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Perform addition, subtraction, multiplication, division, and simplification of fractions with step-by-step results.
A fraction shows how many parts of a whole are being counted. The top value, called the numerator, tells how many parts; the bottom value, the denominator, tells how many equal parts form the whole. In 3/8, for instance, three of eight equal parts are represented. If a pie has eight slices and three are eaten, five-eighths remain. The denominator must not be zero, since division by zero has no defined value.
Fractions can be added once they share a denominator. For example, multiply the top and bottom of 3/4 by 6, and those of 1/6 by 4: 18/24 + 4/24 = 22/24, which reduces to 11/12. This approach also works with more than two fractions, although the result may need to be reduced.
To keep the numbers smaller, find the least common multiple (LCM) of the denominators. For 1/4 + 1/6 + 1/2, the LCM is 12. Rewriting the fractions with denominator 12 gives 3/12 + 2/12 + 6/12 = 11/12.
Use the same denominator rule for subtraction: rewrite each fraction with a shared bottom value, then subtract the numerators. For example, 3/4 - 1/6 becomes 18/24 - 4/24 = 14/24, or 7/12 in simplest form.
For multiplication, multiply the top values together and do the same with the bottom values; no common denominator is needed. Thus 3/4 ร 1/6 = 3/24, which simplifies to 1/8.
Fraction division can be changed into multiplication by flipping the divisor. This flipped value is its reciprocal: the reciprocal of 3/4 is 4/3. For example, 3/4 รท 1/6 = 3/4 ร 6/1 = 18/4 = 9/2.
A fraction is simplified by dividing its numerator and denominator by their greatest common factor (GCF). For example, both 220 and 440 are divisible by 220, so 220/440 reduces to 1/2. A reduced fraction has no shared factor greater than 1 between its numerator and denominator.
For a terminating decimal, count the digits after the decimal point and use the matching power of ten as the denominator. Then reduce the fraction if possible. For example, four decimal places give 0.1234 = 1234/10000 = 617/5000.
To express a fraction as a decimal, division is a reliable method: divide the numerator by the denominator. When the denominator can be changed to 10, 100, or another power of ten, the decimal can also be read directly. For example, 1/2 = 5/10 = 0.5, and 5/100 = 0.05.
Fill in the numerator and denominator for each fraction, choose the operation you want, and select Calculate. The result will appear in simplified form.
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