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 4/7 ÷ 2 10/21 = 9/4 = 2 1/4 = 2.25
The result spelled out in words is nine quarters (or two and one quarter).How do we solve fractions step by step?
- Conversion a mixed number 5 4/7 to a improper fraction: 5 4/7 = 5 4/7 = 5 · 7 + 4/7 = 35 + 4/7 = 39/7
To find a new numerator:
a) Multiply the whole number 5 by the denominator 7. Whole number 5 equally 5 * 7/7 = 35/7
b) Add the answer from the previous step 35 to the numerator 4. New numerator is 35 + 4 = 39
c) Write a previous answer (new numerator 39) over the denominator 7.
Five and four sevenths is thirty-nine sevenths. - Conversion a mixed number 2 10/21 to a improper fraction: 2 10/21 = 2 10/21 = 2 · 21 + 10/21 = 42 + 10/21 = 52/21
To find a new numerator:
a) Multiply the whole number 2 by the denominator 21. Whole number 2 equally 2 * 21/21 = 42/21
b) Add the answer from the previous step 42 to the numerator 10. New numerator is 42 + 10 = 52
c) Write a previous answer (new numerator 52) over the denominator 21.
Two and ten twenty-firsts is fifty-two twenty-firsts. - Divide: 39/7 : 52/21 = 39/7 · 21/52 = 39 · 21/7 · 52 = 819/364 = 91 · 9 /91 · 4 = 9/4
Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 52/21 is 21/52) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, cancel by a common factor of 91 gives 9/4.
In other words, thirty-nine sevenths divided by fifty-two twenty-firsts equals nine quarters.
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:
- Compare fractions
Find which is the larger of the two fractions: 11/32, 7/24 by expressing the numbers as: a) fractions with the same denominator; b) decimals.
- Achievement 66164
The test consisted of 50 questions, each with one possible correct answer. The test result is given by the sum of the correct answers, a maximum of 100 points. The criterion for admission was the achievement of 50 points. The study applicant answered 36 q
- Order fractions
Arrange in ascending order 1 5/6, 11/9, 5/16, 3
- Marcellus
Marcellus has two bottles of ketchup that are the same size. One bottle is 1/5 full, and the other bottle is 1/2 full. Can all the ketchup fit into one bottle without the ketchup overflowing?
- Torque
Torque and Mari each multiplied 1/8 inch times 5/8 inch. Tartaric 5/8 squares point inches. And Marie got 5/64 squared thought inches tall. Which student found a corrupt area?
- Choose
Choose the three equivalent forms of 6.375. A. six and three-eighths, 6.375%, fifty-one eighths B. six and three seventy-fifths, 6.375%, thirty-seven sixths C. six and three seventy-fifths, 637.5%, thirty-seven sixths D. six and three-eighths, 637.5%, fif
- Fruit
There are a total of 28 pear and apple trees in the set. There are no other fruit trees in the set. The numbers of pear and apple trees in this order are in the ratio 3:4. Which is false? A. There are 3/4 apple trees among the fruit trees. B. There are fe
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Last Modified: August 28, 2025