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:

12 3/5 - 7 3/4 = 97/20 = 4 17/20 = 4.85

Spelled result in words is ninety-seven twentieths (or four and seventeen twentieths).

How do you solve fractions step by step?

  1. Conversion a mixed number 12 3/5 to a improper fraction: 12 3/5 = 12 3/5 = 12 · 5 + 3/5 = 60 + 3/5 = 63/5

    To find new numerator:
    a) Multiply the whole number 12 by the denominator 5. Whole number 12 equally 12 * 5/5 = 60/5
    b) Add the answer from previous step 60 to the numerator 3. New numerator is 60 + 3 = 63
    c) Write a previous answer (new numerator 63) over the denominator 5.

    Twelve and three fifths is sixty-three fifths
  2. Conversion a mixed number 7 3/4 to a improper fraction: 7 3/4 = 7 3/4 = 7 · 4 + 3/4 = 28 + 3/4 = 31/4

    To find new numerator:
    a) Multiply the whole number 7 by the denominator 4. Whole number 7 equally 7 * 4/4 = 28/4
    b) Add the answer from previous step 28 to the numerator 3. New numerator is 28 + 3 = 31
    c) Write a previous answer (new numerator 31) over the denominator 4.

    Seven and three quarters is thirty-one quarters
  3. Subtract: 63/5 - 31/4 = 63 · 4/5 · 4 - 31 · 5/4 · 5 = 252/20 - 155/20 = 252 - 155/20 = 97/20
    For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of the both denominators - LCM(5, 4) = 20. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 5 × 4 = 20. In the next intermediate step the fraction result cannot be further simplified by canceling.
    In words - sixty-three fifths minus thirty-one quarters = ninety-seven twentieths.

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:

  • Add sub fractions
    fractions_2 What is 4 1/2+2/7-213/14?
  • Length subtracting
    meter_11 Express in mm: 5 3/10 cm - 2/5 mm
  • Difference mixed fractions
    mixed_fractions_1 What is the difference between 4 2/3 and 3 1/6?
  • School
    skola_16 There are 150 pupils in grade 5 . 2/3 of it are female. By what fractions are the males?
  • Pizza fractions
    pizza Ann ate a third of a pizza and then another quater. Total part of pizza eaten by Ann and how much pizza is left?
  • Cake fractions
    dort Thomas ate 1/3 of cake, Bohouš of the rest of the cake ate 2/5. What fraction of cake left over for others?
  • Mixed numbers
    zlomky_10 Rewrite mixed numbers so the fractions have the same denominator: 5 1/5 - 2 2/3
  • Pounds
    jablka_8 3 pounds subtract 1/3 of a pound.
  • From a
    meter_2 From a 1 meter ribbon, Ericka cut 2/4 meter for her hat and another 1/4 meter for her bag. How long was the remaining piece?
  • King
    kral King had four sons. First inherit 1/2, second 1/4 , third 1/5 of property. What part of the property was left to the last of the brothers?
  • Erica
    meter_10 Erica bought 3 1/2 yards of fabric. If she uses 2/3 of the fabric, how much will she have left?
  • Employees
    workers_45 Of all 360 employees, there are 11/12 women. How many men work in a company?
  • Savings
    savings Eva borrowed 1/3 of her savings to her brother, 1/2 of savings spent in the store and 7 euros left. How much did she save?


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