How to Add and Subtract Fractions with Like Denominators in 2026
To add or subtract fractions with like denominators, keep the denominator the same and add or subtract only the numerators. For example, 2/7 + 3/7 = 5/7, and 5/7 − 2/7 = 3/7. A “denominator” is the bottom number of a fraction and tells you how many equal parts make one whole; a “numerator” is the top number and counts how many of those parts you have. When both fractions are already cut into the same-size pieces, the operation reduces to simple counting, so adding and subtracting fractions with like denominators is the easiest place to start.
What Like Denominators Mean
“Like denominators” means two or more fractions share the same bottom number. In 3/8 and 5/8, both are measured in eighths, so every piece is the same size. That shared unit is what makes the arithmetic straightforward.
Think of it in everyday terms. If one pizza is sliced into 8 equal slices and you take 3, you have 3/8. If a friend takes 5, they have 5/8. Because both counts refer to the same slice size, you can combine them by counting slices — no conversion needed.
This is different from fractions with unlike denominators, such as 1/2 and 1/3, where the pieces are different sizes. Those require finding a common denominator before you can combine them. With like denominators, that entire step disappears, which is why this skill is usually taught first.
One concept ties it together: a fraction is a count of equal parts. The denominator names the part size; the numerator tells how many parts. When the part size is fixed, arithmetic happens in the numerator only.
How to Add Like Fractions
The rule for addition is short: add the numerators, keep the denominator unchanged.
- Check that the denominators match.
- Add the numerators.
- Place the sum over the shared denominator.
- Simplify if the result can be reduced.
Compute 2/9 + 4/9. The denominators match at 9. Add the numerators: 2 + 4 = 6. Keep the denominator: 6/9. Then simplify by dividing the top and bottom by 3 to get 2/3.
Notice what did not happen: the denominator stayed at 9 in the raw sum. Adding 9 + 9 = 18 would produce an entirely wrong fraction. A useful sanity check is that adding two positive fractions must give a result at least as large as either one; 2/9 + 4/9 should be bigger than both, and 2/3 is. Khan Academy’s arithmetic unit walks through this visual approach with bar models if you want to see why the denominator stays fixed.
You can also add more than two fractions at once. For 1/10 + 3/10 + 4/10, add all numerators: 1 + 3 + 4 = 8, giving 8/10, which simplifies to 4/5.
How to Subtract Like Fractions
Subtraction follows the same structure, with one change: subtract the numerators instead of adding them, and keep the denominator.
Compute 7/12 − 3/12. Confirm the denominators match at 12. Subtract the numerators: 7 − 3 = 4. Keep the denominator: 4/12. Simplify by dividing top and bottom by 4 to get 1/3.
Here is the parallel to keep in mind:
| Operation | Numerator step | Denominator step |
|---|---|---|
| Addition | Add numerators | Keep the same |
| Subtraction | Subtract numerators | Keep the same |
The order of subtraction matters in a way that addition does not. 3/12 − 7/12 gives −4/12 = −1/3, a negative fraction, because you are taking away more parts than you have. In arithmetic with positive fractions, subtraction typically assumes the first fraction is the larger or equal one. Math is Fun’s fractions page illustrates this with mixed numbers, showing how the same rule extends to values like 2 1/5 − 1 3/5 after borrowing.
Simplify and Avoid Mistakes
Reducing to lowest terms is not optional in most math courses — a final answer is usually expected in simplest form. Simplest form means the numerator and denominator share no common factor other than 1. Take 6/9 from the addition example: 6 and 9 both divide by 3, so the reduced form is 2/3. If you skip this step on a test, you may lose points even when the value is correct.
The single most frequent error is adding or subtracting the denominators. 2/9 + 4/9 is 6/9, never 6/18. The denominator names the part size and does not change when you combine equal-size parts. Another common slip is forgetting to simplify: 4/12 is correct but not reduced, while 1/3 is the expected form.
Improper fractions are fine. An improper fraction has a numerator greater than or equal to its denominator, like 9/5. So 3/5 + 6/5 = 9/5 is perfectly valid. You can leave it as an improper fraction or convert to the mixed number 1 4/5, depending on what the problem requests. Both represent the same quantity. When a sum simplifies to 1, as in 3/7 + 4/7 = 7/7, write the answer as 1 rather than 7/7. Illustrative Mathematics emphasizes that keeping the meaning of the fraction in view — a count of equal parts — makes these simplification decisions intuitive rather than mechanical.
For most learners, the fastest path to accuracy is a quick two-question check after every problem: Did the denominator stay the same? Is the answer in lowest terms? Answer both correctly and the operation is almost always right.
Working with Mixed Numbers
A mixed number combines a whole number with a proper fraction, like 2 3/8. When the denominators match, you can handle the whole-number parts and the fractional parts separately.
For 2 3/8 + 1 5/8: add the whole numbers to get 3, add the fractions to get 8/8, and notice that 8/8 equals 1, so carry it over. The sum is 4. The fractional parts happened to total a whole, which is common and worth watching for.
Subtraction can require borrowing. For 3 1/4 − 1 3/4, the fractions alone will not subtract cleanly, since 1/4 − 3/4 is negative. Borrow 1 from the whole number 3 and convert it: 1 = 4/4, so 3 1/4 becomes 2 5/4. Now subtract the fractions: 5/4 − 3/4 = 2/4 = 1/2. Subtract the whole numbers: 2 − 1 = 1. The answer is 1 1/2. Borrowing is just a regrouping step, exactly like borrowing in whole-number subtraction.
Why the Rule Works
It helps to see the operation as a form of counting rather than as a mysterious procedure. When you write 2/9 + 4/9, you are really saying “two ninths plus four ninths.” The word “ninths” is the unit, and it behaves like any other unit — the same way “two apples plus four apples” gives six apples without changing what an apple is. This is why the denominator is held constant: it names the thing being counted, and that name does not change just because the count does.
A formal way to express the same idea uses factoring. Since the denominator is shared, you can factor it out: 2/9 + 4/9 = (2 + 4)/9 = 6/9. The numerator sum is multiplied by the common unit 1/9. The same principle appears later in algebra when you combine 2x + 4x to get 6x. Substituting x = 1/9 shows that the two situations are identical in structure, not merely similar.
This is also why the rule breaks down with unlike denominators. In 1/2 + 1/3, the units are halves and thirds — different sizes — so factoring out a single unit is impossible until you rewrite both fractions over a shared denominator such as 6. Once they become 3/6 + 2/6, the addition rule applies again and gives 5/6.
Key Takeaways
- With like denominators, add or subtract the numerators and keep the denominator exactly as it is.
- Like denominators mean the fractions share the same bottom number, so the parts are already the same size.
- Always reduce the result to lowest terms; 6/9 becomes 2/3, and 4/12 becomes 1/3.
- Improper fractions such as 9/5 are acceptable answers and can be written as mixed numbers like 1 4/5.
- The most common error is changing the denominator — never add or subtract the bottom numbers.
