Fraction calculator
This fraction calculator performs basic and advanced fraction operations, expressions with fractions combined with integers, decimals, and mixed numbers. It also shows detailed step-by-step information about the fraction calculation procedure. The calculator helps in finding value from multiple fractions operations. Solve problems with two, three, or more fractions and numbers in one expression.
The result:
3 * 1/3 = 1/1 = 1
Spelled result in words is one.How do we solve fractions step by step?
- Multiple: 3 * 1/3 = 3 · 1/1 · 3 = 3/3 = 1 · 3/1 · 3 = 1
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(3, 3) = 3. In the following intermediate step, cancel by a common factor of 3 gives 1/1.
In other words - three multiplied by one third is one.
Rules for expressions with fractions:
Fractions - use a forward slash to divide the numerator by 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 integer and
fraction and use a forward slash to input fractions i.e., 1 2/3 . An example of a negative mixed fraction: -5 1/2.
Because slash is both sign for fraction line and division, use a colon (:) as the operator of division fractions i.e., 1/2 : 1/3.
Decimals (decimal numbers) enter with a decimal point . 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
• multiplying a fraction by a whole number: 6 * 3/4
• square root of a fraction: sqrt(1/16)
• reducing or simplifying the fraction (simplification) : 4/22 - dividing the numerator and denominator of a fraction by the same non-zero number - equivalent fraction
• 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 of operations are:
PEMDAS - Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
BEDMAS - Brackets, Exponents, Division, Multiplication, Addition, Subtraction
BODMAS - Brackets, Of or Order, Division, Multiplication, Addition, Subtraction.
GEMDAS - Grouping Symbols - brackets (){}, Exponents, Multiplication, Division, Addition, Subtraction.
MDAS - Multiplication and Division have the same precedence over Addition and Subtraction. The MDAS rule is the order of operations part of the PEMDAS rule.
Be careful; always do multiplication and division before addition and subtraction. Some operators (+ and -) and (* and /) have the same priority and must be evaluated from left to right.
Fractions in word problems:
- Puzzle game
In a letter puzzle game, John can use every alphabet only once. He used only 8 alphabets to solve the puzzle. What fraction of the 26 alphabets did he use? Express your answer as a fraction in the simplest form.
- Fraction and a decimal
Write as a fraction and a decimal. One and two plus three and five hundredths
- Samantha
Samantha took 72 pictures on her beach vacation. 3/4 of those pictures are on the beach. How many pictures from her vacation are on the beach?
- A quarter
A quarter of the number 72 is:
- Out 550,000.00
Out of 550,000.00, an amount of 325,000.00 was used. What fraction of the total amount was used?
- Lowest terms 2
We can write the expression 4/12 in its lowest term as 1/3. What is 3/15 expressed in its lowest term?
- A class IV.A
In a class, there are 15 girls and 30 boys. What fraction of the class represents the boys?
- Children 9
There are 11 children in a room. Six of the children are girls. What fraction of the children are girls?
- Mathew
Mathew has eight pencils. Three of them do not have erasers on end. What fraction of the pencils do not have erasers on end?
- A farm 6
A farm has 20 animals. There are four chickens. What fraction of the animals are chickens? Express your answer as a fraction in the simplest form.
- A company
A company has 860 employees, of which 500 are female. Write a fraction to represent the female employees in the company.
- Andy gets
Andy gets five out of 15 questions wrong in his math test. What fraction of the question does andy answer correctly?
- In the cafeteria
There are 18 students in Jacob's homeroom. Six students bring their lunch to school. The rest eat lunch in the cafeteria. In the simplest form, what fraction of students eat lunch in the cafeteria?
- Zdeněk
Zdeněk picked up 15 l of water from a 100-liter full-water barrel. Write a fraction of what part of Zdeněk's water he picked.
- Someone
Someone ate 1/10 of a cake, leaving only 9/10. If you eat 2/3 of the cake left, how much of a whole cake will you have eaten?
more math problems »