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:

5/7 + 25/52 + 7/4 = 268/91 = 2 86/912.9450549

Spelled result in words is two hundred sixty-eight ninety-firsts (or two and eighty-six ninety-firsts).

How do you solve fractions step by step?

  1. Add: 5/7 + 25/52 = 5 · 52/7 · 52 + 25 · 7/52 · 7 = 260/364 + 175/364 = 260 + 175/364 = 435/364
    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(7, 52) = 364. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 7 × 52 = 364. In the next intermediate step, the fraction result cannot be further simplified by canceling.
    In words - five sevenths plus twenty-five fifty-seconds = four hundred thirty-five three-hundred sixty-fourths.
  2. Add: the result of step No. 1 + 7/4 = 435/364 + 7/4 = 435/364 + 7 · 91/4 · 91 = 435/364 + 637/364 = 435 + 637/364 = 1072/364 = 4 · 268/4 · 91 = 268/91
    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(364, 4) = 364. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 364 × 4 = 1456. In the next intermediate step, , cancel by a common factor of 4 gives 268/91.
    In words - four hundred thirty-five three-hundred sixty-fourths plus seven quarters = two hundred sixty-eight ninety-firsts.

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:

  • Expressions
    plusminus Let k represent an unknown number, express the following expressions: 1. The sum of the number n and two 2. The quotient of the numbers n and nine 3. Twice the number n 4. The difference between nine and the number n 5. Nine less than the number n
  • Fe metal sheet
    plech For one product, 5/8 of the metal sheet are consumed, to the second 5/6 of remains. What part of the sheet metal is consumed for both products together?
  • Add two fractions
    fractions14 What is the sum of 2/3 and 3/10?
  • Adding mixed numbers
    fractions Add this two mixed numbers: 1 5/6 + 2 2/11=
  • Addition of mixed numerals
    scientific Add two mixed fractions: 2 4/6 + 1 3/6
  • Circular garden
    seed Alice creates a circular vegetable garden. Tomatoes are planted in 1/3 of the circular garden, carrots are planted in 2/5 of the circular garden, and green peppers are planted in 1/10 of the circular garden. What fraction represents the remaining unplante
  • Playing Cards
    cards Kara has 2 times more cards than Dana, Dana has 4× less than Mary. Together they have 728 cards. How many cards has each of them?
  • Of the 2
    pentagon Of the shapes,1/6 are triangles and 5/12 are pentagons. What fraction of the shapes are either triangles or pentagons?
  • Math homework
    clocks2 It took Jose two-thirds of an hour to complete his math homework on Monday, three-fourths of an hour on Tuesday, any two- fifths of an hour on Wednesday. How many hours did it take Jose to complete his homework altogether?
  • A textile
    meter A textile store sold a bolt of denim (what jeans are made out of). In one day, the following number of yards were purchased from the one bolt: 5 2/3, 7, 4 2/3, 8 5/8, 9 3/5, 10 ½, and 8. How many yards were sold?
  • Monica’s
    fuel Monica's lawnmower had 1/8 of a gallon of gasoline in the tank. Monica started mowing and used all of the gasoline. She put 6/10 of a gallon of gasoline in the tank. After she mowed, 1/4 of a gallon was left in the tank. What was the total amount of gasol
  • Martin
    wood Martin is making a model of a Native American canoe. He has 5 1/2 feet of wood. He uses 2 3/4 feet for the hull and 1 1/4 feet for a paddle. How much wood does he have left? Martin has feet of wood left.
  • Candies
    cukriky There are 150 candies in the bowl. Ivan took 7 thirtieths, Charles 6 fifteenths, and Thomas 3 tenths. How many sweets are left in the bowl?


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