Fraction calculator



The calculator performs basic and advanced operations with fractions, expressions with fractions combined with integers, decimals, and mixed numbers. It also shows detailed step-by-step information about the fraction calculation procedure. Solve problems with two, three, or more fractions and numbers in one expression.

Result:

(5 1/4) : 12 = 7/16 = 0.4375

Spelled result in words is seven sixteenths.

How do you solve fractions step by step?

  1. Conversion a mixed number 5 1/4 to a improper fraction: 5 1/4 = 5 1/4 = 5 · 4 + 1/4 = 20 + 1/4 = 21/4

    To find a new numerator:
    a) Multiply the whole number 5 by the denominator 4. Whole number 5 equally 5 * 4/4 = 20/4
    b) Add the answer from previous step 20 to the numerator 1. New numerator is 20 + 1 = 21
    c) Write a previous answer (new numerator 21) over the denominator 4.

    Five and one quarter is twenty-one quarters
  2. Divide: 21/4 : 12 = 21/4 · 1/12 = 21 · 1/4 · 12 = 21/48 = 3 · 7 /3 · 16 = 7/16
    Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 12/1 is 1/12) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, cancel by a common factor of 3 gives 7/16.
    In other words - twenty-one quarters divided by twelve = seven sixteenths.

Rules for expressions with fractions:

Fractions - use the slash “/” between the numerator and denominator, i.e., for five-hundredths, enter 5/100. If you are using mixed numbers, be sure to leave a single space between the whole and fraction part.
The slash separates the numerator (number above a fraction line) and denominator (number below).

Mixed numerals (mixed fractions or mixed numbers) write as non-zero integer separated by one space and fraction i.e., 1 2/3 (having the same sign). An example of a negative mixed fraction: -5 1/2.
Because slash is both signs for fraction line and division, we recommended use colon (:) as the operator of division fractions i.e., 1/2 : 3.

Decimals (decimal numbers) enter with a decimal point . and they are automatically converted to fractions - i.e. 1.45.

The colon : and slash / is the symbol of division. Can be used to divide mixed numbers 1 2/3 : 4 3/8 or can be used for write complex fractions i.e. 1/2 : 1/3.
An asterisk * or × is the symbol for multiplication.
Plus + is addition, minus sign - is subtraction and ()[] is mathematical parentheses.
The exponentiation/power symbol is ^ - for example: (7/8-4/5)^2 = (7/8-4/5)2


Examples:

adding fractions: 2/4 + 3/4
subtracting fractions: 2/3 - 1/2
multiplying fractions: 7/8 * 3/9
dividing Fractions: 1/2 : 3/4
exponentiation of fraction: 3/5^3
fractional exponents: 16 ^ 1/2
adding fractions and mixed numbers: 8/5 + 6 2/7
dividing integer and fraction: 5 ÷ 1/2
complex fractions: 5/8 : 2 2/3
decimal to fraction: 0.625
Fraction to Decimal: 1/4
Fraction to Percent: 1/8 %
comparing fractions: 1/4 2/3
multiplying a fraction by a whole number: 6 * 3/4
square root of a fraction: sqrt(1/16)
reducing or simplifying the fraction (simplification) - dividing the numerator and denominator of a fraction by the same non-zero number - equivalent fraction: 4/22
expression with brackets: 1/3 * (1/2 - 3 3/8)
compound fraction: 3/4 of 5/7
fractions multiple: 2/3 of 3/5
divide to find the quotient: 3/5 ÷ 2/3

The calculator follows well-known rules for order of operations. The most common mnemonics for remembering this order of operations are:
PEMDAS - Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
BEDMAS - Brackets, Exponents, Division, Multiplication, Addition, Subtraction
BODMAS - Brackets, Of or Order, Division, Multiplication, Addition, Subtraction.
GEMDAS - Grouping Symbols - brackets (){}, Exponents, Multiplication, Division, Addition, Subtraction.
Be careful, always do multiplication and division before addition and subtraction. Some operators (+ and -) and (* and /) has the same priority and then must evaluate from left to right.

Fractions in word problems:

  • Soup from canteen
    soup For how many people is 90 liters of soup enough if we assume 3/8 liter of soup per person in the canteen?
  • The third
    meter The one-third rod is blue, one-half of the rod is red, the rest of the rod is white and measures 8 cm. How long is the whole rod?
  • One half 2
    pizza One half pizza will be divide among 3 pupils. Each pupil receive 1/6. Is it true or false?
  • A baker
    pie A baker has 5 1/4 pies in her shop. She cut the pies in pieces that are each 1/8 of a whole pie. How many pieces of pie does she have?
  • Mrs. Glover
    cookies Mrs. Glover is making brownies for the girls’ tennis team.  She took   1/5 of the leftover brownies to school to give to her 3 friends.  How much did each friend get?
  • Quotient and division
    seq What is the quotient of 2/9 and 1/8?
  • Almonds
    almonds Rudi has 4 cups of almonds. His trail mix recipe calls for 2/3 cup of almonds. How many batches of trail mix can he make?
  • The bird
    zrno The bird feeder holds 1 and 1/2 cups of birdseed. Reagan is using a scoop that holds 1/8 of a cup. How many scoops will she need to fill the bird feeder?
  • Curtain 3
    textiles Mrs Johnson bought 16.4 meters of cloth to make 8 curtains of equal length. What is the length of each curtain in meters?
  • Mario 2
    spagetty Mario is preparing a dinner for his friends. He made 3 bowls of spaghetti sauce. If each bowl holds 3/4 quart, how much sauce did Mario make?
  • How many 17
    numbers How many fifths are there in four wholes? How many 1/5 are there in 4?
  • Reciprocal value 2
    maso Annabelle is making burger patties if each burger patty needs 1/16 kilogram of beef. How many patties can she make with a kilo of beef?
  • Sir Toffie
    seed One hot afternoon, Sir Toffie went to his backyard to plant monggo. In his seed box, he found out that different seeds like monggo, pechay, eggplant, and tomatoes were accidentally mixed because of the strong wind. He sieved the mixed seeds and was able t


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