Fraction calculator
This fraction calculator performs all fraction operations - addition, subtraction, multiplication, division and evaluates expressions with fractions. It also shows detailed step-by-step information.
The result:
2 5/12 + 3 8/12 = 73/12 = 6 1/12 ≅ 6.0833333
The result spelled out in words is seventy-three twelfths (or six and one twelfth).How do we solve fractions step by step?
- Conversion a mixed number 2 5/12 to a improper fraction: 2 5/12 = 2 5/12 = 2 · 12 + 5/12 = 24 + 5/12 = 29/12
To find a new numerator:
a) Multiply the whole number 2 by the denominator 12. Whole number 2 equally 2 * 12/12 = 24/12
b) Add the answer from the previous step 24 to the numerator 5. New numerator is 24 + 5 = 29
c) Write a previous answer (new numerator 29) over the denominator 12.
Two and five twelfths is twenty-nine twelfths. - Conversion a mixed number 3 8/12 to a improper fraction: 3 8/12 = 3 8/12 = 3 · 12 + 8/12 = 36 + 8/12 = 44/12
To find a new numerator:
a) Multiply the whole number 3 by the denominator 12. Whole number 3 equally 3 * 12/12 = 36/12
b) Add the answer from the previous step 36 to the numerator 8. New numerator is 36 + 8 = 44
c) Write a previous answer (new numerator 44) over the denominator 12.
Three and eight twelfths is forty-four twelfths. - Add: 29/12 + 44/12 = 29 + 44/12 = 73/12
Both fractions have the same denominator, which is then the common denominator in the adding them. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, twenty-nine twelfths plus forty-four twelfths equals seventy-three twelfths.
Rules for expressions with fractions:
Fractions - write a forward slash to separate the numerator and the denominator, i.e., for five-hundredths, enter 5/100. If you use mixed numbers, leave a space between the whole and fraction parts.Mixed numerals (mixed numbers or fractions) - keep one space between the whole part and fraction and use a forward slash to input fraction i.e., 1 2/3 . A negative mixed fraction write for example as -5 1/2.
A slash is both a sign for fraction line and division, use a colon (:) for division fractions i.e., 1/2 : 1/3.
Decimals (decimal numbers) enter with a decimal dot . and they are automatically converted to fractions - i.e. 1.45.
Math Symbols
Symbol | Symbol name | Symbol Meaning | Example |
---|---|---|---|
+ | plus sign | addition | 1/2 + 1/3 |
- | minus sign | subtraction | 1 1/2 - 2/3 |
* | asterisk | multiplication | 2/3 * 3/4 |
× | times sign | multiplication | 2/3 × 5/6 |
: | division sign | division | 1/2 : 3 |
/ | division slash | division | 1/3 / 5 |
: | colon | complex fraction | 1/2 : 1/3 |
^ | caret | exponentiation / power | 1/4^3 |
() | parentheses | calculate expression inside first | -3/5 - (-1/4) |
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
• reciprocal of a fraction: 1 : 3/4
• square of a fraction: 2/3 ^ 2
• cube of a fraction: 2/3 ^ 3
• exponentiation of a fraction: 1/2 ^ 4
• 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
• square root of a fraction: sqrt(1/16)
• 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 the order of operations. The most common mnemonics for remembering this order are:
- PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
- BEDMAS: Brackets, Exponents, Division, Multiplication, Addition, Subtraction.
- BODMAS: Brackets, Order (or "Of"), Division, Multiplication, Addition, Subtraction.
- GEMDAS: Grouping symbols (brackets: (){}), Exponents, Multiplication, Division, Addition, Subtraction.
- MDAS: Multiplication and Division (same precedence), Addition and Subtraction (same precedence). MDAS is a subset of PEMDAS.
1. Multiplication/Division vs. Addition/Subtraction: Always perform multiplication and division *before* addition and subtraction.
2. Left-to-Right Rule: Operators with the same precedence (e.g., + and -, or * and /) must be evaluated from left to right.
Fractions in word problems:
- A cake 2
Karen sliced a cake into 10 slices. She ate 2/10 of it and after some time she ate another 4/10 of it. How much of the cake did Karen eat?
- Numbers 5256
What is 4/5 of the sum of numbers (-4.95) and (-11.05)?
- Sum of the fractions
Find the sum, express your answer to lowest terms. 1. 1/4 + 2/4= 2. 1/6 + 3/6= 3. 6/10 + 2/10= 4. ¾ + ⅛= 5. 5 3/5 + 2 ½=
- Two mixed adding
What is 1 and 1/6 + 1 and 3/6?
- Negative fractions
I am a number that is equal to -3/4 subtracted from the sum of 3/5 and -1/3. What number am I?
- Three cakes
There are three cakes an ice cream cake, chocolate, and a sponge cake. We ate 3/4 of the ice cream cake. We cut the chocolate cake into twelve equal pieces, of which We ate nine. The sponge cake was divided into eight equal pieces, with only one remaining
- One-third of the sum
Some number equals 1/3 of the sum of 83.2, -25.1, and 65. What is the number?
more math problems »
Last Modified: June 23, 2025