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Fraction and surd calculator: exact answers
Use the online maths calculator to keep fractions and square roots exact, then switch to a decimal when the question requires one.
Open the free calculatorUsing the calculator for fractions
A fraction represents one value divided by another. The top box is the numerator and the bottom box is the denominator. The fraction key creates both boxes; use the arrow controls to move between them. Put the whole expression belonging to each part into its box.
For example, adding three quarters and two thirds gives seventeen twelfths. The calculator keeps that exact value, so you can round only if the question asks you to.
A denominator cannot be zero. If an answer looks unexpected, check the entire denominator rather than just the last number typed.
Using a surd calculator for square roots
A surd keeps an irrational root in exact form. Some square roots can be simplified by taking out a square factor. For , use , so .
The square-root key groups everything below its root bar. Compare with ; the root bars describe different calculations.
Fractions with a root in the numerator
When a calculation contains a combined numerator, keep the addition above the fraction bar. This is useful when checking a quadratic-formula answer.
Enter in the numerator and 2 in the denominator. The fraction bar divides the entire numerator by 2.
Before calculating, inspect the root bar and both fraction boxes. Use brackets if entering the expression as a line of keyboard input.
Rationalised exact answers
An exact answer may be shown in an equivalent rationalised form. Multiplying the numerator and denominator by the same non-zero value changes its appearance while keeping the value.
GCSE Maths Calculator displays simplified fractions and supported surd forms automatically. For a question asking for a particular form, compare the displayed expression with the requested form and show the required algebra in your working.
Exact answer or decimal?
Use an exact fraction or surd when a question asks for an exact answer. Use S↔D to display a decimal for questions asking for decimal places or significant figures. Decimal displays have finite precision, so a rounded decimal should not replace the exact value in later working.
Press an operator after an answer to continue with Ans. This carries the calculator's stored value into the next calculation, avoiding an unnecessary manual rounding step.
Fraction and square-root questions
Can it simplify a fraction?
Yes. Supported exact arithmetic is reduced to a simplified fraction. For example, gives .
Why do I get a surd rather than a decimal?
The exact form keeps the value unrounded. Press S↔D to see its decimal approximation.
Can I use the same tool for ordinary calculations?
Yes. The calculator also handles addition, subtraction, multiplication, division, powers, trig and logs. Read the scientific calculator guide for more examples.