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:

4 1/7 + 2 1/3 - 3/4 = 481/84 = 5 61/845.7261905

Spelled result in words is four hundred eighty-one eighty-fourths (or five and sixty-one eighty-fourths).

How do you solve fractions step by step?

  1. Conversion a mixed number 4 1/7 to a improper fraction: 4 1/7 = 4 1/7 = 4 · 7 + 1/7 = 28 + 1/7 = 29/7

    To find new numerator:
    a) Multiply the whole number 4 by the denominator 7. Whole number 4 equally 4 * 7/7 = 28/7
    b) Add the answer from previous step 28 to the numerator 1. New numerator is 28 + 1 = 29
    c) Write a previous answer (new numerator 29) over the denominator 7.

    Four and one seventh is twenty-nine sevenths
  2. Conversion a mixed number 2 1/3 to a improper fraction: 2 1/3 = 2 1/3 = 2 · 3 + 1/3 = 6 + 1/3 = 7/3

    To find new numerator:
    a) Multiply the whole number 2 by the denominator 3. Whole number 2 equally 2 * 3/3 = 6/3
    b) Add the answer from previous step 6 to the numerator 1. New numerator is 6 + 1 = 7
    c) Write a previous answer (new numerator 7) over the denominator 3.

    Two and one third is seven thirds
  3. Add: 29/7 + 7/3 = 29 · 3/7 · 3 + 7 · 7/3 · 7 = 87/21 + 49/21 = 87 + 49/21 = 136/21
    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, 3) = 21. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 7 × 3 = 21. In the next intermediate step, the fraction result cannot be further simplified by canceling.
    In words - twenty-nine sevenths plus seven thirds = one hundred thirty-six twenty-firsts.
  4. Subtract: the result of step No. 3 - 3/4 = 136/21 - 3/4 = 136 · 4/21 · 4 - 3 · 21/4 · 21 = 544/84 - 63/84 = 544 - 63/84 = 481/84
    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(21, 4) = 84. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 21 × 4 = 84. In the next intermediate step, the fraction result cannot be further simplified by canceling.
    In words - one hundred thirty-six twenty-firsts minus three quarters = four hundred eighty-one eighty-fourths.

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:

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  • Adding mixed numbers
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  • Expressions with variable
    plusminus This is algebra. Let n represent an unknown number and write the following expressions: 1. 4 times the sum of 7 and the number x 2. 4 times 7 plus the number x 3. 7 less than the product of 4 and the number x 4. 7 times the quantity 4 more than the number
  • Roses and tulips
    flowers At the florist are 50 tulips and 5 times fewer roses. How many flowers are in the flower shop?
  • Lengths of the pool
    bazen2 Miguel swam 6 lengths of the pool. Mat swam 3 times as far as Miguel. Lionel swam 1/3 as far as Miguel. How many lengths did Mat swim?
  • A large 2
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  • Bus vs train
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  • Chestnuts
    vaha Three divisions of nature protectors participated in the collection of chestnut trees.1. the division harvested 1250 kg, the 2nd division by a fifth more than the 1st division and the 3rd division by a sixth more than the second division. How many tons of
  • Area and perimeter 2
    rectangle_diagonals Find the area and the perimeter of a rectangle of length 45 1/2 cm and breadth 16 2/3 cm.
  • Sum of fractions
    fractions What is the sum of 2/3+3/5?
  • Fitness center
    time Every Wednesday, Monica works out for 3/4  of an hour at the fitness center. Every Saturday, he goes to the fitness center again and exercises for 3 times as long. How much time does Wayne spend at the fitness center in all each week?
  • Adding
    eq1 Divide number 135 into two additions so that one adds 30 more than 2/5 of the other add. Write the bigger one.
  • Recipe ingredients
    cup_flour Monica’s cookie recipe calls for Three-fourths of a cup of flour. Her mother’s recipe calls for Two-thirds as much as Monica’s. How many cups of flour does her mother’s recipe require?


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