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:
1 5/6 - 2/3 = 7/6 = 1 1/6 ≅ 1.1666667
The result spelled out in words is seven sixths (or one and one sixth).How do we solve fractions step by step?
- Conversion a mixed number 1 5/6 to a improper fraction: 1 5/6 = 1 5/6 = 1 · 6 + 5/6 = 6 + 5/6 = 11/6
To find a new numerator:
a) Multiply the whole number 1 by the denominator 6. Whole number 1 equally 1 * 6/6 = 6/6
b) Add the answer from the previous step 6 to the numerator 5. New numerator is 6 + 5 = 11
c) Write a previous answer (new numerator 11) over the denominator 6.
One and five sixths is eleven sixths. - Subtract: 11/6 - 2/3 = 11/6 - 2 · 2/3 · 2 = 11/6 - 4/6 = 11 - 4/6 = 7/6
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(6, 3) = 6. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 6 × 3 = 18. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, eleven sixths minus two thirds equals seven 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:
- Orchard 5421
The orchard has 600 apple trees. On the first day, they cut 1/5 and 2/8 of the total number of trees on the second day. How many more trees do they have to harvest?
- Second 82446
Petr read ⅜ of the book in the first week, ¼ of the book in the second week, and ⅒ of the book in the third week. The book has 240 pages. How many pages does Peter have left to read?
- Candy
You stop at hasty to buy candy. You give half of the bag to one friend. Then give a quarter to another friend. Later two more friends come, and you give each of them a third of what is in the bag. How many candies did you start with?
- Gingerbread house
Janka and Marienka calculated that there were 210 gingerbreads on the gingerbread house. Janko ate one-seventh of all gingerbreads, and Marienka ate a third less than Janko. How many gingerbreads remained in the gingerbread house?
- Felipe
Felipe is planning a party. He has $50.00 to spend on sandwiches that cost $2.50 per person, $25.00 to spend on drinks that cost $1.50 per person, and $25.00 to spend on gift bags that cost $3.00 per person. Which expression could be used to show the amou
- Gas tank
The car's tank was two-twelfths full. When Dad filled the tank with gas, the volume of gas increased by five-eighths of the tank's volume. What fraction of gasoline did the car use when the tank is now 1/3 full?
- Mrs. Susan 2
Mrs. Susan received a shipment of 60 novelty baseball caps. Of the caps, 1/3 had bug antennae, 2/5 had moose antlers, and the rest had plastic propellers. How many of the caps had plastic propellers?
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Last Modified: June 23, 2025