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:
17 1/5 - 2 5/8 = 583/40 = 14 23/40 = 14.575
The result spelled out in words is five hundred eighty-three fortieths (or fourteen and twenty-three fortieths).How do we solve fractions step by step?
- Conversion a mixed number 17 1/5 to a improper fraction: 17 1/5 = 17 1/5 = 17 · 5 + 1/5 = 85 + 1/5 = 86/5
To find a new numerator:
a) Multiply the whole number 17 by the denominator 5. Whole number 17 equally 17 * 5/5 = 85/5
b) Add the answer from the previous step 85 to the numerator 1. New numerator is 85 + 1 = 86
c) Write a previous answer (new numerator 86) over the denominator 5.
Seventeen and one fifth is eighty-six fifths. - Conversion a mixed number 2 5/8 to a improper fraction: 2 5/8 = 2 5/8 = 2 · 8 + 5/8 = 16 + 5/8 = 21/8
To find a new numerator:
a) Multiply the whole number 2 by the denominator 8. Whole number 2 equally 2 * 8/8 = 16/8
b) Add the answer from the previous step 16 to the numerator 5. New numerator is 16 + 5 = 21
c) Write a previous answer (new numerator 21) over the denominator 8.
Two and five eighths is twenty-one eighths. - Subtract: 86/5 - 21/8 = 86 · 8/5 · 8 - 21 · 5/8 · 5 = 688/40 - 105/40 = 688 - 105/40 = 583/40
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(5, 8) = 40. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 5 × 8 = 40. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, eighty-six fifths minus twenty-one eighths equals five hundred eighty-three fortieths.
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:
- Nida had
Nida had 1/12 of a pizza. She gave 1/8 of it to her friend Madeeha. Find what part of the whole pizza did Madeeha get.
- Three cakes
There are three cakes an ice cream cake, chocolate, and a sponge cake. We ate 3/4 of the ice cream cake. We cut the chocolate cake into twelve equal pieces, of which We ate nine. The sponge cake was divided into eight equal pieces, with only one remaining
- The cost 7
The cost of a pen is Rs. 20/3, and that of a pencil is 25/6. Which costs more and by how much?
- Sytiel
Sytiel used 3/10 of the water in his tank to wash his car. He used 1/10 to water his plants. Now he is using 5/10 for his laundry. How many parts of water in the tank did he use up?
- Bucket
Kim and Joey share a 30-ounce bucket of clay. By the end of the week, Kim has used 3/10 of the bucket. Joey has used 3/5 of the bucket of clay. How many ounces are left in the bucket?
- 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?
- In grade
In the grade six class, 5/9 of the pupils are boys, and the number of pupils is 180. Find the number of girls.
more math problems »
Last Modified: June 23, 2025