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:
4 * 1/3 = 4/3 = 1 1/3 ≅ 1.3333333
Spelled result in words is four thirds (or one and one third).How do we solve fractions step by step?
- Multiple: 4 * 1/3 = 4 · 1/1 · 3 = 4/3
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(4, 3) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - four multiplied by one third is four thirds.
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:
- Fraction and a decimal
Write as a fraction and a decimal. One and two plus three and five hundredths
- Children 9
There are 11 children in a room. Six of the children are girls. What fraction of the children are girls?
- Value of Z
For x = -9, what is the value of Z, where Z equals fraction numerator x minus 17 over denominator 6.5 end fraction. Give your answer to 2 decimal places.
- A quarter
A quarter of the number 72 is:
- 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 company
A company has 860 employees, of which 500 are female. Write a fraction to represent the female employees in the company.
- Simplify 12
Simplify {1/3 + 1/12} ÷ {2/3 - 5/8}
- 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.
- In fractions
An ant climbs 2/5 of the pole in the first hour and climbs 1/4 of the pole in the next hour. What part of the pole does the ant climb in two hours?
- 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.
- Andy gets
Andy gets five out of 15 questions wrong in his math test. What fraction of the question does andy answer correctly?
- Using money
Out of 575,000.00 given to a school, an amount of 25,000.00 was used. What fraction of the total amount was used?
- 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.
- Dea makes
Dea makes 18 out of 27 shots in a basketball game. Which decimal represents the fraction of shots Dea makes?
- Fraction to decimal
Write the fraction 3/22 as a decimal.
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