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:

(3/4) : (1/10) = 15/2 = 7 1/2 = 7.5

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

How do you solve fractions step by step?

  1. Divide: 3/4 : 1/10 = 3/4 · 10/1 = 3 · 10/4 · 1 = 30/4 = 2 · 15 /2 · 2 = 15/2
    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 1/10 is 10/1) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the next intermediate step, , cancel by a common factor of 2 gives 15/2.
    In words - three quarters divided by one tenth = fifteen halfs.

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:

  • 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?
  • Cooks
    kucharky Four cooks cleaned 5 kg of potatoes for 10 minutes. How many cook would have to work clean 9 kg of potatoes for 12 minutes?
  • Barbara 2
    pizza Barbara get 6 pizzas to divide equally among 4 people. How much of a pizza can each person have?
  • Fraction expression
    fractions Which expression is equivalent to : minus 9 minus left parenthesis minus 4 start fraction 1 divided by 3 end fraction right parenthesis
  • Lauren
    clocks Lauren is tutoring students at the library on Saturday. If she is at the library for a total of 6 hours and she helps each student, one at a time, for three-fourths of an hour, how many students does she tutor?
  • Division by zero
    infinity-512 Fraction 5 by 2. if 3 is added to numerator and 2 is subtracted from the denominator then the new fraction is:
  • Francesca
    meter Francesca is growing 1/2 inch each year. How many years will it take for her to grow 6 inches?
  • 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?
  • Balls
    farebne-gulky The boys changed stamps, beads and balls. For 9 balls is 3 stamps, 2 balls is 44 stamps. How many beads is for 1 ball?
  • Cake 7
    cake 1/3 of a cake shared with 4 people. What share of the whole cake has each people?
  • The quotient
    12466 The quotient of g and 55 is the same as 279. What is g?
  • Evaluate expr with 2 vars
    expr If a=6 and x=2, find the value of (2ax + 7x- 10) /(4ax-3a-2)
  • Minutes
    watch Write as fraction in basic form which part of the week is 980 minutes.


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