Maths · Common misconception
Why can’t you add the denominators?
See why fraction addition needs equal-sized pieces, using one shared whole.
The short answer
A denominator tells you the size of a fraction’s pieces. Before adding fractions, express both amounts using pieces of the same size. Then add how many of those pieces you have.
Conceptual illustration. Colours distinguish parts of the model.
Where the confusion starts
Adding the denominators changes the unit you are counting. One half plus one third is not two fifths. A useful visual check is that the result must be larger than one half when a positive third is added.
WORK IT THROUGH
Find 1/2 + 1/3 using sixths.
- Draw two identical wholes so the sizes can be compared fairly.
- Split each whole into six equal parts. One half covers three sixths; one third covers two sixths.
- Count the shaded sixths: 3/6 + 2/6 = 5/6. The denominator stays six.
CHECK YOUR UNDERSTANDING
Find 1/4 + 1/2. What does the denominator in your answer mean?
Make a prediction or write an answer before opening the explanation.
Reveal the explanation
3/4. Rewrite one half as two quarters, then add one quarter. The denominator means the whole is divided into four equal pieces.
SEE IT. CHANGE IT. EXPLAIN IT.
Take the next step in the lesson.
Use the visual explanation in the lesson, then choose Practice to test the idea with another question.
Spotted something unclear? Send feedback. These are original teaching explanations, not predictions of future exam questions.