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:

(3/5) : (3/10) = 2/1 = 2

Spelled result in words is two.

How do you solve fractions step by step?

  1. Divide: 3/5 : 3/10 = 3/5 · 10/3 = 3 · 10/5 · 3 = 30/15 = 15 · 2 /15 · 1 = 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 3/10 is 10/3) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, cancel by a common factor of 15 gives 2/1.
    In other words - three fifths divided by three tenths = two.

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:

  • 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?
  • Unknown number
    If I reduced the sum of the numbers 70 and the unknown number three times, I would get 100. what is the unknown number?
  • Evaluate expression
    Evaluate expression using BODMAS rule: 1 1/4+1 1/5÷3/5-5/8
  • Imagine 2
    Imagine that you are filling treat bags with jellybeans. You have 3 3/8 cups of jellybeans, and each treat bag will contain 1/4 cup of jellybeans. How many treat bags can you fill before you run out of jellybeans? Show your work (please).
  • Metal rod
    You have a metal rod that’s 51/64 inches long. The rod needs to be trimmed. You cut 1/64 inches from one end and 1/32 inches from the other end. Next, you cut the rod into 6 equal pieces. What will be the final length of each piece?
  • The cost 2
    The cost of 5 apples is $3.45, and 5 oranges are $1.23. If Rachel buys one apple and one orange, then how much must she pay?
  • One half 2
    One half pizza will be divide among 3 pupils. Each pupil receive 1/6. Is it true or false?
  • Fraction expression
    Which expression is equivalent to : minus 9 minus left parenthesis minus 4 start fraction 1 divided by 3 end fraction right parenthesis
  • Jerry
    Jerry has 3/4 of a pizza. He needs to share it with 6 friends. What fraction of the pizza will each friend get? Only write the fraction
  • A teacher
    A teacher baked 5 dozen cookies for the 16 students in her class. If the teacher divided the cookies equally among her students, how many cookies did she give each student?
  • Golf balls
    Of the 28 golf balls, 1/7 are yellow. How many golf balls are yellow? Use the model to help you. Enter your answer in the box.
  • Find the 11
    Find the quotient of 229.12 and 12.32
  • Simplest form 3
    What fraction is 15 of 35 in simplest form?


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