Fraction Calculator

Each number is entered in three boxes, so a plain fraction, a mixed number and a whole number all use the same layout. The boxes start at 1/2 and 1/3, which gives you a working example straight away.

1. Fill in the first number. Type its whole number in First number: whole part (leave it at 0 for a plain fraction), then the top in First: numerator and the bottom in First: denominator. For 2 1/3 enter 2, 1 and 3.
2. Choose the Operation: Add, Subtract, Multiply or Divide.
3. Fill in the second number with Second number: whole part, Second: numerator and Second: denominator.
4. For a whole number such as 4, enter 4 as the whole part and 0 as the numerator, keeping the denominator at 1 or higher.
5. Read the result: the simplified fraction, the mixed number, the decimal, the percentage and the greatest common divisor that was cancelled.
6. Look at the working line underneath, which shows the common denominator used for adding and subtracting, or the flipped fraction used for dividing.

Adding and subtracting need both fractions over the same denominator. The calculator multiplies the denominators together, divides out what they share, rewrites each fraction over that common denominator and then combines the tops. Multiplying simply multiplies tops and bottoms. Dividing multiplies the first fraction by the second one turned upside down. Every answer is then reduced by dividing top and bottom by their greatest common divisor.

In the subtraction row, 2 1/3 first becomes the improper fraction 7/3, which is 14/6 over the common denominator. After subtracting, 9/6 has a greatest common divisor of 3, so it reduces to 3/2.

A whole part turns a fraction into a mixed number: whole 2, numerator 1 and denominator 3 means 2 1/3. When the whole part is not zero, the sign belongs to it, so enter -2 for minus 2 1/3 and read the numerator as a size only. When the whole part is 0, a negative numerator gives a negative fraction, and a negative denominator is moved to the top for you.

• Do not add the denominators. 1/2 + 1/3 is 5/6, not 2/5.
• In a division, only the second fraction is flipped. Flipping the first one gives a different answer.
• An answer such as 9/6 is correct but unfinished. The calculator reports 3/2 and 1 1/2 instead.
• A denominator of zero, or dividing by a second number that equals zero, is refused with a message rather than an answer.

To sanity-check a result, type the same sum into the scientific calculator and compare decimals. To turn the percentage into a share of a real amount, use the percentage calculator.

The boxes take whole numbers only, and anything after a decimal point is ignored. To work with 0.75, write it as 75/100 and let the calculator reduce it to 3/4. If the intermediate numbers pass roughly nine quadrillion, the calculation is refused rather than rounded, because the arithmetic would stop being exact. Only two numbers are combined at a time, so for a longer sum feed each answer into the next calculation.

Everyday uses are mostly about scaling and splitting. A recipe that needs 3/4 of a cup, made one and a half times, is 0 3/4 multiplied by 1 1/2, which gives 9/8, shown as the mixed number 1 1/8. Cutting a 1 1/2 metre board into pieces of 3/4 of a metre is a division: 3/2 times 4/3 is 12/6, so you get exactly 2 pieces. Writing the working beside the answer makes it easy to check homework or a hand calculation line by line, and the percentage row helps when a fraction needs to be quoted as a share.

For a list of values the average calculator is a better fit, and if you need an amount spelled out for a document, try the number to words converter.