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 ÷ 1/3 = 3/2 = 1 1/2 = 1.5

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

How do you solve fractions step by step?

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

Rules for expressions with fractions:

Fractions - simply use a forward 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 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:

  • Denominator 2
    Denominator of a fraction is 5 and numerator is 7. Write the fraction .
  • Chocolate to sweets
    I have 30 basket sweets and 15 chocolate in a basket. If take 5 sweet out of the basket what is the ratio in simplest form of the chocolate to the numbers of sweet left in the basket?
  • Double division
    0.25 divided by 1/2 divided by 14
  • Mass fraction
    2 teaspoons (24 g) of sugar are dissolved in a cup with 500 g of tea. Calculate the weight fraction of sugar in the tea.
  • Which 3
    Which is an equivalent ratio for 12:36
  • Dinner tickets
    At the spring festival, 7 out of the first 25 attendees had pre-purchased their dinner tickets. Based on this information, if 600 people attended the spring festival, then how many attendees could be expected to have pre-purchased their dinner tickets?
  • Tractors
    6 tractors started plowing the field that they together take 12 days. Agronomist hesitates to A) after 2 days to withdraw 2 tractors, or B) after 3 days to withdraw 3 tractors. Help him which of these two cases will be plowing done sooner.
  • Forest nursery
    In Forest nursery plant one pine to 1.9 m2. Calculate how many plants are planting in area 362 acres.
  • Cat food
    Anna has 3/4 bag of cat food. Her cat eats 1/10 of a bag per day. How many days will food last?
  • Players - baseball
    There are 20 players on each of two baseball teams. If 2/5 of the players on team 1 miss practice and 1/4 of the players on team two miss practice, how many more players from team 1 missed practice then team 2?
  • Tablespoon of salt
    Mrs. Monika uses 3/4 tablespoons of salt for every kilogram of ground pork. How many tablespoons of salt will she use for 3 1/2 kilograms of ground pork?
  • Water in body
    Water in the human organism of all the compounds represented constitutes about 3/5 of the total weight. How many kilograms of water is in your body when you weigh 51 kg?
  • Cutting wire
    If you cut a 3 ½ ft length wire into pieces that are 2 inches long, how many pieces of wire will you have?


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