Fraction calculator
This calculator adds two fractions. First, all fractions are converted to a common denominator when they have different denominators. To do this, find the Least Common Denominator (LCD) or multiply all denominators to determine a common denominator. Once all denominators are the same, add the numerators and place the result over the common denominator. Finally, simplify the result to its lowest terms or convert it to a mixed number.
The result:
2/7 + 3/5 = 31/35 ≅ 0.8857143
The result spelled out in words is thirty-one thirty-fifths.How do we solve fractions step by step?
- Add: 2/7 + 3/5 = 2 · 5/7 · 5 + 3 · 7/5 · 7 = 10/35 + 21/35 = 10 + 21/35 = 31/35
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(7, 5) = 35. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 7 × 5 = 35. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, two sevenths plus three fifths equals thirty-one thirty-fifths.
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:
- The sum 49
The sum of two rational numbers is -5. If one of them is -13/6, find the other.
- Summands 5215
Divide the number into two summands, which are in the given ratio: a) 3, 11:4 b) 5.1 8:9 c) 1 7:3 d) 0.42 1:6
- Roses and tulips
At the florist are 50 tulips and five times fewer roses. How many flowers are in the flower shop?
- Arithmetic 81795
In which arithmetic sequence is S5=S6=60?
- One-thirds 2485
Three classmates bought apples. Peter bought two whole one-thirds of the kg, Spring 5 sixths of a kg less than Peter and Daniel 2 times as much as Peter. How many kilograms of apples did the boys buy together?
- Rice cooking
Aunt had 1 3/4 kg of rice, then Aunt bought another 2 1/2 kg of rice, cooked 0.2 kg, calculate the remaining rice Aunt now.
- Two pieces 2
Two pieces of length 12/5 m and 23/9 m are cut from a rope of length 13 m. Find the length of the remaining rope.
more math problems »
Last Modified: June 23, 2025