Fraction calculator

Work with fractions

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 6/10 + 5 5/10 = 181 / 10 = 18 1 / 10 = 18.1

Spelled result in words is one hundred eighty-one tenths (or eighteen and one tenth).

How do you solve fractions step by step?

  1. Conversion a mixed number 12 6 / 10 to a improper fraction: 12 6/10 = 12 6 / 10 = 12 · 10 + 6 / 10 = 120 + 6 / 10 = 126 / 10

    To find a new numerator:
    a) Multiply the whole number 12 by the denominator 10. Whole number 12 equally 12 * 10 / 10 = 120 / 10
    b) Add the answer from previous step 120 to the numerator 6. New numerator is 120 + 6 = 126
    c) Write a previous answer (new numerator 126) over the denominator 10.

    Twelve and six tenths is one hundred twenty-six tenths

  2. Conversion a mixed number 5 5 / 10 to a improper fraction: 5 5/10 = 5 5 / 10 = 5 · 10 + 5 / 10 = 50 + 5 / 10 = 55 / 10

    To find a new numerator:
    a) Multiply the whole number 5 by the denominator 10. Whole number 5 equally 5 * 10 / 10 = 50 / 10
    b) Add the answer from previous step 50 to the numerator 5. New numerator is 50 + 5 = 55
    c) Write a previous answer (new numerator 55) over the denominator 10.

    Five and five tenths is fifty-five tenths

  3. Add: 126 / 10 + 55 / 10 = 126 + 55 / 10 = 181 / 10
    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(10, 10) = 10. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 10 × 10 = 100. In the following intermediate step, it cannot further simplify the fraction result by canceling.
    In other words - one hundred twenty-six tenths plus fifty-five tenths = one hundred eighty-one tenths.

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:

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