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:
3/5 * 2/9 = 2/15 ≅ 0.1333333
Spelled result in words is two fifteenths.How do we solve fractions step by step?
- Multiple: 3/5 * 2/9 = 3 · 2/5 · 9 = 6/45 = 2 · 3/15 · 3 = 2/15
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(6, 45) = 3. In the following intermediate step, cancel by a common factor of 3 gives 2/15.
In other words - three fifths multiplied by two ninths is two fifteenths.
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.
- Simplify 12
Simplify {1/3 + 1/12} ÷ {2/3 - 5/8}
- Fraction to decimal
Write the fraction 3/22 as a decimal.
- A quarter
A quarter of the number 72 is:
- The following 3
The following fraction is reduced to its lowest terms except one. Which of these: A.98/99 B.73/179 C.1/250 D.81/729
- Brown or black
Max has 13 pairs of socks. From this, six pairs are blue, three pairs are brown, two are black, and two are white. What fraction of Max's socks are either brown or black?
- 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?
- Children 9
There are 11 children in a room. Six of the children are girls. What fraction of the children are girls?
- A class IV.A
In a class, there are 15 girls and 30 boys. What fraction of the class represents the boys?
- Fruit basket
If there are seven apples and five oranges in the basket, what fraction of oranges are in the fruit basket?
- 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.
- Fraction and a decimal
Write as a fraction and a decimal. One and two plus three and five hundredths
- 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?
more math problems »