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:
7 2/9 + 6 5/6 = 253/18 = 14 1/18 ≅ 14.0555556
The result spelled out in words is two hundred fifty-three eighteenths (or fourteen and one eighteenth).How do we solve fractions step by step?
- Conversion a mixed number 7 2/9 to a improper fraction: 7 2/9 = 7 2/9 = 7 · 9 + 2/9 = 63 + 2/9 = 65/9
To find a new numerator:
a) Multiply the whole number 7 by the denominator 9. Whole number 7 equally 7 * 9/9 = 63/9
b) Add the answer from the previous step 63 to the numerator 2. New numerator is 63 + 2 = 65
c) Write a previous answer (new numerator 65) over the denominator 9.
Seven and two ninths is sixty-five ninths. - Conversion a mixed number 6 5/6 to a improper fraction: 6 5/6 = 6 5/6 = 6 · 6 + 5/6 = 36 + 5/6 = 41/6
To find a new numerator:
a) Multiply the whole number 6 by the denominator 6. Whole number 6 equally 6 * 6/6 = 36/6
b) Add the answer from the previous step 36 to the numerator 5. New numerator is 36 + 5 = 41
c) Write a previous answer (new numerator 41) over the denominator 6.
Six and five sixths is forty-one sixths. - Add: 65/9 + 41/6 = 65 · 2/9 · 2 + 41 · 3/6 · 3 = 130/18 + 123/18 = 130 + 123/18 = 253/18
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(9, 6) = 18. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 9 × 6 = 54. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, sixty-five ninths plus forty-one sixths equals two hundred fifty-three eighteenths.
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:
- Microorganisms
The first generation of microorganisms has a population of 13500 members. Each subsequent generation is 11/10 times the previous one. Find out how many generations will reach at least three times members of the first generation.
- Tourists 82400
On the first day, tourists covered 3/14 of the planned route, on the second day 1/3 of the route, and on the third day 8/21 of the route. On which day did they walk the longest part of the route (1,2,3)?
- Children 35891
Three children got part of the cake. Which got the most? Tomas 24% Lenka 0.3 Philip 2/7
- Cody states
Cody states that 1/4 + ( - 6/8 ) = 1 whole, while Eddie says that it is - 1/2. Who is correct? Justify your answer and explain your thinking.
- Much 37741
How much is half the half the cube half?
- Subtract and compare
1-5/8 is the same as 11/8, true or false?
- Once simplified
Once simplified, which of the expressions below has a value between 20 and 30? Select all that apply. A) 32÷8×514 B) -18÷6×9 C) 4×12÷2 D) 12×413÷(-2)
more math problems »
Last Modified: June 23, 2025