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:

1/2 ÷ 2/3 = 3/4 = 0.75

Spelled result in words is three quarters.

How do you solve fractions step by step?

  1. Divide: 1/2 : 2/3 = 1/2 · 3/2 = 1 · 3/2 · 2 = 3/4
    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 2/3 is 3/2) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, the fraction result cannot be further simplified by canceling.
    In other words - one half divided by two thirds = three quarters.

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:

  • Evaluate expression
    numbers Calculate the value of the expression z/3 - 2 z/9 + 1/6, for z = 2
  • Fraction and a decimal
    numbs Write as a fraction and a decimal. One and two plus three and five hundredths
  • Kelly
    bag_school Kelly and Dan are collecting clothes for a clothing drive. Dan collected 1/2 as many clothes as Kelly did. If Kelly collected 3 bags of clothes, how many bags of clothes did Dan collect?
  • Paper clips
    paper Mrs. Bright is organizing her office supplies. There are 5 open boxes of paper clips in her desk drawer. Each box has 1/2 of the paper clips remaining. How many boxes of paper clips are left?
  • Adding mixed fractions
    mixed Add this two mixed numbers: 1 5/6 + 2 2/11=
  • Samuel
    sumiac Samuel has 1/3 of a bag of rice and Isabella has a 1/2 bag of rice. What fraction of are bag of rice do they have altogether?
  • Fraction equation
    eq1 Ex over four is equal to two and one-fifth times ex plus three over ten. What is ex>
  • What percent
    percent What percent of 51 3/5 is 47 2/5?
  • Cris had
    stolicky_skola_8 Cris had 15000 . He spent 1/3 of his money on a table and the remaining on 5 similar chairs that cost the same. How much did one chair cost?
  • Adding mixed numbers
    fractions Add this two mixed numbers: 1 5/6 + 2 2/11=
  • Obtuse angle
    UholZSobr2 Which obtuse angle is creating clocks at 17:00?
  • Unit rate
    question Find unit rate: 6,840 customers in 45 days
  • Gingerbread house
    pernikova_ch Janka and Marienka calculated that there are 210 gingerbreads on the gingerbread house. Janko ate one-seventh of all gingerbreads, and Marienka ate a third less than Janko. How many gingerbreads remained in the gingerbread house?


next math problems »