Same denominators
Sixth-pieces already match, so 1/6 + 3/6 means four sixth-pieces.
Fractions topic
How to Add Fractions
See how fractions become the same-sized parts before you combine them. Use the visual tool to work through one problem, then use the guide below to decide what to do first on the next one.
- same denominators
- unlike denominators
- whole numbers
- mixed numbers
Visual addition tool
See how fraction parts become ready to add
Start with one problem, make the parts match when needed, then combine them.
Type the full expression
Examples: 1/4 + 2/3, 2 + 3/4, or 1 1/2 + 2/3.
Visual explanation
Notice the part sizes
The fractions name pieces of different sizes, so they cannot be combined yet.
First addend1/4
Second addend2/3
1/4 part
1/3 part
These pieces are not the same size yet.
How fraction addition works
Add only parts that are the same size
Adding fractions is not about putting every number together. It is about counting more of one shared unit. The denominator tells you the size of that unit; the numerator tells you how many units you have.
Unlike denominators
Fourth-pieces and third-pieces need to be redrawn as one shared unit before they can combine.
Start the problem
Choose the right first move for the problem
Read the denominators before you calculate. This quick decision avoids the most common mistake: adding numbers before checking whether they count the same-sized parts.
The denominators already match
Count more of the same-sized parts.
2/7 + 3/7 = 5/7
Both fractions name sevenths. The denominator stays 7 because the size of every piece has not changed; only the number of seventh-pieces changes.
The denominators are different
Choose a shared part size before adding.
1/4 + 2/3 uses twelfths
Find a denominator both original denominators fit into. For fourths and thirds, 12 works because one fourth is three twelfths and one third is four twelfths.
There is a whole number or mixed number
Keep the whole amount visible, then work with the leftover fraction.
2 + 3/4 = 2 3/4
A whole does not need to be broken apart just to add a fractional remainder. When two remainders make a full bar, regroup that full bar with the wholes.
Problem guides
Once you know the first move, keep the meaning visible. The examples below show what stays the same, what needs to be rewritten, and when a result should become a mixed number.
Like denominators
Add fractions with the same denominator
1/6 + 3/6 = 4/6 = 2/3
The pieces already match, so add the numerators and keep the denominator.
For parents: Say: “These are all sixth-size pieces, so we can count how many sixths we have.”
Unlike denominators
Add fractions with different denominators
1/4 + 2/3 = 3/12 + 8/12 = 11/12
Rewrite both fractions as equal-size pieces before adding.
For parents: Say: “Fourth-pieces and third-pieces are not the same size yet.”
Wholes and mixed numbers
Add whole numbers and mixed fractions
1 1/2 + 2/3 = 1 + 3/6 + 4/6 = 2 1/6
Keep complete wholes visible, then add the fractional leftovers.
For parents: Say: “First keep the whole; then make the leftover pieces match.”
Common mistakes
Avoid changing the size of the parts
- Adding denominators instead of keeping the unit size the same.
- Combining fourths and thirds before rewriting them as matching parts.
- Forgetting that fractional pieces can make one more whole.
- Stopping before simplifying the final answer.
Check the result
Check whether your answer still makes sense
A final answer is stronger when the model, the symbols, and a quick estimate agree. Use these checks before moving on to the next problem.
Check that every part has the same size
Before adding numerators, both fractions should name the same unit, such as twelfths. If one number still counts fourths and the other counts thirds, the addition is not ready.
Use a quick estimate
Estimate with friendly benchmarks. Since 1/4 is less than 1/2 and 2/3 is less than 1, 1/4 + 2/3 should be less than 1; 11/12 fits that estimate.
Simplify or make a mixed number when it helps
Reduce a fraction when numerator and denominator share a factor. When the fractional pieces include a full whole, write that whole beside the remaining fraction.
Practice order
Predict the first move before opening the answer. Then enter one expression into the visual tool and compare your prediction with the bars and the solution path.
- 1.Same denominator: 2/7 + 3/7
- 2.Unlike denominators: 1/3 + 1/4
- 3.Whole number: 3 + 2/5
- 4.Mixed number: 1 1/2 + 1/4
Explain it out loud
“I can add the top numbers once both fractions name the same-sized parts.”
When a child is stuck, ask one question and wait for the model to do some of the explaining. These prompts keep the conversation focused on the size and meaning of the parts instead of rushing to a rule.
- What size is one piece in the first fraction?
- Are the pieces in both fractions the same size yet?
- What shared part size could both fractions use?
- After we combine the pieces, do we have enough to make one whole?
Common questions
Adding Fractions FAQ
The denominator names the size of each part. You can count more equal parts, but you do not change their size just because you are adding them.