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:
5 2/5 + 2 3/5 = 8/1 = 8
The result spelled out in words is eight.How do we solve fractions step by step?
- Conversion a mixed number 5 2/5 to a improper fraction: 5 2/5 = 5 2/5 = 5 · 5 + 2/5 = 25 + 2/5 = 27/5
To find a new numerator:
a) Multiply the whole number 5 by the denominator 5. Whole number 5 equally 5 * 5/5 = 25/5
b) Add the answer from the previous step 25 to the numerator 2. New numerator is 25 + 2 = 27
c) Write a previous answer (new numerator 27) over the denominator 5.
Five and two fifths is twenty-seven fifths. - Conversion a mixed number 2 3/5 to a improper fraction: 2 3/5 = 2 3/5 = 2 · 5 + 3/5 = 10 + 3/5 = 13/5
To find a new numerator:
a) Multiply the whole number 2 by the denominator 5. Whole number 2 equally 2 * 5/5 = 10/5
b) Add the answer from the previous step 10 to the numerator 3. New numerator is 10 + 3 = 13
c) Write a previous answer (new numerator 13) over the denominator 5.
Two and three fifths is thirteen fifths. - Add: 27/5 + 13/5 = 27 + 13/5 = 40/5 = 5 · 8/5 · 1 = 8
Both fractions have the same denominator, which is then the common denominator in the adding them. In the following intermediate step, cancel by a common factor of 5 gives 8/1.
In other words, twenty-seven fifths plus thirteen fifths equals eight.
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:
- Sum two mixed
Which of the following is the sum of 22 7/9 and 6 8/9?
- The bucket
Anna and Joey share an 18-ounce bucket of clay. By the end of the week, Anna has used 1/3 of the bucket, and Joey has used 2/3 of the bucket of clay. How many ounces are left in the bucket?
- Matthew
Matthew is saving up for a car. Last year he saved 3/5 of the total amount. In addition to what he saved last year, he saved 3/10 of the total amount in the summer. If the car costs 15 000$, how much has he saved so far?
- Rica has
Rica has 3 pieces of lace, each measuring 1/7 meter, 5/14 meter, and 3/7 meter. How long are the pieces of lace together?
- The numerator
The numerator of the fraction is 5 more than its denominator. If 4 is added to the numerator and denominator, the fraction obtained is 6/5. What is that fraction?
- Arithmetic 81795
In which arithmetic sequence is S5=S6=60?
- Mrs. Dinah
Mrs. Dinah Tah Tanda divided her lot among her 4 children. The first got 3 1/2 ha, the second 3 1/3 ha, the third 3 1/4 ha, and the fourth 3 2/5 ha. How big is Mrs. Tanda's lot?
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Last Modified: June 23, 2025