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:
4 - 2 3/7 = 11/7 = 1 4/7 ≅ 1.5714286
The result spelled out in words is eleven sevenths (or one and four sevenths).How do we solve fractions step by step?
- Conversion a mixed number 2 3/7 to a improper fraction: 2 3/7 = 2 3/7 = 2 · 7 + 3/7 = 14 + 3/7 = 17/7
To find a new numerator:
a) Multiply the whole number 2 by the denominator 7. Whole number 2 equally 2 * 7/7 = 14/7
b) Add the answer from the previous step 14 to the numerator 3. New numerator is 14 + 3 = 17
c) Write a previous answer (new numerator 17) over the denominator 7.
Two and three sevenths is seventeen sevenths. - Subtract: 4 - 17/7 = 4/1 - 17/7 = 4 · 7/1 · 7 - 17/7 = 28/7 - 17/7 = 28 - 17/7 = 11/7
The first operand is an integer. It is equivalent to a fraction 4/1. 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(1, 7) = 7. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 1 × 7 = 7. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, four minus seventeen sevenths equals eleven sevenths.
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 chocolate 2
A chocolate cake is cut into twelve equal pieces. Mr. Greedy eats five pieces at break time with his mug of tea. What fraction of the cake is left?
- Paul ate
Paul ate 2/8 of a cake and his brother 3/8. What fraction of the cake is left for the parents?
- Difference of two fractions
What is the difference between 1/2 and 1/6? (Write the answer as a fraction in the lowest terms. )
- The recipe
The recipe they are following requires 7/8 cups of milk. Tom already put 3/8 cups of milk. How much milk should Lea add to follow the recipe?
- King
King had four sons. First inherit 1/2, second 1/4, third 1/5 of property. What part of the property was left to the last of the brothers?
- Pizza - sleepover
Petra and Amber had 9 pizzas delivered for a sleepover. Petra ate 2/3 of the pizzas. How many pizzas did Amber eat? Nothing was left.
- The sum 49
The sum of two rational numbers is -5. If one of them is -13/6, find the other.
more math problems »
Last Modified: June 23, 2025