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:

2/3 + 1/4 = 11/120.9166667

Spelled result in words is eleven twelfths.

How do you solve fractions step by step?

  1. Add: 2/3 + 1/4 = 2 · 4/3 · 4 + 1 · 3/4 · 3 = 8/12 + 3/12 = 8 + 3/12 = 11/12
    For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(3, 4) = 12. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 4 = 12. In the next intermediate step, the fraction result cannot be further simplified by canceling.
    In words - two thirds plus one quarter = eleven twelfths.

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:

  • Circular garden
    seed Alice creates a circular vegetable garden. Tomatoes are planted in 1/3 of the circular garden, carrots are planted in 2/5 of the circular garden, and green peppers are planted in 1/10 of the circular garden. What fraction represents the remaining unplante
  • An orchard
    apples During a visit to an orchard Greg picked 3/5 of a bag of golden delicious apples, 4/5 of a bag of Macintosh apples, 2/5 of a bag of Cortland apples, 1/5 of a bag of Bartlett pears, and 4/5 of a bag of Bosch pears. How many bags of fruit to Greg pick in to
  • Adding mixed numbers
    fractions Add this two mixed numbers: 1 5/6 + 2 2/11=
  • Addition of mixed numerals
    scientific Add two mixed fractions: 2 4/6 + 1 3/6
  • Adding mixed 4
    fractions 2 and 1/8th plus 1 and 1/3rd =
  • Math homework
    clocks2 It took Jose two-thirds of an hour to complete his math homework on Monday, three-fourths of an hour on Tuesday, any two- fifths of an hour on Wednesday. How many hours did it take Jose to complete his homework altogether?
  • Math test
    test Brayden was solving some math problems for the math team. He answered 2 math problems. Matthew answered 3, John answered 1 reasoning. Matthew 1/2 times as many. Brayden said that 2/6. Is he correct? Why or why not? Be sure to explain your answer.
  • Faye had
    meter Faye had a piece of ribbon. After using 3/8 meter for her headband, she had 1/4 meter left. How many meters of ribbon did she have at first?
  • A textile
    meter A textile store sold a bolt of denim (what jeans are made out of). In one day, the following number of yards were purchased from the one bolt: 5 2/3, 7, 4 2/3, 8 5/8, 9 3/5, 10 ½, and 8. How many yards were sold?
  • Weigh in total
    hrozno I put 3/5 kg of grapes into a box which is 1/4kg in weight. How many kilograms do the grapes and the box weigh in total?
  • Series and sequences
    seq_sum Find a fraction equivalent to the recurring decimal? 0.435643564356
  • A 14.5-gallon
    fuel A 14.5-gallon gasoline tank is 3/4 full. How many gallons will it take to fill the tank? Write your answer as a mixed number.
  • Flowers 4
    flowers A flower seller has 4.05 kg of orange flowers and 6.50 kg of red flowers. He made flower baskets with 2.11 kg of both red and orange flowers in each. How many baskets did he make?


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