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:
9 - 3 ÷ 1/3 + 1 = 1/1 = 1
The result spelled out in words is one.How do we solve fractions step by step?
- Divide: 3 : 1/3 = 3/1 · 3/1 = 3 · 3/1 · 1 = 9/1 = 9
The first operand is an integer. It is equivalent to a fraction 3/1. Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 1/3 is 3/1) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators.
In other words, three divided by one third equals nine. - Subtract: 9 - the result of step No. 1 = 9 - 9 = 9/1 - 9/1 = 9 - 9/1 = 0/1 = 0
Both fractions have the same denominator, which is then the common denominator in the subtracting them.
In other words, nine minus nine equals zero. - Add: the result of step No. 2 + 1 = 0 + 1 = 0/1 + 1/1 = 0 + 1/1 = 1/1 = 1
Both fractions have the same denominator, which is then the common denominator in the adding them.
In other words, zero plus one equals one.
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:
- Add two fractions
What is 1/2 added to 2/3? * 1 point A. 1 3/12 B. 1 5/6 C. 1 1/6 D.1 1/4
- 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?
- The sum 42
The sum of two fractions is 6 5/6. If the bigger fraction is subtracted by 3/4, the difference is 4 7/12. What is the smaller fraction?
- Mrs Olive
Mrs. Olive used 1 2/5 quarts of syrup and 5 3/10 quarts of water to make lemonade .how many quarts of lemonade did she make?
- Ron walked
Ron walked 3 3/4 km on Monday, 4 1/3 km on Tuesday, and 2 7/12 km on Wednesday. What distance did he walk in all?
- A pole
1/8 of a pole is in mud, 1/3 of it in water, and the rest above water. If the length of the pole is 72 meters, find the length of the pole above the water.
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Last Modified: August 28, 2025