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:
4 5/7 + 3 3/4 = 237/28 = 8 13/28 ≅ 8.4642857
The result spelled out in words is two hundred thirty-seven twenty-eighths (or eight and thirteen twenty-eighths).How do we solve fractions step by step?
- Conversion a mixed number 4 5/7 to a improper fraction: 4 5/7 = 4 5/7 = 4 · 7 + 5/7 = 28 + 5/7 = 33/7
To find a new numerator:
a) Multiply the whole number 4 by the denominator 7. Whole number 4 equally 4 * 7/7 = 28/7
b) Add the answer from the previous step 28 to the numerator 5. New numerator is 28 + 5 = 33
c) Write a previous answer (new numerator 33) over the denominator 7.
Four and five sevenths is thirty-three sevenths. - Conversion a mixed number 3 3/4 to a improper fraction: 3 3/4 = 3 3/4 = 3 · 4 + 3/4 = 12 + 3/4 = 15/4
To find a new numerator:
a) Multiply the whole number 3 by the denominator 4. Whole number 3 equally 3 * 4/4 = 12/4
b) Add the answer from the previous step 12 to the numerator 3. New numerator is 12 + 3 = 15
c) Write a previous answer (new numerator 15) over the denominator 4.
Three and three quarters is fifteen quarters. - Add: 33/7 + 15/4 = 33 · 4/7 · 4 + 15 · 7/4 · 7 = 132/28 + 105/28 = 132 + 105/28 = 237/28
It is suitable to adjust both fractions to a common (equal) denominator for adding fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(7, 4) = 28. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 7 × 4 = 28. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, thirty-three sevenths plus fifteen quarters equals two hundred thirty-seven twenty-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:
- The sum 49
The sum of two rational numbers is -5. If one of them is -13/6, find the other.
- Joe had
Joe had a full tank of petrol in his car. His car consumed 2/9 of the tank of petrol on Saturday and 1/3 of it on Sunday. What fraction of the tank of petrol was left after the weekend?
- Roses and tulips
At the florist are 50 tulips and five times fewer roses. How many flowers are in the flower shop?
- Fraction 82525
Of 32 students in the class, 3/4 of the children were on the trip. Write as a fraction what part of the students stayed at home. How many students were on the trip?
- A farmer 9
A farmer has 3 hectares of an orchard. ½ of the land is occupied by apples, ⅙ of the remainder is occupied by lemon trees, and tree tomatoes occupy the rest of it. Find the fraction of the land occupied by tree tomatoes.
- Sequence 80450
How many terms does the sequence have if a1=4, Sn=589, d=3, n=?
- Xero had
Xero had a piece of ribbon. He used 0.4 of it to tie 2 small boxes and 2 large boxes. The length of ribbon needed for a large box is 3 times the length of ribbon needed for a small box. Xero used 5/6 of the remaining ribbon to decorate the presents. a) Wh
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Last Modified: May 12, 2025