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:
11 3/7 - 8 6/8 = 75/28 = 2 19/28 ≅ 2.6785714
The result spelled out in words is seventy-five twenty-eighths (or two and nineteen twenty-eighths).How do we solve fractions step by step?
- Conversion a mixed number 11 3/7 to a improper fraction: 11 3/7 = 11 3/7 = 11 · 7 + 3/7 = 77 + 3/7 = 80/7
To find a new numerator:
a) Multiply the whole number 11 by the denominator 7. Whole number 11 equally 11 * 7/7 = 77/7
b) Add the answer from the previous step 77 to the numerator 3. New numerator is 77 + 3 = 80
c) Write a previous answer (new numerator 80) over the denominator 7.
Eleven and three sevenths is eighty sevenths. - Conversion a mixed number 8 6/8 to a improper fraction: 8 6/8 = 8 6/8 = 8 · 8 + 6/8 = 64 + 6/8 = 70/8
To find a new numerator:
a) Multiply the whole number 8 by the denominator 8. Whole number 8 equally 8 * 8/8 = 64/8
b) Add the answer from the previous step 64 to the numerator 6. New numerator is 64 + 6 = 70
c) Write a previous answer (new numerator 70) over the denominator 8.
Eight and six eighths is seventy eighths. - Subtract: 80/7 - 70/8 = 80 · 8/7 · 8 - 70 · 7/8 · 7 = 640/56 - 490/56 = 640 - 490/56 = 150/56 = 2 · 75/2 · 28 = 75/28
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(7, 8) = 56. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 7 × 8 = 56. In the following intermediate step, cancel by a common factor of 2 gives 75/28.
In other words, eighty sevenths minus seventy eighths equals seventy-five 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:
- Subtraction equation
What should be subtracted from -3/5 to get -2/3?
- Subtract and compare
1-5/8 is the same as 11/8, true or false?
- 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?
- Dive Attempt
Dive Attempt ; Fraction of the distance to the pool bottom Dive 1; 1/4 Dive 2; 2/3 Dive 3; 5/6 Tony's second dive was deeper than his first dive by what fraction of the pool?
- Her garden
Lira harvested 135 different flowers in her garden. Two-ninths of them are roses, and the rest are tulips. How many tulips are?
- Negative fractions
I am a number that is equal to -3/4 subtracted from the sum of 3/5 and -1/3. What number am I?
- Three cakes
There are three cakes an ice cream cake, chocolate, and a sponge cake. We ate 3/4 of the ice cream cake. We cut the chocolate cake into twelve equal pieces, of which We ate nine. The sponge cake was divided into eight equal pieces, with only one remaining
more math problems »
Last Modified: May 12, 2025