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Fraction Calculator

Add, subtract, multiply, divide and simplify fractions and mixed numbers, and see every step with pictures of the pieces.

For a mixed number like 2 ¾, put 2 in the small box on the left. Use a minus sign for negative fractions.

Answer

19/12 = 1 7/12

3/4 + 5/6 = 19/12 = 1 7/12, or 1.58333… as a decimal.

Show me how

All steps as text

    Tip: press ← and → to move between steps, or click any step.

    How to add and subtract fractions

    You can only add pieces of the same size, so first give both fractions the same denominator.

    1. Find the lowest common denominator: the smallest number both denominators divide into. For 3/4 and 5/6, multiples of 4 are 4, 8, 12 and multiples of 6 are 6, 12, so it is 12.
    2. Rewrite each fraction by multiplying its top and bottom by the same number: 3/4 = 9/12 and 5/6 = 10/12.
    3. Add or subtract the numerators and keep the denominator: 9/12 + 10/12 = 19/12.
    4. Simplify and, if you like, write it as a mixed number: 19/12 = 1 7/12.

    Never add the denominators: 1/2 + 1/3 is 5/6, not 2/5.

    How to multiply and divide fractions

    Multiply the tops together and the bottoms together: 2/3 × 9/10 = 18/30, which simplifies to 3/5. No common denominator is needed.

    Divide by turning the second fraction upside down and multiplying (keep, change, flip): 3/4 ÷ 5/6 = 3/4 × 6/5 = 18/20 = 9/10.

    Turn mixed numbers into improper fractions first: 1 1/2 × 2 2/3 = 3/2 × 8/3 = 24/6 = 4.

    How to simplify a fraction

    Divide the top and the bottom by their greatest common divisor (GCD). For 84/126 the GCD is 42, so 84/126 = 2/3. Simplify a fraction with the calculator.

    To find the GCD of big numbers, use Euclid’s method: divide the bigger number by the smaller and keep the remainder, then repeat with the smaller number and the remainder. The last number you divide by is the GCD: 126 = 1 × 84 + 42, then 84 = 2 × 42 + 0, so the GCD is 42.

    Mixed numbers and improper fractions

    Mixed to improper: multiply the whole number by the denominator and add the numerator. 2 3/4 = (2 × 4 + 3)/4 = 11/4.

    Improper to mixed: divide. 19 ÷ 12 = 1 remainder 7, so 19/12 = 1 7/12.

    To a decimal: divide the top by the bottom. 3/4 = 0.75, and 1/3 = 0.333… repeats forever. The long division calculator shows how.

    Questions

    What is the lowest common denominator?

    The smallest number that both denominators divide into exactly. For 4 and 6 it is 12. Using it keeps the numbers small, but any common denominator, such as 4 × 6 = 24, also works if you simplify at the end.

    Why do you flip the second fraction when dividing?

    Dividing asks "how many of these fit?", and multiplying by the flipped fraction answers the same question. For example, 3 ÷ 1/2 = 6 because six halves fit into 3, and 3 × 2/1 = 6.

    Can a fraction be negative?

    Yes. −3/4 is three quarters below zero. Type the minus sign on the top number, or on the whole number of a mixed number.

    What is an improper fraction?

    A fraction whose top is as big as or bigger than its bottom, like 7/4. It is more than one whole: 7/4 = 1 3/4.

    How do I turn a decimal into a fraction?

    Write it over a power of ten and simplify: 0.75 = 75/100 = 3/4.