Your Brain Puts Fractions and Whole Numbers on the Same Number Line
Most children meet whole numbers first: 1, 2, 3, and so on, in a neat line from small to large. Fractions arrive later, and they often feel like a different kind of number altogether. What is one-third, exactly, and where does it belong next to 3?
New brain research suggests that, in educated adults at least, the brain does not keep the two kinds apart. It places fractions and whole numbers on one shared, orderly map of size. The findings were published on 22 October 2026 in the journal PLOS Biology, by researchers led by Dr Daniela Valério and Professor Stanislas Dehaene at the INSERM-CEA Cognitive Neuroimaging Unit in France.
Scanning the brain while it compares numbers
The team recorded brain activity in 20 native French-speaking adults using functional MRI (fMRI) — scans that track changes in blood flow as different parts of the brain work harder. While being scanned, each participant was shown a series of whole numbers (integers) and fractions, and asked whether each number was bigger or smaller than the one before it. The task was designed to make participants think about size, or magnitude, rather than about the symbols themselves.
The scans revealed an organised pattern of activity in the intraparietal sulcus, a fold of the parietal cortex already known to be involved in processing numbers. As participants compared numbers, the patterns of activity shifted in a structured way, suggesting that this region contains a spatial map of numerical magnitude running from smaller to larger numbers.
In the paper, the researchers describe a topographic map — a map in which neighbouring positions in the brain prefer neighbouring values — in the anterior inferior parietal cortex, common to both whole numbers and fractions. Activity across a wider network, including parts of the temporal, prefrontal and hippocampal cortex, could be arranged in a two-dimensional space organised by numerical size and by whether the number was a fraction or an integer. In other words, the brain kept track of the difference between the two kinds of number, while still placing them on a common scale of size.
"Our study shows that when we focus on the magnitude of numbers, the brain organizes quantities into a highly structured internal map," the authors write. "This map brings fractions and integers together along a shared mental number line, allowing us to represent and compare different kinds of numbers within the same system."
Fractions cost more effort
The behaviour of the participants matched the brain picture. People made more errors in ordering numbers when fractions were involved, and they were slower when two fractions were close together in value — exactly what you would expect if the brain were comparing positions on a line, where near neighbours are harder to tell apart than distant ones.
That effort is worth noting for learners. A fraction is not just a whole number with extra decoration: working out its size means working out a ratio, and the brain appears to do extra work for that. But the result, in these adults, was still a single ordered system — one-third had a place on the same line as three, even if finding that place took longer.
The researchers are careful about the limits of the finding. It comes from educated adults doing an explicit size-comparison task, so it does not show how the map develops in children, or how it behaves in other kinds of task. What it does show is that the familiar "mental number line" from psychology may be more than a metaphor: in the parietal cortex, size really does seem to be laid out in space, and fractions are invited onto the same line.
That is encouraging news for anyone who finds fractions hard. The difficulty is real — the brain works harder for them — but it is the difficulty of placing a new kind of number on a line the brain already knows how to use. Book your first lesson and compare verified maths tutors for help with fractions, number lines and confidence with numbers, online, in person or in a group class.
Sources:
- Valério D, Debray S, Karami A, Cauté M, Gravel N, Dehaene S, "A cortical semantic map integrates fractions and integers in the human brain", PLOS Biology 24(10): e3003820, published 22 October 2026, DOI: 10.1371/journal.pbio.3003820: https://journals.plos.org/plosbiology/article?id=10.1371/journal.pbio.3003820
- Medical Xpress, "Your brain maps out numbers, including integers and fractions", 22 October 2026, reporting the PLOS Biology study: https://medicalxpress.com/news/2026-10-brain-integers-fractions.html