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 + 5/8 = 11/8 = 1 3/8 = 1.375

Spelled result in words is eleven eighths (or one and three eighths).

How do you solve fractions step by step?

  1. Add: 3/4 + 5/8 = 3 · 2/4 · 2 + 5/8 = 6/8 + 5/8 = 6 + 5/8 = 11/8
    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 both denominators - LCM(4, 8) = 8. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 4 × 8 = 32. In the following intermediate step, the fraction result cannot be further simplified by canceling.
    In other words - three quarters plus five eighths = eleven eighths.

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:

  • Integer add to fraction
    fractions 7 is added to the sum of 4/5 and 6/7
  • Equation 20
    eq222 In given equation: 8/9-4/5=2/9+x, find x
  • A korean
    banan A korean mart sells banana milk, strawberry milk, and melon milk. 65% of the milks sold is banana and 14% is strawberry. What percentage is melon milk?
  • Adding mixed numerals
    zlomky 3 3/4 + 2 3/5 + 5 1/2 Show your solution.
  • What is one third
    decimals What is 1/3 as a decimal? Give your answer rounded to 2 decimal places.
  • Erika admin
    machine Erika’s career consists of filing, typing and answering phones. She spends 1/6 of her time filing and 5/8 of her time typing. What fraction of her time does she spend answering phone calls?
  • Michael
    chocholate Michael had a bar of chocolate. He ate 1/2 of it and gave away 1/3. What fraction had he left?
  • Vehicle tank
    fuel_pump2 A vehicle tank was 3/5 full of petrol. When 21 liters of fuel was added it was 5/6 full. How many liters of petrol can the tank hold?
  • Tyreek
    friends4 Tyreek, Antuan and Alex are given a total of $3500 to be shared among themselves in the ratio 3:5:12. How much each get money?
  • Orchard
    tree 3/5 of the trees in the orchard are apples, 1/3 are cherries and the remaining five trees are pear. How many trees are in the orchard?
  • Holiday trip
    penize Pavel is saving for the holiday trip. He received 1100 CZK from his father. He saved a fifth himself and received the rest 500 CZK from his mother. How much did his holiday trip cost?
  • Calories 2
    energy Ben eats approximately 2400 calories per day. His wife Sarah eats 5/8 as much. How many calories does Sarah eat per day?
  • Visit to grandfather
    family Shane's family traveled 3/10 of the distance to his grandfather’s house on Saturday. They traveled 4/7 of the remaining distance on Sunday. What fraction of the total distance to his grandfather’s house was traveled on Sunday?


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