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:
3 1/2 - 1 1/3 = 13/6 = 2 1/6 ≅ 2.1666667
The result spelled out in words is thirteen sixths (or two and one sixth).How do we solve fractions step by step?
- Conversion a mixed number 3 1/2 to a improper fraction: 3 1/2 = 3 1/2 = 3 · 2 + 1/2 = 6 + 1/2 = 7/2
To find a new numerator:
a) Multiply the whole number 3 by the denominator 2. Whole number 3 equally 3 * 2/2 = 6/2
b) Add the answer from the previous step 6 to the numerator 1. New numerator is 6 + 1 = 7
c) Write a previous answer (new numerator 7) over the denominator 2.
Three and a half is seven halves. - Conversion a mixed number 1 1/3 to a improper fraction: 1 1/3 = 1 1/3 = 1 · 3 + 1/3 = 3 + 1/3 = 4/3
To find a new numerator:
a) Multiply the whole number 1 by the denominator 3. Whole number 1 equally 1 * 3/3 = 3/3
b) Add the answer from the previous step 3 to the numerator 1. New numerator is 3 + 1 = 4
c) Write a previous answer (new numerator 4) over the denominator 3.
One and one third is four thirds. - Subtract: 7/2 - 4/3 = 7 · 3/2 · 3 - 4 · 2/3 · 2 = 21/6 - 8/6 = 21 - 8/6 = 13/6
It is suitable to adjust both fractions to a common (equal) denominator for subtracting fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(2, 3) = 6. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 3 = 6. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, seven halves minus four thirds equals thirteen sixths.
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:
- Subtract 27
Subtract these mixed fractions: 7 2/3 and 3 1/9.
- Closer to one
Here are two sums: A=1/2 + 1/3 and B=1/5 + 1/3. Which of the two sums is closer in value to 1? You must show your work and state clearly whether the answer is A or B.
- Shopping 7
I went into a shop with 210.00 and spent 1/7 of it on eggs and 1/2 of it on fruits. How much did I have left?
- Dive Attempt
Dive Attempt ; Fraction of the distance to the pool bottom Dive 1; 1/4 Dive 2; 2/3 Dive 3; 5/6 Tony's second dive was deeper than his first dive by what fraction of the pool?
- 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?
- Ahsan
Ahsan has a large pizza. He gives 1/3 to his sister and 1/4 to his mother. What fraction of the pizza does Ahsan have left?
- Illustrate
Illustrate the following expressions, then solve. 1. 3-8/10= 2. 4-2/5= 3. 2-3/8= 4. 3-3/7= 5. 5-4/9=
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Last Modified: June 23, 2025