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:

7 2/9 + 6 5/6 = 253/18 = 14 1/1814.0555556

Spelled result in words is two hundred fifty-three eighteenths (or fourteen and one eighteenth).

How do you solve fractions step by step?

  1. Conversion a mixed number 7 2/9 to a improper fraction: 7 2/9 = 7 2/9 = 7 · 9 + 2/9 = 63 + 2/9 = 65/9

    To find new numerator:
    a) Multiply the whole number 7 by the denominator 9. Whole number 7 equally 7 * 9/9 = 63/9
    b) Add the answer from previous step 63 to the numerator 2. New numerator is 63 + 2 = 65
    c) Write a previous answer (new numerator 65) over the denominator 9.

    Seven and two ninths is sixty-five ninths
  2. Conversion a mixed number 6 5/6 to a improper fraction: 6 5/6 = 6 5/6 = 6 · 6 + 5/6 = 36 + 5/6 = 41/6

    To find new numerator:
    a) Multiply the whole number 6 by the denominator 6. Whole number 6 equally 6 * 6/6 = 36/6
    b) Add the answer from previous step 36 to the numerator 5. New numerator is 36 + 5 = 41
    c) Write a previous answer (new numerator 41) over the denominator 6.

    Six and five sixths is forty-one sixths
  3. Add: 65/9 + 41/6 = 65 · 2/9 · 2 + 41 · 3/6 · 3 = 130/18 + 123/18 = 130 + 123/18 = 253/18
    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(9, 6) = 18. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 9 × 6 = 54. In the next intermediate step, the fraction result cannot be further simplified by canceling.
    In words - sixty-five ninths plus forty-one sixths = two hundred fifty-three eighteenths.

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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