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:
2 7/8 - 1 7/9 = 79/72 = 1 7/72 ≅ 1.0972222
The result spelled out in words is seventy-nine seventy-seconds (or one and seven seventy-seconds).How do we solve fractions step by step?
- Conversion a mixed number 2 7/8 to a improper fraction: 2 7/8 = 2 7/8 = 2 · 8 + 7/8 = 16 + 7/8 = 23/8
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 7. New numerator is 16 + 7 = 23
c) Write a previous answer (new numerator 23) over the denominator 8.
Two and seven eighths is twenty-three eighths. - Conversion a mixed number 1 7/9 to a improper fraction: 1 7/9 = 1 7/9 = 1 · 9 + 7/9 = 9 + 7/9 = 16/9
To find a new numerator:
a) Multiply the whole number 1 by the denominator 9. Whole number 1 equally 1 * 9/9 = 9/9
b) Add the answer from the previous step 9 to the numerator 7. New numerator is 9 + 7 = 16
c) Write a previous answer (new numerator 16) over the denominator 9.
One and seven ninths is sixteen ninths. - Subtract: 23/8 - 16/9 = 23 · 9/8 · 9 - 16 · 8/9 · 8 = 207/72 - 128/72 = 207 - 128/72 = 79/72
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(8, 9) = 72. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 8 × 9 = 72. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, twenty-three eighths minus sixteen ninths equals seventy-nine seventy-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:
- Subtraction equation
What should be subtracted from -3/5 to get -2/3?
- Fractions - minus
What is the difference used estimation to justify your thinking? 11/12 - 1/3 - 1/6
- Breakfast 83989
Peter ate a quarter of the pizza for breakfast and a sixth of the rest for lunch. How much of the pizza did he have left for dinner?
- Fraction operations
For items - fractions 1/6 - 1/9 perform the indicated operation/s. Write your answer in improper fractions, and it must be in the simplest form.
- The cat
The cat starts with 4/6 of a cup in his bowl. It eats 1/4 of a cup of food. How much food is left?
- Marbles - cube
How many marbles do I have if I am missing a fifth of 15 marbles?
- You have 4
You have eaten ⅔ of a pizza. Your friend eats what is left. How much of the original pizza is left?
more math problems »
Last Modified: June 23, 2025