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:
1/3 * 2/3 = 2/9 ≅ 0.2222222
Spelled result in words is two ninths.How do we solve fractions step by step?
- Multiple: 1/3 * 2/3 = 1 · 2/3 · 3 = 2/9
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(2, 9) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - one third multiplied by two thirds is two ninths.
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:
- 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? - 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? - Doughnuts
2/3 of the doughnuts in a box have frosting. 1/2 of the doughnuts with frosting have sprinkles. What fraction of the doughnuts in the box have frosting and sprinkles? - 10 children
Ten children in the park, four-tenths are wearing a red shirt. How many children in the park are wearing a red shirt?
- A quarter 2
A quarter of the 72 sandwiches contain cheese. The rest contain ham. How many are ham sandwiches? - Tiffany
Tiffany ate 1/4 of a pizza. If there were 16 slices of pizza, to begin with, how many slices did Tiffany eat? - Bella
Bella collected 3/5 of a bin of glass bottles to recycle. Ian collected 9 times as many bins as Bella. How many bins of bottles did Ian collect? - Pencils
You have 36 pencil crayons. How many pencil crayons makeup 1/2 of the total? - Scouts 4
4/7 out of the students in a school are boys. If 3/8 of the boys are scouts, how many scouts are there in a school of 1878 students?
- There 12
There are 42 students in the class, and 2/3 of them are girls. How many girls are there in the class? - Bryce
Bryce collected 1/4 of a bin of glass bottles to recycle. Megan collected 5 times as many bins as Bryce. How many bins of bottles did Megan collect? - Roy harvested
Roy harvested 3/4 crate of guavas. He sold 1/2 of them in the neighborhood. What part of a crate of guavas sold? - A total 2
A total of 42 candies if divided among boys and girls. If boys receive 3/7, then how much will girls receive? - Two fractions multiply
What is 4/5 when multiplied by 9/10?
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