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:
1/12 + 4 + 13/28 = 191/42 = 4 23/42 ≅ 4.547619
The result spelled out in words is one hundred ninety-one forty-seconds (or four and twenty-three forty-seconds).How do we solve fractions step by step?
- Add: 1/12 + 4 = 1/12 + 4/1 = 1/12 + 4 · 12/1 · 12 = 1/12 + 48/12 = 1 + 48/12 = 49/12
The second operand is an integer. It is equivalent to the fraction 4/1. It is suitable to adjust both fractions to a common (equal) denominator for adding fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(12, 1) = 12. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 12 × 1 = 12. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, one twelfth plus four equals forty-nine twelfths. - Add: the result of step No. 1 + 13/28 = 49/12 + 13/28 = 49 · 7/12 · 7 + 13 · 3/28 · 3 = 343/84 + 39/84 = 343 + 39/84 = 382/84 = 2 · 191/2 · 42 = 191/42
It is suitable to adjust both fractions to a common (equal) denominator for adding fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(12, 28) = 84. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 12 × 28 = 336. In the following intermediate step, cancel by a common factor of 2 gives 191/42.
In other words, forty-nine twelfths plus thirteen twenty-eighths equals one hundred ninety-one forty-seconds.
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:
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There is 5/8 of a pizza in one box and 9/12 of a pizza in another box. How much do you have altogether?
- Sum of fractions
What is the sum of 2/3+3/5?
- A miner
A miner is working at an elevation of -64 7/9 and then ascends 22 1/3. What is the miner's new location?
- Fresh chickens
In the market, one stall is selling fresh chickens worth P120 per kilo. A person bought two fresh chickens weighing 1 1/2 and 1 1/4 kilos each. What is the total weight of the two chickens?
- Plus minus mixed numbers
If possible, perform the indicated operation/s and reduce your answer to the lowest term. 1. 3 1/8 + 3/5= 2. 6 3/7 + 4/9= 3. 9 6/13 + 1 3/7= 4. 10 4/5 - 2/3= 5. 13 6/7 - 3/11=
- Students 82194
Out of 30 students in the class, 2 thirds of the children were on a trip, and all the others were at home. How many students stayed at home?
- What is 23
What is the answer to sum 2 1/2 and 1 3/8 minus 5 1/4?
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Last Modified: June 23, 2025