fractions.
Example: 104 = 52 = 212.
Two More Worked Examples
Here are two more examples showing how to scale both fractions to a common denominator and handle cases where the first fractional part is smaller.
Scaling Both Fractions to a Common Denominator
Question: Work out 513 - 327, giving your answer in its simplest form.
Worked Method
Step 1: Convert to improper fractions: 513 = 163 and 327 = 237.
Step 2: The lowest common denominator of 3 and 7 is 21. Multiply the numerator and denominator of the first fraction by 7, and those of the second fraction by 3:
163 = 16 × 73 × 7 = 11221.
237 = 23 × 37 × 3 = 6921.
Step 3: Subtract: 11221 - 6921 = 4321.
Step 4: Divide 43 by 21: the quotient is 2 with remainder 1, so 4321 = 2121.
Answer: 2121.
Tip: Check whether the fractional part can be reduced. Here, 1/21 is already in simplest form.
When the First Fractional Part Is Smaller
Question: Work out 715 - 614, giving your answer in its simplest form.
Worked Method
Step 1: Convert to improper fractions: 715 = 365 and 614 = 254.
Step 2: Use denominator 20: 365 = 14420 and 254 = 12520.
Step 3: Subtract: 14420 - 12520 = 1920.
Why the answer is less than 1: The whole-number difference is 7 − 6 = 1, but 1/5 is smaller than 1/4. Using twentieths, the full difference is 1 + 4/20 − 5/20 = 1 − 1/20 = 19/20.
Tip: When the first fractional part is smaller, regroup one whole or use improper fractions. Keep the subtraction in its original order; do not swap the fractional parts to get a positive difference.
