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:
23 1/2 - 3 5/8 = 159/8 = 19 7/8 = 19.875
The result spelled out in words is one hundred fifty-nine eighths (or nineteen and seven eighths).How do we solve fractions step by step?
- Conversion a mixed number 23 1/2 to a improper fraction: 23 1/2 = 23 1/2 = 23 · 2 + 1/2 = 46 + 1/2 = 47/2
To find a new numerator:
a) Multiply the whole number 23 by the denominator 2. Whole number 23 equally 23 * 2/2 = 46/2
b) Add the answer from the previous step 46 to the numerator 1. New numerator is 46 + 1 = 47
c) Write a previous answer (new numerator 47) over the denominator 2.
Twenty-three and a half is forty-seven halves. - Conversion a mixed number 3 5/8 to a improper fraction: 3 5/8 = 3 5/8 = 3 · 8 + 5/8 = 24 + 5/8 = 29/8
To find a new numerator:
a) Multiply the whole number 3 by the denominator 8. Whole number 3 equally 3 * 8/8 = 24/8
b) Add the answer from the previous step 24 to the numerator 5. New numerator is 24 + 5 = 29
c) Write a previous answer (new numerator 29) over the denominator 8.
Three and five eighths is twenty-nine eighths. - Subtract: 47/2 - 29/8 = 47 · 4/2 · 4 - 29/8 = 188/8 - 29/8 = 188 - 29/8 = 159/8
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(2, 8) = 8. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 8 = 16. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, forty-seven halves minus twenty-nine eighths equals one hundred fifty-nine eighths.
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:
- A chocolate 2
A chocolate cake is cut into twelve equal pieces. Mr. Greedy eats five pieces at break time with his mug of tea. What fraction of the cake is left?
- Paul ate
Paul ate 2/8 of a cake and his brother 3/8. What fraction of the cake is left for the parents?
- Difference of two fractions
What is the difference between 1/2 and 1/6? (Write the answer as a fraction in the lowest terms. )
- The recipe
The recipe they are following requires 7/8 cups of milk. Tom already put 3/8 cups of milk. How much milk should Lea add to follow the recipe?
- King
King had four sons. First inherit 1/2, second 1/4, third 1/5 of property. What part of the property was left to the last of the brothers?
- Pizza - sleepover
Petra and Amber had 9 pizzas delivered for a sleepover. Petra ate 2/3 of the pizzas. How many pizzas did Amber eat? Nothing was left.
- The sum 49
The sum of two rational numbers is -5. If one of them is -13/6, find the other.
more math problems »
Last Modified: April 16, 2025