---
license: mit
task_categories:
- text2text-generation
language:
- en
tags:
- math
- maths
- simplifications
pretty_name: psm500k
size_categories:
- 100K<n<1M
---

## Primary School Maths-500k Dataset

This repository contains a synthetic dataset of arithmetic expressions designed for fifth-grade level practice. The dataset is formatted in JSON and includes both the step-by-step intermediate results and the final rounded answer.

---

### Dataset Overview

* **Purpose**: Provide a collection of basic arithmetic problems (addition, subtraction, multiplication, and division) that any fifth grader could solve.
* **Data Type**: JSON file containing a list of problem instances.
* **Split**: 90% training, 10% testing.

---

### Data Format

Each entry in the JSON list has the following structure:

```json
{
  "question": "<expression>",
  "steps": [
    "<intermediate step 1>",
    "<intermediate step 2>",
    ...
  ],
  "answer": <float or null>
}
```

* **question**: A string containing the arithmetic expression, using Python syntax. Only the operators `+`, `-`, `*`, and `/` are used. Nested operations follow standard precedence rules, and chained division `x/y/z` is parsed as `(x/y)/z`.
* **steps**: A list of strings capturing each major intermediate calculation (up to five decimal places). If a division by zero occurs at any step, the final step records an error message (e.g., `"Division by Zero is not possible"`).
* **answer**: The final result rounded to two decimal places, or `null` if the expression could not be evaluated (e.g., due to division by zero).

---

### Numerical Precision

* Intermediate results are computed and recorded with **five decimal digits** of precision.
* Final answers are rounded to **two decimal digits**.
* All absolute answers satisfy `0.005 < |answer| < 100000`.

---

### Value Range

* All numeric values in the questions range from **1** to **100**.
* The final answer for each valid expression lies outside the interval `[-0.005, 0.005]` and within `(-100000, 100000)`.

---

### Train/Test Split

* The dataset is split into **90% training** and **10% testing** subsets.
* Filenames:

  * `train.json` — 90% of the data.
  * `test.json` — 10% of the data.

---

### Examples

**Valid expression**:

```json
{
  "question": "87*38",
  "steps": ["3306"],
  "answer": 3306
}
```

**Expression with step-by-step precision**:

```json
{
  "question": "(61/48/90)/((17-38)+((83.34-14.71*41.33)-(10.36*1.72*36.11)-(56*53*98))+(23.72*49.97/77.8))+(43.88*30.28)",
  "steps": [
    "0.01412/(-21+(-524.6243-643.45131-290864)+15.23507)+1328.6864",
    "0.01412/(-21+-292032.07561+15.23507)+1328.6864",
    "0.01412/-292037.84054+1328.6864",
    "1328.6864"
  ],
  "answer": 1328.69
}
```

**Division by zero**:

```json
{
  "question": "(36-27)/(98-98)",
  "steps": ["9/0" , "Division by Zero is not possible"],
  "answer": null
}
```

---

### Licensing and Attribution

This dataset is released under the **MIT** license.

---