Calculator
Example Data Table
| Example A | Example B | Operation | Simplified Result | Mixed Form |
|---|---|---|---|---|
| 1/2 | 3/4 | 1/2 divided by 3/4 | 2/3 | 2/3 |
| 1 2/3 | 2/5 | 1 2/3 divided by 2/5 | 25/6 | 4 1/6 |
| -3/8 | 1/2 | -3/8 divided by 1/2 | -3/4 | -3/4 |
| 7 | 2 1/4 | 7 divided by 2 1/4 | 28/9 | 3 1/9 |
Formula Used
To divide fractions, multiply the first fraction by the reciprocal of the second: a/b divided by c/d = a/b times d/c.
- Convert mixed numbers to improper fractions first.
- Flip the divisor (reciprocal), then multiply numerators and denominators.
- Reduce the final fraction by dividing top and bottom by their GCD.
How to Use This Calculator
- Enter Fraction A and Fraction B as integers, fractions, or mixed numbers.
- Keep numerator and denominator empty to use only the whole value.
- Choose whether to simplify, show mixed form, and set decimal precision.
- Press Submit to view the result above the form.
- Use the download buttons to export your latest result.
Everyday reasons to divide fractions
Fraction division appears in cooking, scaling drawings, and unit rates. If a recipe uses 3/4 cup per batch, dividing 2 1/4 cups by 3/4 estimates three batches. In measurement, dividing 5/8 meter by 1/4 meter shows a length is 2.5 segments. In speed work, 9/10 hour divided by 3/5 hour compares two job times. These problems require exact rational results, not only rounded decimals.
Reciprocal method and step tracing
The calculator follows the standard rule: a/b divided by c/d equals a/b multiplied by d/c. Each submission shows the reciprocal, the multiplication, and the reduction. Most examples finish in 4 to 6 lines for easy checking. This makes it easier to spot mistakes, such as flipping the first fraction or ignoring the sign.
Simplification and lowest terms
After multiplying, the result is reduced using the greatest common divisor (GCD). For example, 12/18 reduces to 2/3 by dividing top and bottom by 6. Another quick check is 14/21, which reduces to 2/3 by a GCD of 7. Working in lowest terms improves readability, prevents large numbers in later steps, and matches most textbook answers. When a denominator is negative, the sign is moved to the numerator.
Mixed numbers and negative inputs
Inputs accept integers, proper fractions, improper fractions, and mixed numbers. A mixed number like 1 2/3 is converted to 5/3 before division. Negative values are handled consistently so -3/8 divided by 1/2 becomes -3/4. The divisor cannot be zero, because division by zero is undefined, and the tool blocks it with a warning.
Decimal precision and visual comparison
Alongside the fraction, the tool prints a decimal rounded to a chosen precision from 0 to 12 places. A Plotly bar chart compares the decimal values of A, B, and the quotient, helping learners see when the quotient grows (dividing by numbers below 1) or shrinks (dividing by numbers above 1). This is useful for estimation checks before simplifying.
Exports for practice logs
CSV and PDF exports store inputs, simplified results, mixed form, and the rounded decimal. This supports homework checking, tutoring notes, and classroom demonstrations. Using the exported rows, you can build a practice set of 10 to 20 problems and review patterns in errors over time.
FAQs
1) What does “multiply by the reciprocal” mean?
You flip the second fraction (swap numerator and denominator), then multiply. This converts division into multiplication while keeping the exact value of the operation.
2) Can I divide mixed numbers like 2 1/4?
Yes. Enter the whole part and the fraction part. The calculator converts the mixed number into an improper fraction automatically before applying the division rule.
3) Why can the quotient be larger than the first fraction?
Dividing by a number between 0 and 1 increases the result. For example, dividing by 1/2 doubles the value because you are counting how many halves fit.
4) How is the simplified answer produced?
After multiplication, the numerator and denominator are divided by their greatest common divisor. This reduction puts the fraction into lowest terms without changing its value.
5) What happens if a denominator is zero or negative?
A zero denominator is rejected because the fraction is undefined. If a denominator is negative, the sign is moved to the numerator so the final fraction format stays standard.
6) What do the CSV and PDF downloads include?
They include both inputs, the simplified fraction result, mixed form (if enabled), the rounded decimal, and a short method summary. Run a calculation first, then use the download buttons.
Educational tool only. Double-check work for graded submissions.