Mixed fractions (also called mixed numbers) look intimidating, but the strategy is consistent: convert to improper fractions, do the operation, simplify, and convert back if required. Most mistakes come from skipping the conversion step or forgetting a common denominator.
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A mixed number looks like a whole number plus a fraction, for example 3 2/5. Convert it into one fraction so you can do operations cleanly.
Example: Convert 3 2/5.
The safest method: convert both to improper, find a common denominator, add, then simplify.
Example: 1 1/4 + 2 2/3
Subtraction is the same as addition: convert, find LCD, subtract numerators. If the result is negative, that’s okay—just simplify.
Example: 4 1/6 − 2 3/4
Convert to improper, then multiply across. If possible, cancel common factors before multiplying to keep numbers small.
Example: 1 2/5 × 3 1/2
Convert to improper, then multiply by the reciprocal of the second fraction.
Example: 2 1/3 ÷ 1 3/4
Many answers end up as improper fractions like 17/5 or 47/12. If the problem expects a mixed number, divide the numerator by the denominator: the quotient is the whole number and the remainder stays on top.
Example: Convert 47/12 to a mixed number.
This is the same result you saw in the addition example above; converting back is just a clean “final formatting” step.
If the fractional parts already share a denominator, you can add the whole numbers and fractions separately. This is not a replacement for the improper-fraction method, but it can be faster in simple cases.
Example: 2 3/8 + 1 1/8
If the fractions don’t share a denominator, go back to the reliable approach: convert to improper and use the LCD.
Be careful with negatives. A common convention is that −2 1/3 means −(2 1/3), not (−2) + (1/3). When in doubt, convert to an improper fraction with the negative applied to the whole value.
Example: Convert −2 1/3 to an improper fraction.
Converting early prevents sign mistakes later when you add, subtract, multiply, or divide.
The safest approach is still “convert to improper fractions.” But if you subtract mixed numbers directly, you may need to borrow 1 from the whole number (just like borrowing in whole-number subtraction).
Example: 3 1/4 − 1 3/4
Since 1/4 is smaller than 3/4, borrow 1 from the 3. One whole equals 4/4.
This is equivalent to converting both to improper fractions, but borrowing can be more intuitive for some students.
Problem: A board is 4 3/4 feet long. You cut off 1 2/5 feet. How much board is left?
Convert to improper fractions so you can subtract with one LCD.
Answer: 3 7/20 feet. In measurement settings, mixed-number answers are common because they match ruler markings.
You can sometimes convert mixed numbers to decimals, but it’s usually best to keep fractions when the problem expects an exact answer. Decimals are convenient for money or measurements that are already given in decimals, but repeating decimals can make exact work harder.
Example: 1 1/3 as a decimal is 1.333…
If you keep it as 4/3, then 4/3 + 2/3 = 2 exactly. If you round 1.333… too early, you might get 1.99 or 2.01. That’s why fraction form is often more reliable for multi-step problems.
1/4 + 1/4 = 2/4 = 1/2. The denominator stays the same when denominators are already equal.
For 1/6 + 1/4 you must rewrite to twelfths first. Without an LCD, you are combining different-sized pieces.
Division of fractions becomes multiplication by the reciprocal. Don’t divide numerators by numerators.
Reduce fractions when possible. Simplifying early prevents big numbers and reduces errors.
If you want a quick refresher on fraction operations and why common denominators work, the short explanations in OpenStax on adding fractionscan be a handy reference.
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