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:

7.5 = 15/2 = 7 1/2

Spelled result in words is fifteen halfs (or seven and one half).

How do you solve fractions step by step?

  1. Conversion a decimal number to a fraction: 7.5 = 75/10 = 15/2

    a) Write down the decimal 7.5 divided by 1: 7.5 = 7.5/1
    b) Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)
    7.5/1 = 75/10
    Note: 75/10 is called a decimal fraction.

    c) Simplify and reduce the fraction
    75/10 = 15 * 5/2 * 5 = 15 * 5/2 * 5 = 15/2

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:

  • Fraction to decimal
    decimals Write the fraction 3/22 as a decimal.
  • Fraction and a decimal
    numbs Write as a fraction and a decimal. One and two plus three and five hundredths
  • Rolls
    rohliky Mom bought 13 rolls. Dad ate 3.5 rolls. How many rolls left when Peter yet put two at dinner?
  • Product of two fractions
    numbers Product of two fractions is 9 3/5 . If one of the fraction is 9 3/7. Find the other fraction.
  • Withdrawal
    penize If I withdrew 2/5 of my total savings and spent 7/10 of that amount. What fraction do I have in left in my savings?
  • Cupcakes 2
    cake Susi has 25 cupcakes. She gives 4/5. How much does she have left?
  • Simple equation 6
    eq1 Solve equation with one variable: X/2+X/3+X/4=X+4
  • New bridge
    bridge Thanks to the new bridge, the road between A and B has been cut to one third and is now 10km long. How much did the road between A and B measure before?
  • One-third 2
    test One-third of the people in a barangay petitioned the council to allow them to plant in vacant lots, and another 1/5 of the people petitioned to have a regular garbage collection. What FRACTION of the barangay population made the petition?
  • Pizza 5
    pizza You have 2/4 of a pizza, and you want to share it equally between 2 people. How much pizza does each person get?
  • Cakes
    cookies On the bowl were a few cakes. Jane ate one-third of them, and Dana ate a quarter of those cakes that remained. a) What part (of the original number of cakes) Dana ate? b) At least how many cakes could be (initially) on the bowl?
  • Passenger boat
    boy Two-fifths of the passengers in the passenger boat were boys. 1/3 of them were girls and the rest were adult. If there were 60 passengers in the boat, how many more boys than adult were there?
  • Miss competition
    dancers How many girls took part in the Miss School competition if the nines grade made up half of the contestants, two-thirds of the remaining girls were eighth grade, and the seventh grade were three?


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